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Modeling Formamide Denaturation of Probe-Target Hybrids for Improved Microarray Probe Design in Microbial Diagnostics


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Application of high-density microarrays to the diagnostic analysis of microbial communities is challenged by the optimization of oligonucleotide probe sensitivity and specificity, as it is generally unfeasible to experimentally test thousands of probes. This study investigated the adjustment of hybridization stringency using formamide with the idea that sensitivity and specificity can be optimized during probe design if the hybridization efficiency of oligonucleotides with target and non-target molecules can be predicted as a function of formamide concentration. Sigmoidal denaturation profiles were obtained using fluorescently labeled and fragmented 16S rRNA gene amplicon of Escherichia coli as the target with increasing concentrations of formamide in the hybridization buffer. A linear free energy model (LFEM) was developed and microarray-specific nearest neighbor rules were derived. The model simulated formamide melting with a denaturant m-value that increased hybridization free energy (ΔG°) by 0.173 kcal/mol per percent of formamide added (v/v). Using the LFEM and specific probe sets, free energy rules were systematically established to predict the stability of single and double mismatches, including bulged and tandem mismatches. The absolute error in predicting the position of experimental denaturation profiles was less than 5% formamide for more than 90 percent of probes, enabling a practical level of accuracy in probe design. The potential of the modeling approach for probe design and optimization is demonstrated using a dataset including the 16S rRNA gene of Rhodobacter sphaeroides as an additional target molecule. The LFEM and thermodynamic databases were incorporated into a computational tool (ProbeMelt) that is freely available at
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Modeling Formamide Denaturation of Probe-Target
Hybrids for Improved Microarray Probe Design in
Microbial Diagnostics
L. Safak Yilmaz
*, Alexander Loy
, Erik S. Wright
, Michael Wagner
, Daniel R. Noguera
1Department of Biochemistry and Molecular Pharmacology, University of Massachusetts Medical School, Worcester, Massachusetts, United States of America,
2Department of Civil and Environmental Engineering, University of Wisconsin-Madison, Madison, Wisconsin, United States of America, 3Department of Microbial Ecology,
Vienna Ecology Center, Faculty of Life Sciences, University of Vienna, Wien, Austria
Application of high-density microarrays to the diagnostic analysis of microbial communities is challenged by the
optimization of oligonucleotide probe sensitivity and specificity, as it is generally unfeasible to experimentally test
thousands of probes. This study investigated the adjustment of hybridization stringency using formamide with the idea that
sensitivity and specificity can be optimized during probe design if the hybridization efficiency of oligonucleotides with
target and non-target molecules can be predicted as a function of formamide concentration. Sigmoidal denaturation
profiles were obtained using fluorescently labeled and fragmented 16S rRNA gene amplicon of Escherichia coli as the target
with increasing concentrations of formamide in the hybridization buffer. A linear free energy model (LFEM) was developed
and microarray-specific nearest neighbor rules were derived. The model simulated formamide melting with a denaturant m-
value that increased hybridization free energy (DGu) by 0.173 kcal/mol per percent of formamide added (v/v). Using the
LFEM and specific probe sets, free energy rules were systematically established to predict the stability of single and double
mismatches, including bulged and tandem mismatches. The absolute error in predicting the position of experimental
denaturation profiles was less than 5% formamide for more than 90 percent of probes, enabling a practical level of accuracy
in probe design. The potential of the modeling approach for probe design and optimization is demonstrated using a
dataset including the 16S rRNA gene of Rhodobacter sphaeroides as an additional target molecule. The LFEM and
thermodynamic databases were incorporated into a computational tool (ProbeMelt) that is freely available at http://
Citation: Yilmaz LS, Loy A, Wright ES, Wagner M, Noguera DR (2012) Modeling Formamide Denaturation of Probe-Target Hybrids for Improved Microarray Probe
Design in Microbial Diagnostics. PLoS ONE 7(8): e43862. doi:10.1371/journal.pone.0043862
Editor: Cynthia Gibas, University of North Carolina at Charlotte, United States of America
Received October 31, 2011; Accepted July 30, 2012; Published August 27, 2012
Copyright: ß2012 Yilmaz et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits
unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: This research was supported by National Science Foundation grants CBET-0606894 to DRN and CBET-0636533 to DRN and LSY, the Austrian Science
Fund (P20185-B17 to AL), and the Austrian Federal Ministry of Science and Research (GEN-AU III InflammoBiota to MW and AL). The funders had no role in study
design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing Interests: The authors have declared that no competing interests exist.
* E-mail:
The field of microbial ecology aims to resolve the composition
of complex microbial communities in engineered and natural
ecosystems, with the ultimate goal of establishing the link between
community structure and function. To this end, microarrays can
be quite effective in determining community composition as they
allow the simultaneous capture of the different types of a marker
molecule (typically a functional gene or rRNA) in complex target
mixtures using a large set of organism- and group-specific single-
stranded DNA probes [1]. Besides traditional low throughput
techniques such as Sanger sequencing of clone libraries [2] and
fluorescence in situ hybridization (FISH) [3], as well as the recently
established high throughput sequencing approaches [4], micro-
arrays are an important component of the microbial ecologist’s
molecular toolbox. However, the routine use of microarrays for
diagnostic applications is challenged by the difficulty of designing
thousands of oligonucleotide probes with optimal sensitivity and
specificity to phylogenetic markers.
Probe optimization is complicated by the overwhelming
diversity of microorganisms as observed with the sequence
databases of small subunit rRNA, the most commonly used
phylogenetic marker [5,6,7]. While probes in the longer range
(.30 nucleotides) can generally assure sensitivity by efficient target
capture, they cause specificity problems in two ways. First, due to
within-group sequence variability, the longer the target site, the
poorer the coverage of the probe over its targeted group of
organisms (e.g., a species or a genus). Second, the higher affinity of
long probes to their target molecules undermines their ability to
discriminate the perfectly matching target sequences of interest
from mismatching out-group sequences, thereby causing false
positive identifications. Oligonucleotide probes on microarrays
targeting rRNA (genes) are thus mostly in the shorter size range
(,30 nucleotides). However, using shorter probes with lowered
affinity can obviously cause sensitivity problems due to inefficient
target capture, leading to false negatives. Therefore, in microbial
ecology applications of microarrays, probe design and optimiza-
tion of hybridization conditions require establishing a delicate
PLOS ONE | 1 August 2012 | Volume 7 | Issue 8 | e43862
balance between sensitivity and specificity in the oligonucleotide
size range.
Since the accurate prediction of probe sensitivity and specificity
is difficult [8], earlier studies with spotted microarrays relied on
experimental evaluations of probes. Single targets from culture
collections or clone libraries hybridized on separate microarrays
were used as references to verify the relationship between probe
response and organism identification in environmental samples
[9,10,11,12]. Although tedious, empirical testing of almost every
individual probe was feasible due to the small enough number of
probes (tens to hundreds) on such microarrays. However,
advanced high-density microarray technology currently allows
the synthesis of thousands to millions of probe features on the same
slide (e.g.,, http://www.affymetrix.
com). While this has brought the great advantage of using more
comprehensive probe sets, as in the design of 16S rRNA-based
microarrays for the identification of large numbers of different
phylogenetic groups of microorganisms [13,14,15,16], experimen-
tal testing of all probes is no longer an option. Rather, in addition
to using standard mismatch probes as in Affymetrix setups [15,17],
which are not necessarily adequate controls for cross hybridization
[18], high-density microarray applications rely on the ability to
design multiple probes for each taxonomic group to reduce the
chance of misidentification. Certainly, it is still desirable to develop
a robust strategy for the design of the individual probes with
optimal sensitivity and specificity, thus increasing the accuracy of
identifications based on organism-specific probe sets. We are
therefore interested in establishing stringent and predictable
hybridization conditions to maximize the confidence in the
analyses of microbial communities.
In this study, we propose the methodical use of formamide
during microarray hybridizations to develop design rules for the
optimization of probe sensitivity and specificity. Formamide is a
denaturant routinely used in hybridization techniques to adjust
stringency [19,20,21]. As formamide concentration in the
hybridization buffer is increased, probe/target duplexes denature,
usually resulting in a sigmoidal decrease in signal response and
generating a so-called melting curve [22,23]. Since the denatur-
ation proceeds more rapidly for mismatched duplexes than for
perfect matches, there is generally an optimal range of formamide
concentration that effectively eliminates signal response from
mismatched non-target organisms while maintaining high signal
for still non-denatured perfect match targets. Unlike other
hybridization techniques, systematic evaluations of formamide
denaturation are not available for microarrays, although prelim-
inary formamide series during hybridization have been reported
[24]. We show here that sigmoidal formamide melting profiles can
be obtained with microarray probes, as in FISH [20,23]. For this
approach to be effective in probe design, one needs to be able to
predict formamide denaturation and determine the optimal
concentration range for mismatch discrimination. Thus, we also
use equilibrium thermodynamics to develop a linear free energy
model (LFEM) of formamide melting [23,25] and employ this
model to systematically derive thermodynamic parameters that
characterize the stability of both perfect match and mismatched
duplexes. Our analysis shows that the predictive ability of
microarray LFEM is much better than similar models devised
for FISH [23]. When combined with the multiple-probe strategy
in high-density arrays, the overall approach can potentially
facilitate the optimization of probe sensitivity and specificity for
the high-confidence identification of organisms in complex
microbial communities.
Targets and Target Labeling
Single 16S rRNA gene clones of Escherichia coli K-12 and
Rhodobacter sphaeroides 2.4.1 were used as pure target templates. A
small subunit rRNA gene clone library was developed and
sequenced to determine the clones retrieved from the rRNA
operons that encoded for the sequences used in probe design (see
below). Briefly, plasmid inserts of clones were obtained from pure
cultures by cell-PCR amplification with 27f [26] and 1492r [27]
primers, followed by ligation and transformation with the
TOPO10 cloning kit and TOP10 competent cells (Invitrogen,
Carlsbad, CA). The insert was amplified with M13 primers and
purified using Ampure (Agencourt Bioscience Corporation,
Beverly, MA). The purified product was sequenced (primed with
27f) at the University of Wisconsin Biotechnology center using
Sanger’s method. Partial sequences (ca. 800 nucleotides) were used
to match sequences to known rRNA operons and one clone that
matched the design template was selected for each organism.
For target labeling, the cloned and purified 16S rRNA gene was
first re-amplified with the 27f and 1492r primers, and the product
was purified using a QIAquick spin column (Qiagen, Valencia,
CA) and Cy3-labeled according to a previously published protocol
[11]. Briefly, Cy3-dCTPs (Amersham, GE Healthcare; Little
Chalfont; UK) were incorporated into 200 ng PCR product
during random prime amplification with Klenow fragment and a
decalabel DNA labeling kit (Fermentas, St Leon-Rot, Germany).
The product of labeling was purified with a QIAquick spin column
and the yield was measured using a Nanodrop 1000 spectropho-
tometer (NanoDrop Products, Wilmington, DE). The target
concentrations were in the range of 25–35 ng/mL, with an
incorporated dye concentration of 0.8–1.2 ng/mL. The applied
labeling procedure results in a fragmented target due to the linear
random priming amplification. This was confirmed by measuring
the labeled product length with an Agilent RNA 6000 Pico Kit
(Agilent, Santa Clara, CA), which showed lengths ranging between
25 and 150 bases, with an average of 65 bases.
Microarrays and Probes
High-density 4-plex microarray slides were obtained from
Nimblegen (Madison, WI). Each of the four subarrays accommo-
dated 72,000 features. Most probes were replicated three times on
the array, with a total of ,24,000 independent probe sequences
produced, of which, 15,394 were used in this study (Table 1). For
designing probes targeting E. coli and R. sphaeroides (Table 1),
rRNA gene sequences with accession codes U00006 and X53853
were used, respectively. A poly-T chain of 20 bases was added to
the 39end of the probe sequence, to provide an elevation above
the slide surface in addition to the default linker of Nimblegen
design. This was done to minimize the brush effect due to the
surface-proximal tails of target molecules, which may reduce signal
intensity in ways difficult to predict [28,29,30]. All Ts in the first
three nucleotides (nearest to probe sequence) of the poly-T linker
that matched an A or G in the target sequence were converted to
As, to avoid the additional free energy of binding from dT-dA or
dT-dG type interactions between the poly-T linker and target.
The names, sequences, experimental signal intensity values, and
calculated free energy changes of probes used in this study were
deposited at the public database Gene Expression Omnibus
(, with the accession code
GSE33021, following MIAME guidelines. The naming of probes
(e.g. R101–122, E1013–1034_10AC) was based on the following
convention: Target (‘‘E’’ for E. coli, ‘‘R’’ for R. sphaeroides), target
site positions (59–39) on the target gene, position of mismatch
Formamide Denaturation in Microarrays
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from the 59end of the probe (if available), and the change in base
(original followed by modification) to create the mismatch (if
available). For deletions and inserts, ‘‘gap’’ and ‘‘I’’ preceded the
mismatch position, respectively.
Hybridization and Wash
Before hybridization, slides were pre-processed with 6–7 hrs of
incubation in Nimblegen reuse buffer, a denaturing reagent that is
normally used for stripping hybridized targets. The purpose of this
step was to remove unknown surface-related factors that seemed to
make probes less accessible at lower formamide concentrations
(data not shown). For hybridization, a total of 6 or 60 ng (ca. 2 mL)
of labeled and purified target was combined with 0.5 mL
alignment oligo (Nimblegen), dried using a Vacufuge Plus vacuum
centrifuge (Eppendorf, Hamburg, Germany) at 30uC, and then re-
suspended in 10 mL of hybridization buffer (1M Na
, 20 mM Tris
[pH = 7.2], 0.02% SDS, and variable amounts of formamide). To
dissociate the complementary strands of DNA, the suspension was
heat denatured by a 5-min incubation at 95uC, followed by fast
cooling on ice. The hybridization buffer was then applied to the
array surface using NimbleGen 4-plex mixers adhered to the
slides. A total of ca. 8 mL suspension was transferred to each array,
bringing the used target mass to ca. 5 or 50 ng. The slides were
placed in a 12-bay NimbleGen Hybridization System for
overnight (,20 hrs) hybridization at a controlled constant
temperature of 42uC, and with active mixing of the hybridization
buffer to improve mass transfer.
After hybridization, slides were washed in pairs, using a series of
three wash buffers (I, II, and III) provided by Nimblegen and
following Nimblegen guidelines. All buffers were amended with
0.1 mM dithiothreitol according to manufacturer’s recommenda-
tions. Each slide was first submerged in 250 mL of pre-warmed
(40–45uC) wash buffer I to detach the mixer from slide surface and
immediately taken through the wash series in buffers I (2 min), II
(1 min), and III (15 secs) at room temperature with constant
manual agitation. The slides were dried using Arrayit High-Speed
Microarray Centrifuge (Telechem, Silicon Valley, CA) and
subsequently stored in a dark and dry environment.
Scanning and Analysis
Microarrays were scanned with an Axon 4000B laser scanner
and GenePix Pro 6.0 software (Molecular Devices, Sunnyvale,
CA). The wavelength and PMT gain were set at 532 nm and 430,
respectively. Two lines were averaged during scanning. Fluores-
cence data was saved in TIFF files, which were processed with
Nimblescan software (Nimblegen). Using the signal from the
alignment oligomers a custom grid was aligned with the images to
derive raw data for each feature. It should be noted that this
procedure produces data in the form of pixel intensity values
ranging from 0 to 65536, the latter representing a saturation point.
Raw data was saved as pair files and analyzed using Matlab (The
MathWorks, Natick, MA). For each probe, the average and
standard deviation of the brightness of three replicate features
were calculated. An outlier test was also performed, such that if
one of the replicates gave a value that was more than three
standard deviations (of the remaining two) away from the average
of the remaining two it was eliminated. Then, the average of
control (Nonsense) probes (see Table 1) was subtracted from all
averages to obtain background-corrected results (standard devia-
tions were calculated with error propagation).
Linear Free Energy Model (LFEM)
To simulate probe/target hybridization in the presence of
formamide, the LFEM previously developed for FISH [23] was
Table 1. Probe sets used in modeling.
Set N
Probe Length Description Use
1380 22 22-nucleotide-long perfect match probes tiling the 16S rRNA
gene of Escherichia coli.
Comparison to mismatches.
Length 1045
18–26 Probes with varied lengths (18, 20, 24, 26) targeting 209
random sites on 16S rRNA.
Models M1–M3; fitting.
4140 22 TileE set with all three types of mismatches inserted in the 11th
position of each probe.
Models M4, M5; fitting.
PosM 4092
22 62 probes from TileE set with all types of single mismatches
inserted in all positions.
Models M4, M5; verification and positional
Gap 248 22 62 probes from TileE set with a deletion at the 5
or 18
Models M6, M7; fitting.
Insertion 248 23 62 probes from TileE set with all types of single insertion between
and 12
Models M6, M7; fitting.
TwoM 1674 22 62 probes from TileE set with all types of mismatches inserted in
positions 5 and 11, 11 and 18, or 5 and 18.
Models M4, M5; verification and double-
mismatch effects.
Tandem 558 22 62 probes from Tile set with all types of 2 mismatches
inserted in positions 11 and 12.
Models M8, M9; fitting.
1301 22 22-nucleotide-long perfect match probes tiling the 16S
rRNA gene of Rhodobacter sphaeroides.
Target effects; evaluation of the extent of
cross hybridization.
1 22 Nonsense sequences not complementary to targets used. Background fluorescence
Number of probes in set. Not all probes are directly used in model development (see next footnote, text, and Table 2).
Probes targeting positions before the 50
and after the 1450
nucleotide (in E. coli positioning) were excluded from all analyses to avoid unamplified terminals of the
targeted genes and other possible end effects.
209 probes shared with TileE set.
186 probes shared with OneM set.
Ten replicates of the probe 59-AGAGAGAGAGAGAGAGAGAGAG-39.
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reduced to a two-state hybridization system describing the local
equilibrium at the probe’s microenvironment (P+T=PT, where P,
T, and PT denote probe, target, and hybrid, respectively). The
modified microarray LFEM defines hybridization efficiency (i.e.,
the ratio of probe-bound target to all locally available: [PT]/[T]
as shown in Equation 1, where, DGuis the free energy change for
no formamide condition, the m–value defines the linear increase in
the free energy change with increasing formamide concentration
([FA]) [23,31,32], and Rand Tstand for the gas constant
(0.00199 kcal/molK) and hybridization temperature (315.15 K),
respectively. During the derivation of Equation 1, the activity
coefficients of P,T, and PT were added to the reaction
stoichiometry, as different from the LFEM for FISH [23], and
embedded in the effective probe concentration term ({P}
), which
is treated as an unknown parameter to be derived by model-fitting
(see below).
RT fPgo
RT fPgo
The free energy value in Equation 1 was calculated as described
elsewhere [22,33,34,35]. Briefly, DGuof perfect match hybrids was
obtained by summing the free energies of all nearest neighbors and
adding an initiation free energy to this sum [34,35]. For
mismatched duplexes, the free energy difference introduced by
the mismatch was formulated using a DDGuterm described in
Equation 2 [22,33], which reflects both the destabilizing effect of
losing a nearest neighbor pair (second term on the right hand side)
and the contribution of the newly formed internal loop (first term
on the right hand side). Both solution-based and microarray-
specific parameters were used for nearest neighbor and loop terms
in this study. Solution based parameters were obtained from
UNAFold [36], whilst microarray parameters were derived by
Curve Fitting
Predicted hybridization efficiency in a formamide series was
matched to normalized experimental melting profiles with
Equation 3, where Iis the background-corrected probe signal
intensity at a specific formamide concentration, I
is the
maximum Ivalue achieved in the whole formamide series, and c
represents a probe-specific proportionality constant that aligns
experimental and theoretical trends. Theoretical formamide
curves of multiple probes were simultaneously fitted to their
experimental profiles using a bi-level fitting approach. Thus, the
parent fitting function changed general modeling parameters ({P}
and the m-value in Equation 1 along with free energy parameters),
while a secondary fitting function determined the probe-specific
proportionality constants according to Equation 3 (i.e., a particular
cvalue for each probe). Curve-fitting was done via non-linear
regression [37] using the ‘nlinfit’ routine in the Statistics Toolbox
of MATLAB, as described previously [23]. The goodness of fit was
evaluated by the coefficient of determination (R
) in Equation 4,
where y,r, and nrepresent experimental data points, residuals, and
the total number of formamide data points used in the fitting,
respectively. To compare the performance of different models with
varied number of parameters, the error squares function (s
Equation 5 was used. Here, nrepresents the degree of freedom
(i.e., nminus all parameters, including one cvalue for each probe
used in the fitting).
Curve fitting was based on data from modeling probe sets in
Table 1 using 5 ng of E. coli 16S rRNA gene as the target.
Experimental signal intensity values of some of these probes were
close to the background over the entire formamide series or all
points but 0% formamide. Since these probes were observed to
bias fitting parameters by random noise, they were eliminated
from curve-fitting (,15% of all probes; the final number of probes
used in fitting are provided in Table 2 by the parameter N
; see
below). Eliminations included perfect and mismatched probes with
values ,1000 a.u. and ,500 a.u. respectively, and
mismatched probes whose signal decreased by more than 50%
in the first increment of the formamide series (i.e., from 0 to 5%).
After model development, retrospective analyses showed that
99%, 93%, and 56% of these filtered probes were predicted to
have half denaturation points (see below) at or below 15%, 10%,
and 5% (v/v) formamide, respectively. Thus, filtered data was
mainly a result of predictable poor hybridization efficiency and did
not significantly affect modeling evaluations.
We obtained probe denaturation profiles with a formamide
series of eight concentrations: 0, 5, 10, 15, 20, 25, 32.5, and 45%
on a volume by volume basis (v/v). For each target, this was
achieved by parallel hybridizations with two slides (4 arrays per
slide). Typical experimental profiles are shown in Figure 1A for
selected perfectly matched and mismatched probes from the
hybridization experiment with 5 ng of amplified, fragmented, and
Cy3-labeled E. coli 16S rRNA gene used in model development.
As expected, increasing formamide creates a sigmoid-like loss of
signal as the efficiency of target capture decreases, and the melting
occurs at lower concentrations when mismatches are inserted in
the duplex (Figure 1A). For those probes with a full sigmoid trend,
there is a general increase of signal with increasing formamide at
lower formamide concentrations, as exemplified by the perfect
match probe in Figure 1A, which may be due to the removal of
structural kinetic limitations by formamide as in FISH [38,39] or
other unknown complications in microarray hybridizations. In any
case, the gradual loss of signal at higher stringency creates a
window of formamide concentrations (15–25% in the example in
Figure 1A), where the signal from perfect match duplex is easily
detectable, while the mismatched duplexes are close to the
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Table 2. Model development and curve-fitting
Model Description
Name Type Free Energy Change (kcal/mol)
m (kcal/mol/%)
/n e
M1 Perfect Match DGo
sln 0.522 211.6 na na 500/1033 0.0207 0.0210 0.0240 0.0209 0.87 3/2.2 81.3
M2 Perfect Match DGo
sln,withdangling 0.528 212.4 na na 500/1033 0.0212 0.0211 0.0246 0.0211 0.87 3/2.3 80.6
M3 Perfect Match DGo
0.173 22.0
na na 500/1033 0.0083 0.0080 0.0096 0.0081 0.95 2.1/1.7 93.4
M4 Central Single Mismatch DGo
NN{,ma zaDGo
SM,sln zb0.173 22.0 0.354 0.487 1750/3594 0.0093 0.0091 0.0107 0.0092 0.94 2.2/1.7 92.6
M5 Central Single Mismatch DGo
NN{,ma zDGo
SM,ma 0.173
2.0 na na 3594/3594 0.0078 na 0.0090 0.0078 0.95 2/1.6 94.5
M4 Positional Single Mismatch DGo
NN{,ma zaDGo
SM,sln zb0.173 22.0 0.354 0.487 3815/3815 na na 0.0117 0.0101 0.93 2.4/1.8 90.2
M5 Positional Single
NN{,ma zDGo
SM,ma 0.173
2.0 na na 3815/3815 na na 0.0107 0.0093 0.94 2.3/1.7 91.6
M6 Bulged Mismatch DGo
NN{,ma zaDGo
BM,sln zb0.173 22.0 0.132 0.296 250/467 0.0098 0.0099 0.0113 0.0098 0.94 2.4/1.8 91.4
M7 Bulged Mismatch DGo
NN{,ma zaDGo
BM,s ln 0.173
na 250/467 0.0098 0.0098 0.0113 0.0099 0.94 2.4/1.8 90.8
M4 Two Mismatches DGo
NN{,ma zaDGo
SM,sln zb0.173 22.0 0.354 0.487 1086/1086 na na 0.0126 0.0111 0.92 1.4/1.4 98.1
M5 Two Mismatches DGo
NN{,ma zDGo
SM,ma 0.173
2.0 na na 1086/1086 na na 0.0111 0.0098 0.93 1.2/1.2 98.8
M8 Tandem Mismatch DGo
NN{,ma zaDGo
TM,sln zb0.173 22.0 0.198 1.167 300/401 0.0117 0.0118 0.0133 0.0117 0.92 1.6/1.5 97.3
M9 Tandem Mismatch DGo
NN{,ma zDGo
TM,ma0.173 22.0 na na 300/401 0.0107 0.0112 0.0123 0.0108 0.92 1.5/1.3 97.8
M9 Tandem Mismatch DGo
NN{,ma zDGo
2.0 na na 401/401 0.0108 na 0.0124 0.0108 0.92 1.5/1.3 97.5
Concluding (optimal) models are indicated in bold and their details are presented in other tables and figures.
SM, single (non-bulge) mismatch; BM, bulge mismatch; TM, tandem mismatch; sln, for in solution hybridization; ma, for microarray hybridization.
Parameters in italics are used in best-fitting. The use of additional parameters aand b, when applicable, is shown in the free energy column under model description (see text for best-fitting values). Other parameters derived using
M3, M5, and M9 are the free energy rules in Tables S1A, S1B, and S1D, with 10, 104, and 8 additions, respectively.
, number of probes used in fitting; N
, total number of probes; e
and e
, average squares of prediction errors in validation set (i.e., not used in fitting) and overall set, respectively. See Materials and Methods for other
Absolute value of the deviation of predicted half-denaturation point (% formamide) from the apparent experimental value, as described by its average/standard deviation (
/s) and percentage of values below 5% formamide.
DGufor perfect matches and DDGufor mismatches (see Materials and Methods).
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background, thereby allowing mismatch discrimination as desired.
Thus, our modeling efforts aimed at predicting the observed
melting behavior for probe design and optimization.
Our mathematical framework depends on the estimation of the
standard Gibbs free energy change (DGu) of the hybridization
reaction (Equation 1). Initially, we used UNAFold [36] to predict a
DGuvalue based on thermodynamic parameters from in-solution
hybridizations (hence designated DGu
) and evaluated its
correlation with the experimental observations. As shown in
Figure 1B, this free energy value poorly correlated with maximum
signal intensity of probes in a formamide series (I
). The low
correlation can be attributed to non-thermodynamic factors that
may influence the signal intensity of individual probes, such as the
biases introduced during the amplification and fragmentation of
the target (e.g., fragment concentration and dye labeling
efficiency). Indeed, I
showed non-random positional depen-
dence in the 16S rRNA gene with regions of peaks and sinks
(Figure 1D), which may presumably reflect these biases. It is
noteworthy that, patterns as in Figure 1D have been reported
before for single target molecules [40], but could be related to
binding free energy unlike with our dataset (Figure 1B). A more
robust descriptor of thermodynamic stability would be the melting
behavior, since positional and other non-thermodynamic factors
for a given probe likely remain constant in a formamide series.
Figure 1. Characteristics of formamide denaturation profiles. (A) Example formamide curves with perfect match, one-mismatch, and two-
mismatch probes targeting the same site on 16S rRNA gene of E. coli. Curves represent theoretical profiles. Observed maximum signal intensity (I
experimental ([FA]
) and predicted ([FA]
) half-denaturation points, and the prediction error (err[FA]
) are illustrated. [FA]
estimated by linear interpolation between two subsequent experimental points that are greater than and less than I
, respectively. Panels (B) and
(C) show the correlation of solution-based free energy predictions with I
and [FA]
, respectively, with r defining the Pearson’s correlation
coefficient. (D)I
plotted against position of target site, as represented by the middle point. All data were obtained from probes belonging to the
TileE set (Table 1). Amount of hybridized target was 5 ng.
Formamide Denaturation in Microarrays
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Consistently, the point of half-denaturation ([FA]
), defined
as the formamide concentration where signal intensity decreased
to half of I
, was largely predictable by DGu
(Figure 1C). This
term represents the melting point of the duplex when a nearly full
sigmoidal profile is obtained as is the case for most perfect matches
used in this analysis. In retrospect, [FA]
also does not
correlate with I
itself (r = 20.22; not shown), further pointing to
the dependence of I
on factors not related with stability. Thus,
we focused our modeling strategy on the normalized melting
profiles where thermodynamically irrelevant signal variations as in
Figure 1D are mostly eliminated.
Our methodology is based on simulating the formamide-based
denaturation of a probe/target duplex with the linear free energy
model (LFEM) in Equation 1. This defines hybridization efficiency
as a sigmoidally decreasing function with increasing formamide
concentration, which takes values up to 1 at low formamide and 0
at full denaturation. The resulting theoretical curves are simulta-
neously fitted to large sets of experimental probe profiles
normalized using Equation 3 for each probe (see Figure 2 for
example fits). In what follows, we describe the stepwise use of
LFEM for the systematic establishment of free energy rules and
calibration of formamide denaturation models for perfect and
mismatched duplexes (Table 2).
Perfect Matches
To calibrate LFEM for perfect matching duplexes, we formed a
set of 1045 probes of variable length (Length set, Table 1), of
which, 1,033 were used for modeling after elimination of probes
close to the background (N
= 1033, Table 2). This set was
designed to have a wide variability of half denaturation points
(range, 4–30%; median, 18%) for a robust calibration of key
modeling parameters. A randomly selected subset of 500 probes
= 500, Table 2) was used for curve fitting, and the rest for
model validation. In addition, signal intensity values that were to
the left of I
and less than 80% of I
(e.g. the 0% formamide
data point in the perfect match example of Figure 1A) were
discarded to prevent the influence of possible kinetic factors at
lower formamide concentrations. Thus, a total of 3,630 data points
were used in the fitting with 500 probes. Using this data set we
compared three models (M1–M3) with different degrees of
Initially, we evaluated the simplest model (M1, Table 2) where
obtained from UNAFold was used to predict the binding
free energy. Therefore, the only general parameters of fitting were
mand {P}
. The best-fitting m-value showed 0.522 kcal/mol free
energy increase with every percent of formamide added, while the
effective probe concentration was equivalent to 0.0025 nM
(Table 2). These parameters can be assumed to have converged
to true values, as the average residual squares of 0.0207 units per
data point agreed well with the average error squares in the
validation set of 533 independent probes (e
= 0.021) (Table 2).
The residual squares translated into a significantly larger s
of 0.024 (Table 2), since this statistic is based on a degree of
freedom (Equation 5) that takes into account all individual c
constants in addition to the two general fitting parameters and is
therefore significantly smaller than the total number of formamide
data points of 3,630 (i.e., n=n–(500+2) = 3128). Thus, the s
of the simple model was set as the reference point to test against
the goodness of fit for the other models, in addition to the
coefficient of determination (R
), which was 0.87 (Table 2).
Next, we evaluated a slightly modified model, designated M2
(Table 2), which included dangling end effects in free energy
calculations. Dangling ends, including terminal mismatches, have
been shown to contribute significantly to duplex stability with in-
solution hybridizations [41,42]. We therefore employed UNAFold
to derive DGu
values with dangling parameters (DGu
). The calibrated and validated model showed a higher s
than M1 (Table 2), and therefore, we excluded dangling ends from
our framework.
It has been shown that the establishment of specific nearest
neighbor free energy rules for microarray hybridizations can
improve predictive ability [33,43]. We therefore developed model
M3 for better predictions of perfect matching duplexes (Table 2).
The DGuvalue (designated DGu
) was calculated for every probe
using the free energies of ten DNA/DNA nearest neighbors, which
were derived as part of the general fitting parameter set in addition
to mand {P}
. To get the total free energy of binding, a constant
initiation free energy penalty (DGu
= 1.96 kcal/mol) was used
rather than deriving it for microarrays. This was because DGu
and {P}
were interdependent by the constant multiplication
because of the way free energy is summed
and Equation 1 is constructed. Between the two variables we
selected {P}
to vary, since there was an in-solution based
approximation available for DGu
[34]. The best-fitting param-
eters point to a constant value of 4.37?10
for the term
, and DGu
and {P}
values can be
arbitrarily changed without affecting model fits as long as this
constant is satisfied. The results with M3 (Table 2) showed
significantly lower average residual squares (Sr
/n= 0.0083) than
M1, as confirmed with the error squares of the validation set
= 0.0080). This was also reflected in an increase of the R
value from 0.87 to 0.95 and a significant reduction of 0.0144 units
in the s
statistic, which was more than twice the experimental
variance calculated as 0.0061 based on the standard deviation of
all data points (not shown), and therefore, the statistical difference
between M1 and M3 was remarkable [44].
Example predictions with M3 are shown for 12 perfect match
probes in Figure 2 (biased sampling) and 100 more in Figure S1A
in Supporting Information (random sampling). The upper panels
of Figure 2 show better fits than the lower ones. To evaluate the
global fitting quality, we calculated the distance between
theoretical and experimental profiles based on half-denaturation
points (|err[FA]
|), as illustrated in Figure 1A. The theoretical
half-denaturation point, [FA]
, is defined the same as [FA]
(see above and Figure 1A), except that it is calculated for the
continuous theoretical curve where the maximum value is always
attained at 0% formamide. The resulting distribution of the
predictive errors in formamide curve positioning is shown in
Figure 3A. Most predictions were represented by the good fits in
Figures 2A–F, as can be seen from respective labelings in
Figure 3A. In fact, average absolute distance between theoretical
and experimental profiles was 2.161.7% in formamide concen-
tration, with more than 93 percent of probes having ,5% distance
(Table 2). These numbers also show significant advancement of
predictive power over the solution-based M1 model (Table 2).
Best-fitting nearest neighbor free energies of M3 are presented
in Table S1A, together with their in-solution matches and plotted
in Figure 4. Although the scale of microarray parameters seems
lower (about 1 kcal/mol reduction in magnitude of free energy)
this was offset by a high effective probe concentration of ca.
0.010 M, compared to that when in-solution parameters were
used (Table 2). The resulting m-value showed 0.173 kcal/mol
decrease in the magnitude of free energy at every percentage of
formamide, not very different from what was previously obtained
for FISH (0.2–0.3 kcal/mol/%, [23]). Given the excellent
correspondence with experimental profiles, the nearest neighbor
parameters, the m-value, and the effective probe concentration
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PLOS ONE | 7 August 2012 | Volume 7 | Issue 8 | e43862
obtained from M3 formed the backbone of our modeling
framework for the evaluation of mismatches (Table 2).
Central Single Matches
The destabilization effect of a single mismatch (DDGu)is
represented by a loss term and a gain term (Equation 2) due to the
Figure 2. Formamide melting profiles of 12 arbitrarily selected perfect match probes and their mismatched versions. All perfect
matches are from the TileE set, since only this set has mismatched versions (for examples from the Length set, see Figure S1A). Solid and dashed
curves indicate theoretical profiles for perfect matches and mismatches, respectively. x-axis, formamide concentration; y-axis, normalized signal
intensity; error bars, standard deviations.
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PLOS ONE | 8 August 2012 | Volume 7 | Issue 8 | e43862
replacement of two nearest neighbors with an internal loop
[33,45]. The loss term can now be calculated based on the
microarray nearest neighbor parameters from M3 (hence desig-
nated DGu
). To establish the free energy rules for loop
stability, we used a large set of probes named OneM (Table 1).
Probes were created by inserting all three possible single
mismatches in the central 11
position of the perfect matches of
the TileE set (Table 1) to avoid positional effects initially.
Based on the good correlation between in-solution and
microarray nearest neighbor free energies previously obtained
with M3 (Figure 4), we initially assumed that the loop free energy
is a linear function of the in-solution values (i.e., DGu
+b, see M4 in Table 2). The calibrated and
validated model M4 showed an s
value (0.0107) higher than the
perfect match model M3, and yet showed a similar goodness of fit
based on R
and |err[FA]
| evaluations (Table 2). However, for
best predictions, we developed M5 to derive specific free energy
parameters for all individual loops (DGu
MM Loop
Table 2). These loops are represented by 104 mismatch triplets
that have all combinations of a middle mismatch and two flanking
base pairs (Table S1B). Curve fitting was done separately for each
triplet to find the best-fitting values of DGu
as listed in Table
S1B. Since the number of available probes was as low as 7 for
some triplets (highest sampling size was 65), we included all probes
in this analysis for the maximal use of the experimental data. The
results showed that M5 outperformed M4 in terms of all goodness
of fit criteria (Table 2).
The relationship between in-solution and microarray loop free
energies was significantly scattered (Table S1B, Figure 4), hence
the better fitting quality of M5 than M4. However, microarray and
in-solution mismatch stabilities seemed to be on a similar scale
unlike with nearest neighbor values (Figure 4). Example model fits
with these values are shown in Figures 2A, 2G, 2J, 2K, and 2L and
their representative ability is indicated in Figure 3B. In addition,
Figure S1B presents profiles for 100 randomly selected probes. We
see in Figure 2 both well-developed (2A) and truncated (2G and
2F) sigmoidal profiles with perfect fits, implicating the accurate
identification of a large range of overall free energy values
=22.5 to 25.2 kcal/mol). Although the best-fits were not
validated by an independent subset in this case (i.e., N
Table 2), other mismatch datasets were used for the verification of
the choice of M5, as will be seen below.
Positional Single Matches
The positional dependence of mismatch stability has been
shown in multiple studies (e.g. [8,43,46,47]) with a general
agreement that mismatches towards the ends are less destabilizing
than those in central positions. We addressed positional effects
mechanistically, using the PosM set (Table 1) and the idea of
relaxed ends illustrated in Figure 5A. In theory, a probe with a
Figure 3. Histograms of prediction errors. (A) Perfect match (Length set), (B) central mismatch (OneM set; open bars, right axis) and bulged
mismatch (Gap and Insertion sets; grey bars, left axis), (C) positional mismatch (PosM set), and (D) two-mismatch (TwoM set; open bars, right axis) and
tandem-mismatch (Tandem set; grey bar, left axis) probes. Lower case letters indicate bins to which probes in corresponding panels of Figure 2
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mismatch in a terminal position may have a more favorable (more
negative) free energy in a relaxed conformation that leaves the
bases spanning positions from the mismatch to the end unpaired.
This happens when the free energy penalty of the loop (i.e., a
positive DGu
MM Loop
value) is larger in magnitude than the
cumulative negative contribution of terminal base pairs clamping
the duplex together, thereby causing an overall positive free energy
contribution in the closed conformation. Therefore, the free
energy of both imposed and relaxed conformations (Figure 5A)
should be calculated and the most negative used. We adjusted our
free energy calculations to include this effect for the positional
dataset and compared the modified DDGuterm (i.e., the free
energy difference from the perfect match duplex) with the
experimental shift in the half-denaturation point (D[FA]
upon the insertion of the mismatch (i.e., the distance between the
denaturation profiles of a mismatched probe and its perfect match
version). The average D[FA]
shifts shown in Figure 5B
revealed a very strong positional trend starting at the 4
from each terminal, which was almost perfectly captured by the
modified free energy calculations.
We tested models M4 and M5 against the positional dataset
without making additional calibrations. The results revealed better
goodness of fit values for M5 in all terms, thus confirming that the
derived microarray-specific mismatch parameters were more
informative than in-solution parameters. The error squares with
M5 were larger in the positional dataset compared to the central
mismatch dataset (i.e., compare s
and e
values in both sets), but
the fitting quality was still satisfactory with a comparably high R
value of 0.94 and more than 91 percent of the probes having less
than 5% (v/v, formamide concentration) error in the prediction of
half-denaturation points (Table 2 and Figure 3C). Example fits in
Figure 2 show two terminal mismatches that are very difficult to
discriminate from the perfect match (2C and 2E), as well as one
with moderate discrimination potential (2I), which were captured
by the M5 model. Figure S1C presents profiles of 100 randomly
selected probes from this dataset. The relaxation adjustment
adopted during the positional analysis was consistently imple-
mented in the models presented below.
Bulged Mismatches
A bulged mismatch occurs when there is an insertion or deletion
in an otherwise conserved target site and can potentially have a
comparable stability to an average single mismatch [48,49]. We
combined the Gap (deletions) and Insertion (insertions) probe sets
(Table 1) to develop free energy rules for bulged mismatches. The
strategy was the same as with single mismatches, except that
deletions removed two nearest neighbors and insertions only one
nearest neighbor for the calculation of the loss term in Equation 2,
which still required existing nearest neighbor values from M3
). Thus, modeling aimed at the derivation of the
missing loop terms for bulged mismatches (DGu
), which were
represented by 64 triplets in total, including all combinations of a
bulged mismatch and two flanking base pairs (see Table S1C).
The general screening procedure yielded 467 probes for testing.
Although this set covered all mismatch triplets, there was not
sufficient information for deriving specific free energy values for
each loop (2 to 14 probes per loop). Thus, we only tested models
assuming a linear relationship between in-solution loop parameters
and microarray parameters (i.e., DGu
Results with and without the constant term of the linear
relationship (b) revealed that it did not contribute to the overall
Figure 4. Relationship between in-solution and microarray free
energy values (at 426C). Red circles, nearest neighbors; blue
triangles, single mismatch loops; blue squares, single bulged mismatch
loops; green dots, tandem mismatch loops.
Figure 5. Effect of mismatch position on free energy and
formamide denaturation. (A) Example probe (E844–865_4GT) with
lower free energy at relaxed conformation as compared to imposed
duplex with one mismatch. (B) Experimentally observed shift in the
half-denaturation point (D[FA]
– open squares and black error
bars) and calculated minimum free energy change (DDGu- grey circles
and error bars) upon insertion of a single mismatch, as a function of
mismatch position. Values, averages; error bars, standard deviations.
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fitting quality (i.e., s
values were the same for M6 and M7,
Table 2). We therefore selected M7 as the preferred method,
which showed goodness of fit parameters similar to single
mismatch models (Table 2). The relationship of loop free energies
to original in-solution parameters is depicted in Figure 4, with a
line of data points of slope a(0.238). As an interesting result, the
plot suggests that bulged mismatches are similar to moderate single
mismatches in microarray-based stability, in contrast with in-
solution parameters where bulged mismatches are generally more
destabilizing. Example fits are illustrated in Figures 2F and 2H,
both of which show poor mismatch discrimination potential due to
stable bulged mismatches. Figure S1D presents 100 additional
randomly selected probes. The distribution of predictive errors at
half-denaturation points was similar to other mismatch datasets
(Figure 3B).
Two Mismatches
In principle, the stability of two separate single mismatches can
be calculated by adding their respective DDGuvalues. Thus, we
tested M4 and M5 developed for single mismatches, using a set of
two separate mismatches (TwoM, Table 2). Once again, error
square parameters in Table 2 showed that microarray-specific free
energy rules (M5) were better predictors than the linear mapping
from in-solution values (M4), although they also showed lowered
fitting quality in comparison to single mismatches. The predictive
errors were least of all according to the distribution in Figure 3D,
but this was biased by the fact that complete denaturation
happened at very low formamide concentrations (0–10%) in
general with double mismatches. An example is provided in
Figure 2D, while 100 more randomly selected probes are
presented in Figure S1E.
Tandem Mismatches
A special type of double-mismatch is the tandem mismatch,
which involves two adjacent mismatches [50]. Thus, the loss term
in Equation 2 should include three nearest neighbors and the loop
term a quadruplet that accommodates a tandem mismatch pair in
the middle flanked by two base pairs. In the simplest case (model
M8, Table 2), we again assumed a linear relationship of the loop
term (DGu
) with in-solution parameters (DGu
) obtained
from UNAFold. However, the massive number of 1,176 combi-
nations of tandem quadruplets lowers the confidence in the
indirect calculation of in-solution parameters based on limited
data [42]. Thus, simple microarray-specific rules may again be
preferred to solution-based modeling.
We developed M9 with a set of eight rules (see Table S1D)
describing the stability of tandem mismatches based on our
observations with single mismatches (Table S1B). The model first
divides tandem mismatch quadruplet into two halves, each having
a closing base pair and a mismatch. Based on single mismatch
data, whether the closing pair is an AT- or GC-type affects the
loop stability, such that GC pairing generally stabilizes the
mismatch. As for the mismatch type, GG, GA, and GT
mismatches show significantly higher stability than others.
Therefore, our eight rules (Table S1D) are established to give a
different score to each one of the 8 combinations of closing pair
(two types) and mismatches (four types). The two scores from
either half of the quadruplet are then added to obtain the overall
free energy of the loop (DGu
). Initial results with 300 probes
used for model calibration yielded a better s
statistic than the
solution-based M8 model. However, the validation set showed
somewhat different error squares than residual squares indicating
there was benefit of using more probes (Table 2). We therefore
obtained final best-fitting scores (Table S1D) using the entire
probe set for curve fitting (Table 2). The free energies of the
quadruplets in our dataset were related to in-solution values in a
way similar to single mismatches (Figure 4), except for some
combinations of GT and GG base pairs that were predicted by
UNAFold to stabilize the loop by a significantly negative free
energy, but according to our parameters did not show a negative
contribution (Table S1D). The error distribution of this model
(Table 2 and Figure 3D) was similar to separate double
mismatches. An example fit is provided in Figure 2B, while 100
more randomly selected probes are presented in Figure S1F.
The Effect of Target Concentration
In this study, a uniform amount of target (5 ng in a
hybridization buffer of 8 mL) was used during the model
development. Although total DNA concentration can be con-
trolled in environmental applications, relative abundances of
organisms in the analyzed sample can cause a large range of target
and non-target concentrations. Therefore, it is important to know
if target concentration affects formamide curves in a way that
undermines model predictions. To test this effect, we used an
order of magnitude greater concentration of our target (50 ng) in
independent hybridizations with the same formamide series.
Furthermore, we analyzed an additional dataset obtained with
50 ng of the 16S rRNA gene of R. sphaeroides. As exemplified in
Figure 6A with a probe perfectly matching both targets, when the
signal did not reach saturation levels in the signal scale, 50 ng
target yielded fluorescence values consistent with the 10X increase
in concentration. Despite the remarkable gap in fluorescence
levels, the profiles aligned well when normalized and the
theoretical prediction was not significantly affected (Figure 6C).
When concentrated targets were used, the experimental profiles
of most probes were affected by signal saturation, which was
evident at fluorescence levels of about 40,000 units and above (see
Figure S2). Importantly, this was not the case with the modeling
datasets, since the highest probe signal intensity encountered was
less than 40,000. Typical profiles affected by saturation are shown
in Figure 6B, with another probe that targets both E. coli and R.
sphaeroides. While the level of maximum signal was about
10,000 units with the 5 ng target, the 10X increase in concentra-
tion could not carry this beyond a level of around 60,000 units,
implicating that the full sigmoidal profile could not be observed.
Accordingly, normalized curves could be matched only at higher
formamide concentrations provided that the normalization was
adjusted to offset the signal saturation effect (Figure 6D).
The data in Figure 6 represent the general case except for small
deviations that can be explained by experiment-to-experiment
variability. It follows from the agreement of experimental profiles
that the predictive ability of our models should not be significantly
affected by even large concentration changes. Indeed, a total of
181 E. coli probes (perfect matches) not affected by saturation (i.e.
,40,000 a.u.) showed |err[FA]
| values of 1.8961.33%
when hybridized with the 50 ng E. coli target. The same analysis
applied to 50 such R. sphaeroides probes (TileR set, Table 1) resulted
in an absolute error of 1.8261.22% with the 50 ng R. sphaeroides
target. These numbers agree well with the data in Table 2. We
therefore conclude that our models should be applicable to
environmental samples with a range of concentrations, as long as
signal supersaturation is prevented by the optimization of total
target concentration.
We adopted the idea of formamide denaturation from FISH
protocols, where the strategy is successfully used for balancing
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probe sensitivity and specificity [3,20]. In FISH, the optimization
is generally carried out experimentally by establishing probe
denaturation profiles (similar to those in Figure 1A) with pure
cultures or clones of target and non-target organisms, an option
that is clearly not feasible for high density microarrays given the
large number of probes. Therefore, we did not only show the proof
of principle for formamide denaturation in microarrays, but also
developed mathematical models for predicting the melting profiles
of perfect and mismatched probe/target pairs. The predictive
accuracy for the position of the melting curves is generally within
5% formamide of the half-denaturation point, remarkably better
than what was previously achieved for FISH with a multi-state
LFEM [23]. This must be in part due to the absence of a stable
secondary structure in the fragmented DNA target of the
microarray method studied, in comparison to the full length
rRNA target in FISH. However, the derived nearest neighbor free
energies in our current two-state model may be reflecting an
averaged out partitioning of nearest neighbors between different
states, including secondary interactions within or between target
fragments. This is consistent with the fact that the scale of nearest
neighbor parameters turned out to be lower in microarrays than in
solution, while that of mismatch loops were consistent (Figure 4).
Overall, we believe that the predictive power achieved by the two-
state LFEM in this study can significantly improve probe design
and optimization in microbial ecology applications of oligonucle-
otide microarrays, as will be discussed below.
The curve-fitting procedure used in this study was carefully
devised to include probes with a large range of melting points. A
key aspect of the mathematical framework was the use of cfactors
to adjust theoretical curves when a full sigmoidal profile was not
obtained (Equation 3). We graphically explain how the cfactor
affects curve-fitting, and compare alternative approaches to
estimate these factors in Figure S3. For nearly full sigmoidal
profiles, lower formamide concentrations represent points of
approximately 100% hybridization efficiency. In these cases, it is
sufficient to match experimental profiles normalized by I
theoretical profiles with c= 1. On the other hand, when a probe
melts at low formamide concentrations, the sigmoidal curve is
truncated and the experimental hybridization efficiencies cannot
be determined with high enough confidence. Hence, an adjust-
ment of the theoretical curve using c?1 provides a better match of
theoretical and experimental profiles. We tested three different
approaches to calculate cfactors. In our preferred approach, c
factors were included as best-fitting parameters. This did not affect
the modeling of formamide denaturation since the loss of the
degrees of freedom by best-fitting cvalues was taken into account
in key statistics (Equation 5) and cfactors do not mathematically
change the melting point, which our modeling effort aims to
Figure 6. Effect of target concentration and type of target molecule on formamide denaturation profiles. Probes E338–359 (Aand C)
and E763–780 (Band D) are shown. Both probes perfectly match the 16S rRNA gene of both E. coli (Eco) and R. sphaeroides (Rsp).
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predict. Nonetheless, the use of one cfactor per probe may seem
to have caused overparameterization during model development.
We did additional statistical tests to independently show that this is
not the case (Table 3). The details of these analyses are explained
in Text S1. In one set of tests, the selected models were calibrated
with c= 1 for all probes. In another set, we set cequal to the
inverse of the maximum predicted hybridization efficiency (i.e.,
efficiency at 0% formamide) so that the truncated denaturation
profile always started at a value of 1, consistent with the
normalization of experimental intensities with I
. On the overall,
our evaluations demonstrate that the model predictions were
driven by thermodynamic parameters. Although the alternative
methods resulted in similar conclusions for the test models (Text
S1 and Table 3), a unique advantage of using best-fitted cfactors is
the effective buffering of experimental artifacts such as the increase
in signal intensity at low formamide concentrations (Figure S3C)
and general experimental noise. Thus, with the help of cfactors,
we were able to estimate a series of thermodynamic parameters,
with minimal influence of experimental artifacts, for the prediction
of probe denaturation in a large range of melting points.
Certainly, our model does not capture free energy parameters
for all possible mismatch conformations in a probe/non-target
duplex (e.g., bulged mismatches with two deletions or inserts, three
adjacent mismatches, etc.) to directly predict their effect on
hybridization efficiency. But the most important (stable) ones were
systematically covered, which allowed us to extend the predictive
algorithm to other (complex) mismatch conformations by penal-
izing them with conservative parameters (see Text S2; Table S2
shows the list of extended free energy rules). The extended model
can be used in the calculation of the hybridization efficiency of
most duplexes with reasonable confidence (see Text S2 and Figure
S4D). The algorithm that simulates formamide denaturation with
LFEM using all thermodynamic parameters established in this
study (Table S1 and Table S2) is named ‘‘ProbeMelt’’ and made
freely available both as an on-line web tool at http://DECIPHER. and a package in R programming language (R
Foundation for statistic computing, Vienna, VA) (see Text S2 for
Differences with Previous Approaches
The governing equation of our mathematical framework
(Equation 1) is similar to Langmuir isotherms commonly used
for describing the relationship between target concentration and
the fraction of target-bound probes [33,51,52,17]. In addition to
lacking a denaturation term (i.e., m-value and formamide
concentration), Langmuir models differ from LFEM with the
assumption that the target is in excess of probe. This assumes
probes are saturated at a hybridization efficiency of 1, which was
clearly not the case in our experiments as the fluorescence intensity
at the plateaus of sigmoidal melting profiles (i.e., points of
hybridization efficiency ,1) largely varied and was consistently
elevated by increased target (Figure 6). As shown in Figure 6B, we
encountered signal saturation with the highly concentrated target,
but this is likely due to the sensitivity of the scanner as the signal
always converged to the upper limit of the measurable signal scale
(Figure S2). At lower signal values, 10 times more target caused
around 10 times higher signal intensity (Figure 6A and Figure S2).
Thus, the data was more consistent with the depletion of the target
rather than the probe, as was assumed in the derivation of
Equation 1. When the Langmuir model is rejected, the compe-
tition for the limited target molecules may need to be addressed
[53]. However, this competition effect would be evidenced by a
Table 3. Additional statistical tests
Parameters Statistics |err[FA]
Test Model eliminated permuted randomized fitted
/n s
T1 M3 c-factors na na na na na na 0.0118 0.93 2.1 93.4
T2 M3 na c-factors na na na na na 0.0158 0.90 2.1 93.4
T3 M3 na DGu
na na na na na 0.035 0.78 5.7 52.5
T4 M3 na DGu
, Probe
na na na na na 0.052 0.68 7.7 38.5
T5 M3 na Na P
,m na na na na 0.19 20.18 14 10
T6 M1 c-factors Na na Po, m 0.0321 0.0322 0.0319 0.0320 0.80 2.7
T7 M3 c-factors Na na Po, m, DGu
0.0118 0.0119 0.0115 0.0116 0.93 2.1 93.8
T8 M5 c-factors Na na na na na na 0.0147 0.90 2.0 94.5
T9 M5 na c-factors na na na na na 0.028 0.815 2.0 94.5
T10 M5 c-factors
Na na na na na na 0.0107 0.93 2.0 94.5
T11 M5 na DGu
MM Loop
na na na na na 0.0144 0.905 3.0 82
T12 M5 c-factors
Na na DG
MM Loop
0.0104 0.0107 0.0104 0.0104 0.93 2.0 94.4
See Table 2 for the definition of models and parameters and the reference values. See Text S1 for the details of the statistical tests.
Randomization and permutation tests are based on at least 100 runs until convergence. Significant figures in these results reflect the uncertainty in the converged
Probes were permuted while maintaining the original sequence of each probe. This test corresponds to permuting the probe length in addition to the nearest
neighbor free energies.
Show improvement over original models although statistical parameters indicate otherwise. The discrepancy reflects the fact that half-denaturation point is not a
perfect representation of the melting point for experimental profiles without a plateau (e.g., see Figure S3C). This adversely affects the results with c-factors more than
without, as the models without c-factors tend to compensate for the lack of good fitting in the vertical by moving closer to experimental values in the horizontal,
although this movement does not mean a better match. Since the original models in the main text always use c-factors, the evaluation of model predictions are
conservative and more accurate with respect to half-denaturation points. This analysis provides just another way of seeing how c-factors buffer experimental artifacts as
discussed in Text S1.
Best-fitted creplaced by a model-derived factor (see Text S1).
Formamide Denaturation in Microarrays
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good correlation between predicted hybridization free energy and
fluorescence intensity, which also was not the case in our study
(Figure 1B). The actual mechanism of surface hybridizations on
microarrays is not well understood [18,28,54]. It is beyond the
scope of this study to justify the conceptual model behind our
mathematical framework, except to show that the simulations with
the equilibrium model adequately represented experimental
denaturation profiles, thereby fulfilling our main goal.
Unlike most other models of oligonucleotide microarray
hybridization [51,53], the aim of the LFEM is not to find the
concentration of the target molecules, but to predict the
hybridization efficiency at a given formamide concentration,
which produces the normalized melting profiles regardless of the
concentration. Focusing the predictive power on target concen-
tration is problematic for diagnostic applications in several ways.
First of all, since most DNA-targeted protocols are end point PCR-
dependent, the concentration in question is a biased quantity even
if accurately predicted [55]. Secondly, concentration predictors
work on the signal intensity variation assuming it is a function of
relative target concentration as well as binding free energy.
However, if the target is labeled by the common random priming
method as in this study, there will be significant differences in
signal intensity over different fragments within the same target
(e.g., the fluctuations in Figure 1D), which clearly undermines the
ability to pick target to target differences. But most important for
microbial ecology applications, a strong signal response that leads
to the prediction of a concentration may be both from a target or a
closely related non-target as depicted in Figure 7 (e.g., at 0%
formamide). Thus, detecting the absence/presence of organisms at
high stringency (e.g., 20–25% formamide, Figure 7), rather than
measuring their concentration, seems to be a more feasible
approach, which requires the calculation of melting curves.
Another property of hybridization that our LFEM is not trained
to capture is the decrease in signal intensity upon the insertion of a
mismatch (e.g., the lowered plateaus of mismatches in Figures 2A
and 2H). Since the theoretical hybridization efficiency is close to 1
in the plateau of both perfect and mismatched duplexes, the
LFEM cannot directly address this issue, although the model is
unaffected by it because of the normalization by I
. Arguably,
mismatch stability (i.e., DDGu) can be quantified by the decrease in
signal intensity level as another way of developing free energy rules
for mismatch discrimination, as was done previously [33].
However, the prediction of the change in plateau levels is also
not a viable approach for applications in microbial ecology,
because the moderate decrease in signal associated with a
mismatch can be easily offset by the relative abundance of the
non-target organism. Figure 7 illustrates this phenomenon as well.
Once again, a more realistic approach is to force the mismatched
duplex to dissociate by applying stringent conditions, so that it
counts as absent even when it is highly abundant (e.g., Figure 7,
20–25% formamide).
To the best of our knowledge, the only other systematic use of
denaturation trends for microarray optimization appears in the
non-equilibrium thermal dissociation (NTD) approach [10,46].
Applications of NTD involve the derivation of dissociation profiles
with reference organisms as well as environmental samples for
matching the two [9,56,57]. This approach is not feasible with
high-density microarrays designed to target thousands of organ-
isms at once [13,15,16]. In addition to the use of formamide rather
than temperature for denaturation, an important difference that
sets apart our methodology from NTD is the adjustment of
stringency during the long hybridization period to achieve
equilibrium-like conditions, whereas NTD is based on a kineti-
cally-driven dissociation during the wash step [58]. Thus, we took
advantage of equilibrium thermodynamics and developed predic-
tive algorithms to create a feasible alternative to the experimental
testing of probes for optimization. Furthermore, we do not
recommend the matching of predicted melting profiles to
experimental ones, as not only would this require an even higher
accuracy of predictions than what we have obtained, but also the
possible superimposition of signals from perfectly matching and
mismatched targets could undermine the curve-matching ap-
proach [58]. The recommended use of our modeling approach for
the rationalization of probe design and optimization is described
Application of LFEM to Diagnostic Probe Design
In this section, we describe how the LFEM-based calculations of
hybridization efficiency can be useful for the optimization of probe
sensitivity and specificity in microbial ecology applications. The
general practice aims at determining the absence/presence of
organisms by setting a signal intensity threshold to define
successful target capture [13,19,59,60]. When there is sufficient
signal from the capture of a mismatched non-target gene, probe
specificity is compromised. To minimize the chance of false
positive identification because of cross hybridizations, multiple
probes with identical or nested coverage are designed per target
group (i.e., operational taxonomic unit; OTU), and nearly all of
these are demanded to be bright in order to call a target group as
present (e.g. 9 out of 10 probes). This assumes the probes are
designed with high enough sensitivity to avoid signal intensities
below the threshold when the perfect match target is captured
(e.g., if 2 out of 10 probes targeting an existing OTU fail to give
bright signal, then it is a false negative identification). Therefore,
the obvious target for our predictive denaturation approach is the
design of optimal probes and hybridization conditions to obtain
the highest possible hybridization efficiency with the targets while
keeping the hybridization efficiency with the non-targets at the
lowest possible level, thus minimizing the chance of false positive
and false negative identification of OTUs.
For the demonstration of optimization, we did sensitivity and
specificity analysis with the 16S rRNA gene of two organisms,
E. coli and R. sphaeroides, such that E. coli served as target for
perfect-match E. coli probes (TileE and Length sets in Table 1) and
non-target for R. sphaeroides probes (TileR, Table 1), and vice versa.
Figure 7. Formamide denaturation profiles with conventional
target and highly abundant non-target. The example probe,
E751–772, is a perfect match to the 16S rRNA gene of E. coli and has one
mismatch to R. sphaeroides. Curves are theoretical predictions fitted to
the experimental scale. Eco, E. coli; Rsp, R. sphaeroides.
Formamide Denaturation in Microarrays
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It is important to note that probes that would be filtered due to
poor signal intensity during model development (see Methods)
were included in these tests to avoid biasing the results. The
amount of E. coli target was 5 ng and it represented an organism of
moderate abundance assuming total DNA used in an environ-
mental application was 50–100 ng. This number is consistent with
our signal-optimized applications with real mixed communities
where 70 ng of total target is used for hybridization without
causing frequent signal saturation problems (not shown). The
amount of R. sphaeroides target was 50 ng, and therefore, it
represented an unlikely abundance of a single organism in total
DNA causing signal saturation with most probes and challenging
specificity at the extreme levels. The optimization of probe
sensitivity and specificity by predictive modeling follows two steps.
First, since microarray hybridizations are typically performed at
a single level of stringency, it is important to be able to design
probes with similar formamide-based stabilities (i.e., similar
melting points), to achieve a consistent level of hybridization
efficiency with target organisms over thousands of probes. We can
do this with the ProbeMelt algorithm by predicting melting points.
In Figure 8A, we show the mismatch discrimination potential for
probes designed to have a narrow range of predicted melting
points, between 18–22% formamide. In the E. coli set there are
561 such probes that have one or more mismatches to
R. sphaeroides. We tested the mismatch discrimination ability of
these probes against this extremely abundant non-target. The
results show that, when formamide is not present, the discrimi-
nation for 1–2 mismatches is not possible at all and about half of
the probes with .2 mismatches give a bright signal. The situation
changes radically at 20% formamide (Figure 8A), which represents
the targeted melting point in the design of these probes. However,
there is about a 12% chance of poor target capture at this high
level of stringency (i.e., the corresponding perfect match column in
Figure 8A shows only 88% above signal threshold) implying that
sensitivity is not optimal. As a compromise, hybridization can be
done at 15% formamide (i.e., ,5% less than the predicted melting
points), to decrease the rate of low signal from target to ,2% and
bring the rate of high signal from non-targets to about 72% for 1–
2 mismatches and 13% for more mismatches (Figure 8A).
Although mismatch discrimination potential seems low for 1–2
mismatches, it should be considered within the context of a
multiple-probe strategy, which results in a false positive identifi-
cation only when several non-target OTUs are captured by
different probes. Since it is unlikely to have many such non-targets
in the same environmental sample (i.e., total DNA is 50–100 ng
while the tested non-target was 50 ng), these results show that the
predictive formamide denaturation strategy can be useful to avoid
false positive identification of even extremely abundant non-
targets. The second half of Figure 8A shows the experimental
simulation with 378 R. sphaeroides probes tested against 5 ng E. coli
as the moderately abundant non-target. In this more likely
scenario, using 15% formamide is enough to effectively suppress
the signal intensity of mismatched probes (Figure 8A). Thus, 15%
formamide can be an optimal point for the sensitivity and
specificity of probes designed with a predicted melting point
around 20% formamide.
It is clear from the experimental simulations in Figure 8A that
not all mismatches can be perfectly discriminated even under
optimal conditions, as could be anticipated by the proximity of
some denaturation profiles encountered (e.g., Figures 2E and 2H).
Therefore, an important question is whether problematic
mismatches can be predicted beforehand. This brings us to the
second step in optimization: the prediction of worst non-targets
based on hybridization efficiency calculations during the design
process. We show in Figure 8B the relationship between predicted
hybridization efficiency and percent above threshold for all
mismatched duplexes at four formamide concentrations. Consis-
tent with our goals, the predicted efficiency of R. sphaeroides probes
hybridizing with the moderately abundant E. coli non-target
dictates the frequency of false signal. An important result here is
that more than 2 mismatches can also bind effectively, as captured
by the thermodynamic model. On the other hand, the extremely
abundant non-target R. sphaeroides causes specificity problems with
E. coli-targeted probes starting at ,0.1 hybridization efficiency
(Figure 8B). Nonetheless, probes predicted to have ,0.05
hybridization efficiency, which are the majority of the population
at all formamide points considered (e.g. 72% of the probes for
15% formamide), are still dim even when they have 1 or 2
mismatches. Thus, by defining probe specificity based on the
hybridization efficiency with potential non-targets, probes with the
best specificity scores can be selected during probe design with the
help of the ProbeMelt algorithm.
Figure 8. Fraction of probes above an arbitrarily defined
threshold of 1750 fluorescence units. (A) Probes designed to have
a melting point of 18–22% formamide and hybridized at 0% (red), 15%
(green), and 20% (blue) formamide. Left panel, E. coli probes hybridized
with 5 ng E. coli target (PM data) and 50 ng R. sphaeroides non-target
(MM data); right panel, R. sphaeroides probes hybridized with 50 ng R.
sphaeroides target (PM) and 5 ng E. coli non-target (MM). (B) The
predictive power of hybridization efficiency for E. coli probes hybridized
with 50 ng R. sphaeroides (dashed lines) and R. sphareoides probes
hybridized with 5 ng E.coli (solid lines) for all mismatches (red), 1–2
mismatches (green), and 3–5 mismatches (blue). Data from formamide
concentrations 10, 15, 20, and 25% were combined to maximize the
sample space for each data point. x-axis shows midpoints of bins with a
hybridization efficiency window of 0.1, except for end bins (window of
Formamide Denaturation in Microarrays
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In summary, we recommend the following steps for the
systematic optimization of microarray protocols with LFEM: (i)
prescribe a single formamide concentration for hybridization (e.g.,
15% formamide), (ii) design multiple probes per target group (e.g.,
10) to allow predictive errors without compromising identification,
(iii) at every target site, adjust probe length to obtain a uniform
probe stability throughout the array, such that the theoretical
melting points are always slightly higher than the prescribed
experimental formamide concentration (e.g., keep the probe
melting points in the range of 18–22% formamide), (iv) set a
specificity score for each probe candidate by calculating the
hybridization efficiency with mismatched non-targets and select
for probes that have best specificity scores. Steps iii and iv are
applicable for designs with large target datasets since the
ProbeMelt algorithm can evaluate more than a million probes
per second. Step iv is also a significant departure from traditional
design approaches based on mismatch numbers or types [61,62],
since it takes advantage of the thermodynamic parameter sets that
were rigorously developed in this study. In addition to helping with
the design and optimization phase, we expect our models to be
useful for the interpretation of signal patterns from hybridized
microarrays. Advanced algorithms for organism detection from
complex array data have been developed [63,64,65], but they
either lack predictive tools for the evaluation of probe hybridiza-
tion with non-targets [64,65], or use in-solution free energy
parameters as a preliminary approach [63]. Therefore, it is not
hard to imagine hybridization efficiency predictions improving the
accuracy of interpretation algorithms for diagnostic microarrays.
Application to other Platforms
Because of platform- and protocol-specific variables such as
probe density and fragment length, our model should be applied to
other types of microarrays with care. Obviously, the modeling
parameters are optimized for 4-Plex Nimblegen arrays hybridized
at 42uC, and therefore, the ProbeMelt algorithm developed in this
study should be directly applied only for these conditions. While
we do not expect the free energy rules to differ significantly in
other similar platforms (if the temperature and hybridization
buffers are not changed), it is anticipated that the effective probe
concentration ({P}
) may need to be re-optimized when probe
concentration or configuration are altered. On the other hand,
more significant adjustments may be necessary if the target
labeling procedure is different. For instance, if long, unfragmented
target nucleic acids are prepared [66], significant competition with
stable secondary structures may change the thermodynamics of
binding. Thus, re-optimization may need to be extended to
nearest neighbor rules or the m-value. In any case, probe sets
similar to those used in this study can be included in a custom
array design, so that the parameters can be re-optimized if
necessary, following our modeling approach. Also, since our
modeling framework is derived assuming the probes are not
depleted by the local target the validity of this assumption needs to
be verified as probe saturation has been clearly shown in some
studies with other platforms [52]. If probe depletion appears to be
the case, the hybridization efficiency term of this study can be
redefined based on the ratio of target-bound probes as in
Langmuir models [51,52] and the same linear free energy
approach can be applied. With the current technology of
microarray fabrication allowing the placement of millions of
probes on a slide, a set of ,15,000 probes allocated for modeling
can be a negligible amount. Extension of the specific formamide
denaturation LFEM to other platforms could also be informative
about the general applicability of the modeling framework,
thereby helping with the efforts to understand the mechanisms
of hybridization.
In conclusion, the thermodynamic modeling framework estab-
lished to simulate formamide denaturation can be effectively used
for the design and optimization of probes in microbial ecology
analyses. For similar platforms and protocols obeying the
assumptions of this work, the LFEM can be directly applied using
the online ProbeMelt algorithm. For others, the systematic
approach developed can be followed to customize the thermody-
namic parameters.
Supporting Information
Figure S1 Figures of additional experimental and
theoretical formamide melting profiles.
Figure S2 Signal saturation with highly concentrated
Figure S3 Curve fitting with different methods to align
theoretical curves with normalized experimental pro-
Figure S4 Figures for Text S2.
Table S1 Tables of free energy parameters describing
duplex stability.
Table S2 Extended free energy rules for quadruplets of
nucleotide pairs in a DNA duplex.
Text S1 Best-fitted cFactors and Additional Statistical
Text S2 Free energy calculations with nucleotide qua-
We thank Daniel Gall for his technical help with R. sphaeroides experiments
and Jeffrey A. Starke for valuable discussions about the practical use of the
model. We also acknowledge the training of LSY by Doris Steger (target
labeling) and Richard Grant (Nimblegen hybridization) for the microarray
protocols used.
Author Contributions
Conceived and designed the experiments: LSY AL DRN MW. Performed
the experiments: LSY. Analyzed the data: LSY ESW. Contributed
reagents/materials/analysis tools: DRN MW. Wrote the paper: LSY
DRN AL ESW MW. Developed the model: LSY. Developed ProbeMelt:
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... Among the different hybridization variables, temperature, time and formamide concentration are crucial to guarantee the probe accessibility and binding to the target sequence (Bouvier & Del Giorgio, 2003;Yilmaz & Noguera, 2004). The temperature relates with the probe affinity to the target and time with the hybridization kinetics, while formamide is routinely used to lower the hybridization temperature, as it denatures the target region (Yilmaz, Loy, Wright, Wagner, & Noguera, 2012;Yilmaz & Noguera, 2004). ...
... The interaction between temperature and formamide concentration, and temperature and time, were found to be the most relevant and are shown in Figs. 1 and 2, respectively. Fig. 1 shows that, during 60 min hybridization (time fixed at its 0 value), the fluorescence intensity improved gradually as the formamide concentration increased, probably due to the favorable formamide effect on the probe hybridization kinetics (Yilmaz et al., 2012). This happened until a formamide concentration of about 45% (v/v), beyond which the hybridization efficiency reduced, as the excessive formamide probably started destabilizing the probetarget hybrid (Yilmaz & Noguera, 2004). ...
Saccharomyces cerevisiae (S. cerevisiae) is a crucial fermenting microorganism for the beer, wine and bread industry. As such, an accurate and rapid method for its identification and monitoring is required. In here, a peptide nucleic acid (PNA) probe was first designed to target S. cerevisiae by fluorescence in situ hybridization (FISH). This PNA-FISH method was then systematically optimized, employing response surface methodology (RSM). The interaction between the critical hybridization temperature, time and formamide concentration and their effect on the FISH efficiency were modelled. The model predicted optimal fluorescence intensity upon hybridization at 53.9 °C, during 57.8 min and using 43.8% (v/v) formamide in the hybridization buffer, which was experimentally confirmed. RSM showed to be a valuable tool to optimize and better understand the dynamics of yeast FISH, which can impact the performance evaluation of related fermentation processes.
... Therefore, after the design of the probes, it is necessary to proceed to the experimental evaluation, as well as to tests to optimize the stringency conditions, in which the hybridization reaction occurs between the probe and its complementary target (generally located in the rRNA), as well as how to test the probe against non-target organisms from the same ecosystem as the target organism. The stringency of the reaction is adjusted by varying the incubation temperature or the concentration of formamide in the hybridization buffer in concentration steps of 5% (v/v) [38][39][40]. ...
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Paenibacillus, rod-saped gram-positive endospores forming aerobic or facultative anaerobic bacteria, colonize diverse ecosystems and are involved in the biodegradation of cultural heritage assets. Biodeteriogenic microorganisms can be easily detected/identified by ribonucleic acid- fluorescent in situ hybridization RNA-FISH with specific probes. In this work, probes designed in silico were analyzed to calculate hybridization efficiency and specificity by varying the formamide concentration in the hybridization. The Pab489 probe showed excellent in silico performance with high theoretical maximum efficiency hybridization (99.99%) and specificity and was selected for experimental assays with target Paenibacillus sp. and non-target biodeteriogenic microorganisms. Results assessed by epifluorescence microscopy and flow cytometry revealed that, regardless of the formamide concentration, it was possible to observe that the Pab489-Cy3 probe had a similar signal intensity to the EUB338-Cy3 probe (positive control), so the presence of formamide, a highly toxic and carcinogenic compound used to aid the hybridization process, is not necessary. The designed probe used in FISH assays allows specific in situ identification of Paenibacillus spp. in microbial communities in a culture-independent way. This approach can be employed for screening Paenibacillus spp., showing great potential for future application in biodeterioration of heritage assets, in the search for Paenibacillus strains that produce compounds with biotechnological or medical potential.
... In step 2, pairs of forward and reverse primers are used to 'amplify' the DNA in silico. In order to rapidly amplify many groups using a large number of primer pairs (500), we configured a fast method for predicting mismatched hybridization efficiency (Yilmaz et al., 2012) to use DNA/DNA thermodynamic parameters. Regions of the DNA that are predicted to amplify with at least moderate efficiency (>50% by default) are include in the set of PCR products. ...
For numerous experimental applications, PCR primers must be designed to efficiently amplify a set of homologous DNA sequences while giving rise to amplicons with maximally diverse signatures. We developed DesignSignatures to automate the process of designing primers for high-resolution melting (HRM), fragment length polymorphism (FLP) and sequencing experiments. The program also finds the best restriction enzyme to further diversify HRM or FLP signatures. This enables efficient comparison across many experimental designs in order to maximize signature diversity. Availability and implementation: DesignSignatures is accessible as a web tool at, or as part of the DECIPHER open source software package for R available from BioConductor. Contact: kalin{at} Supplementary information: Supplementary data are available at Bioinformatics online.
... In order to improve predictions of formamide denaturation in FISH another approach was used from the same authors for microarrays hybridizations (Yilmaz et al., 2012), the singlereaction computationally model (SRM) (Wright et al., 2014). The SRM model converts the DG values from DNA/RNA NN rules to a specific DG using a linear relationship with only two parameters, instead of 17, and was considered the best model in predicting the melting point, with the error being less than 10%. ...
Full-text available
The thermodynamics and kinetics of DNA hybridization, i.e. the process of self-assembly of one, two or more complementary nucleic acid strands, has been studied for many years. The appearance of the nearest-neighbor model led to several theoretical and experimental papers on DNA thermodynamics that provide reasonably accurate thermodynamic information on nucleic acid duplexes and allow estimation of the melting temperature. Because there are no thermodynamic models specifically developed to predict the hybridization temperature of a probe used in a fluorescence in situ hybridization (FISH) procedure, the melting temperature is used as a reference, together with corrections for certain compounds that are used during FISH. However, the quantitative relation between melting and experimental FISH temperatures is poorly described. In this review, various models used to predict the melting temperature for rRNA targets, for DNA oligonucleotides and for nucleic acid mimics (chemically modified oligonucleotides), will be addressed in detail, together with a critical assessment of how this information should be used in FISH.
... Besides, the observed non-specific signal (0.14 -nF cm -2 ) at working temperature of 40°C, was below the lowest detection limit of the system. In particular, the hybridization was performed at very high stringency conditions; in other words, the presence of 30% formamide in the mobile phase, lowers the melting temperature of the complementary probes from 57.5°C to 35.9°C; since for every 1% of formamide reduces the melting temperature by 0.72°C [30,40,41], consequently, raising the working temperature to 40°C, makes the hybridization temperature to be slightly higher than the melting temperature. These results suggest that one could discriminately detect E. coli by injecting its whole genomic DNA in the presence of whole genomic DNA of L. reuteri at 40°C hybridization temperature, and 30% formamide in the mobile phase, without involving any DNA amplification step. ...
This paper presents a flow-based ultrasensitive capacitive biosensor for the detection of bacterial DNA. The used sensor chip consists of a gold electrode, insulated with a polytyramine layer and covalently tagged with a DNA capture probe. The hybridization of target DNA to the capture probe resulted in sensor response. The sensor response was linear vs. log concentration in the range 1.0 × 10⁻¹² to 1.0 × 10⁻⁷ moles per litre with a detection limit of 6.5 × 10⁻¹³ M. An alternative approach to bacterial DNA sample preparation for a flow-based analysis is also reported. The approach involved application of a thermostable ssDNA binding protein to prevent re-annealing of a heatdenatured target DNA prior to analysis. During analysis, formamide was integrated in the running buffer to denature ET SSB. E. coli DNA corresponding to 10 cells per millilitre of sample was detected in 15 min by this DNA-sensor. The sensor chip could be re-used up to 20 times with RSD of < 6%. The DNA-sensor chip was able to discriminate between Enterobacteriaceae (E. coli) and Lactobacillaceae (L. reuteri) DNAs. The reported DNA-sensor lays the groundwork for incorporating the method into an integrated system for in-field bacteria detection.
Non-coding RNAs are often neglected during genome annotation due to their difficulty of detection relative to protein coding genes. FindNonCoding takes a pattern mining approach to capture the essential sequence motifs and hairpin loops representing a non-coding RNA family and quickly identify matches in genomes. FindNonCoding was designed for ease of use and accurately finds non-coding RNAs with a low false discovery rate. Availability: FindNonCoding is implemented within the DECIPHER package (v2.19.3) for R (v4.1) available from Bioconductor. Pre-trained models of common non-coding RNA families are included for bacteria, archaea, and eukarya. Supplementary information: Supplementary data are available at Bioinformatics online.
In pathogen diagnostics, conventional culture-based assays remain the gold-standard; however, they are time-consuming, and shows the low positivity rate. Prior treatment with antibiotics is one of the major factors lowering the culture positivity rate. It is therefore important to evaluate the effects of prior antibiotic treatment on established detection methods and to develop sensitive and specific methods for detecting pathogens. Here, we report the detection of bacteria in samples containing antibiotics. Escherichia coli and Klebsiella pneumoniae were chosen as model and they were independently inoculated into culture flasks along with ceftriaxone (0.5× MIC, 1× MIC, 2× MIC). After 0, 2, 4, 6, 12, and 24 h, samples were collected from each flask and divided into two for evaluation using microarray or BacT/Alert culture-based systems. The newly designed probes showed a detection limit of 101 CFU for E. coli and 102 CFU for K. pneumoniae with high specificities. DNA microarray obtained true positive results at approximately 4 to 24 h after antimicrobial treatment, in which the culture-based method failed to detect the pathogenic bacteria. The DNA microarray-based assay could be useful for efficient detection of pathogenic bacteria in a clinical setting, allowing for appropriate administration of antibiotics in infected patients.
DNA detection is usually conducted under nondenaturing conditions to favor the formation of Watson-Crick base-paring interactions. However, although such a setting is excellent for distinguishing a single-nucleotide polymorphism (SNP) within short DNA sequences (15-25 nucleotides), it does not offer a good solution to SNP detection within much longer sequences. Here we report on a new detection method capable of detecting SNP in a DNA sequence containing 35-90 nucleotides. This is achieved through incorporating into the recognition DNA sequence a previously discovered DNA molecule that forms a stable G-quadruplex in the presence of 7 molar urea, a known condition for denaturing DNA structures. The systems are configured to produce both colorimetric and fluorescent signals upon target binding.
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Analysis of the increasing wealth of metagenomic data collected from diverse environments can lead to the discovery of novel branches on the tree of life. Here we analyse 5.2 Tb of metagenomic data collected globally to discover a novel bacterial phylum (‘Candidatus Kryptonia’) found exclusively in high-temperature pH-neutral geothermal springs. This lineage had remained hidden as a taxonomic ‘blind spot’ because of mismatches in the primers commonly used for ribosomal gene surveys. Genome reconstruction from metagenomic data combined with single-cell genomics results in several high-quality genomes representing four genera from the new phylum. Metabolic reconstruction indicates a heterotrophic lifestyle with conspicuous nutritional deficiencies, suggesting the need for metabolic complementarity with other microbes. Co-occurrence patterns identifies a number of putative partners, including an uncultured Armatimonadetes lineage. The discovery of Kryptonia within previously studied geothermal springs underscores the importance of globally sampled metagenomic data in detection of microbial novelty, and highlights the extraordinary diversity of microbial life still awaiting discovery.
Brucella, E. coli O157, Staphylococcus aureus, [3-Streptococcus, Erysipelothrix rhusiopathiae, Pseudomonas aeruginosa and Bovine viral diarrhea virus, Sheep pox virus, Goat pox virus, Bluetongue virus, foot and mouth disease virus are common pathogens in fur animal. An oligonucleotide microarray able to detect simultaneously the 6 bacteria and 5 viruses is reported in the present study. The assay was highly specific for detecting the 6 bacteria and 5 viruses in single or multiple infections and as few as 100 copies of specific pathogens target fragments were detected successfully. The 320 archived samples were tested by this assay and the results were 100% consistent with previous results based on conventional PCR and sequencing. The assay is appropriate for the screening of 11 pathogens infections in fur animal due to its high throughput, low-cost, high specificity and sensitivity.
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A 16S rRNA gene database ( addresses limitations of public repositories by providing chimera screening, standard alignment, and taxonomic classification using multiple published taxonomies. It was found that there is incongruent taxonomic nomenclature among curators even at the phylum level. Putative chimeras were identified in 3% of environmental sequences and in 0.2% of records derived from isolates. Environmental sequences were classified into 100 phylum-level lineages in the Archaea and Bacteria.
The hybridization of complementary strands of DNA is the underlying principle of all microarray-based techniques for the analysis of DNA variation. In this paper, we study how probe immobilization at surfaces, specifically probe density, influences the kinetics of target capture using surface plasmon resonance (SPR) spectroscopy, an in situ label-free optical method. Probe density is controlled by varying immobilization conditions, including solution ionic strength, interfacial electrostatic potential and whether duplex or single stranded oligonucleotides are used. Independent of which probe immobilization strategy is used, we find that DNA films of equal probe density exhibit reproducible efficiencies and reproducible kinetics for probe/target hybridization. However, hybridization depends strongly on probe density in both the efficiency of duplex formation and the kinetics of target capture. We propose that probe density effects may account for the observed variation in target-capture rates, which have previously been attributed to thermodynamic effects.
Based on comparative analyses of 16S and 23S ribosomal RNA sequences we have located sites specific for the alpha-, beta-, and gamma-subclasses of Proteobacteria. Short oligodeoxynucleotides complementary to these signature regions were evaluated as potential nucleic acid probes for the differentiation of the major subclasses of Proteobacteria. Hybridization conditions were optimized by the addition of formamide to the hybridization buffer and high stringency post-hybridization washing. Single-mismatch discrimination of probes was further improved by blocking nontarget probe binding sites with competitor oligonucleotides. Nonisotopic dot-blot hybridization to reference strains demonstrated the expected probe specificities, whole cell hybridization with fluorescent probe derivatives allowed the classification of individual microbial cells. The probes will be useful for determinative studies and for the in situ monitoring of population distribution and dynamics in microbial communities.
Solvent denaturation is developed along thermodynamic lines rather than from multiple-binding theory. Almost all the relations derivable from site-binding theory have their counterparts in the thermodynamic formulation showing that the details of binding models may be sufficient but are not necessary for the general description of solvent denaturation. Equations are derived for the effect of denaturant concentration on stability at constant temperature and on tm. It is recommended that the thermodynamic treatment be used instead of binding models unless stoichiometric interactions are demonstrable experimentally.