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\begin{document}
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\title{Design Primers That Yield Group-Specific Signatures}
\author{Erik S. Wright \\
  University of Wisconsin \\
  Madison, WI}
\date{\today}
\maketitle

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\tableofcontents

%------------------------------------------------------------
\section{Introduction}
%------------------------------------------------------------

The \Rpackage{DECIPHER} function \Rfunction{DesignSignatures} was created to perform the most common primer design task:  to efficiently amplify a shared region of DNA that will produce maximal amplicon diversity.  This goal is independent of the method being used to differentiate amplicons, although some of the design details may depend on the technique being employed.  \Rfunction{DesignSignatures} supports three common methods for distinguishing amplicons:  sequencing, High Resolution Melting (HRM) analysis, and Fragment Length Polymorphism (FLP) analysis.  As a case study, this tutorial focuses on designing primers to differentiate SNP alleles using HRM analysis.  However, the methods described here can easily be adjusted to the other experimental techniques.

As input, we will use known sequence variants of the Isocitrate Dehydrogenase 2 (\href{https://en.wikipedia.org/wiki/IDH2}{\textit{IDH2}}) gene that have been implicated in human gliomas.  First, a database is constructed where the variants are identified by their unique name.  Next, this database is used to design primers that will yield maximal amplicon diversity.  The top scoring primers are further investigated to determine whether they can easily be distinguished experimentally.  Finally, the process is repeated using a restriction enzyme to further diversify the amplicons' signatures.  Note that much of the functionality described here is accessible via a web tool at \url{http://DECIPHER.cee.wisc.edu}.

%------------------------------------------------------------
\section{Getting Started}
%------------------------------------------------------------

\subsection{Startup}

To get started we need to load the \Rpackage{DECIPHER} package, which automatically loads several other required packages.

<<startup,results=hide>>=
library(DECIPHER)
@

Help for the \Rfunction{DesignSignatures} function can be accessed through:
\begin{Schunk}
\begin{Sinput}
> ? DesignSignatures
\end{Sinput}
\end{Schunk}

If this vignette was installed on your system then the code in each example can be obtained by:
\begin{Schunk}
\begin{Sinput}
> browseVignettes("DECIPHER")
\end{Sinput}
\end{Schunk}

\subsection{Creating a Sequence Database}

We begin with a set of \textit{IDH2} sequences in a FASTA file that is included as part of the \Rpackage{DECIPHER} package.  The file contains the common IDH2 allele, and three alleles with single nucleotide polymorphisms (SNPs).  Our goal is to design primers that can distinguish all four variants of the IDH2 gene.  If you wish to follow along with your own FASTA file of unaligned sequences, be sure to change the path names to those on your system by replacing all of the text inside quotes labeled ``$<<$path to ...$>>$'' with the actual path on your system.

<<expr1,eval=TRUE>>=
# specify the path to your sequence file:
fas <- "<<path to FASTA file>>"
# OR find the example sequence file used in this tutorial:
fas <- system.file("extdata", "IDH2.fas", package="DECIPHER")
@

Next, there are two options for importing the sequences into a database:  either save a database file or maintain the database in memory.  Here we will build the database in memory because it is a small set of sequences and we do not intend to use the database later:

<<expr2,eval=TRUE>>=
# specify a path for where to write the sequence database
dbConn <- "<<path to write sequence database>>"
# OR create the sequence database in memory
dbConn <- dbConnect(SQLite(), ":memory:")
N <- Seqs2DB(fas, "FASTA", dbConn, "")
N # number of sequences in the database
@

\subsection{Defining Groups}

At this point it is necessary to define groups of related sequences in the database we have just created.  Ideally, groups should designate the different organisms (i.e., strains or alleles) that we hope to distinguish.  In the example described here, we will define groups based on the allele's name, which was included in the description of each FASTA record that we imported.  In the simplest case, where each sequence is its own variant, we could also have simply assigned the groups numbers as described below.  In more complex cases, we could use the functions \Rfunction{IdentifyByRank}, \Rfunction{FormGroups}, or \Rfunction{IdClusters} to define groups.

<<expr3,eval=TRUE>>=
# if each sequence belongs to its own group,
# then identify the sequences with a number:
desc <- as.character(seq_len(N)) # N is the number of sequences
# OR get the FASTA record description:
desc <- dbGetQuery(dbConn, "select description from DNA")$description
# show the unique descriptors:
unique(desc)
@

Now that we have unique names for our four variants, we must add them to the database as the identifier of each sequence.

<<expr4,eval=TRUE>>=
Add2DB(data.frame(id=desc), dbConn)
@

%------------------------------------------------------------
\section{Designing primers with diverse signatures}
%------------------------------------------------------------

\subsection{Adjusting Input Parameters}

Before using our database to design primers, we must carefully consider the inputs that will be used.  These inputs can have a large impact on the outcome, and therefore should be tailored to the experimental goal.  Below are recommended inputs for sequencing, FLP, and HRM:

<<expr5a,eval=TRUE>>=
# Designing primers for sequencing experiments:
TYPE <- "sequence"
MIN_SIZE <- 300 # base pairs
MAX_SIZE <- 700
RESOLUTION <- 5 # k-mer signature
LEVELS <- 5 # max number of each k-mer
@

<<expr5b,eval=TRUE>>=
# Designing primers for community fingerprinting (FLP):
TYPE <- "length"
# it is important to have a width range of lengths
MIN_SIZE <- 200 # base pairs
MAX_SIZE <- 1400
# define bin boundaries for distinguishing length,
# the values below require high-resolution, but
# the bin boundaries can be redefined for lower
# resolution experiments such as gel runs
RESOLUTION <- c(seq(200, 700, 3),
                seq(705, 1000, 5),
                seq(1010, 1400, 10))
LEVELS <- 2 # presence/absence of the length
@

<<expr5c,eval=TRUE>>=
# Designing primers for high resolution melting (HRM):
TYPE <- "melt"
MIN_SIZE <- 55 # base pairs
MAX_SIZE <- 400
# the recommended values for resolution
RESOLUTION <- seq(80, 100, 0.25) # degrees Celsius
LEVELS <- 10
@

\subsection{Select Restriction Enzymes}

The following step is not applicable to sequencing experiments (i.e., the \code{TYPE} above is \code{"sequence"}), and is optional for other types of experiments.  If using HRM or FLP analysis to differentiate amplicon signatures, a digestion step following PCR amplification may generate fragments with widely different signatures.  This is especially useful when trying to distinguish a large number of different groups based on small variations.  Potential enzymes can be selected from the built-in \Robject{RESTRICTION_ENZYMES} dataset, which includes all of the standard enzymes sold by \href{https://www.neb.com/}{New England BioLabs}.

<<expr6,eval=TRUE>>=
ENZYMES <- NULL # required for sequencing
# OR select restriction enzymes to consider
data(RESTRICTION_ENZYMES)
# for this tutorial we will use the enzyme MslI
ENZYMES <- RESTRICTION_ENZYMES["MslI"]
ENZYMES
@

\subsection{Designing Primers}

Now we can design primers that target all of the groups and result in maximal amplicon diversity:

<<expr7,eval=FALSE>>=
primers <- DesignSignatures(dbConn,
                            type=TYPE,
                            minProductSize=MIN_SIZE,
                            maxProductSize=MAX_SIZE,
                            resolution=RESOLUTION,
                            levels=LEVELS,
                            enzymes=ENZYMES)
@

\begin{Schunk}
\begin{Sinput}
Tallying 8-mers for 4 groups:
  |======================================================================| 100%

Time difference of 0.49 secs

Designing primer sequences based on the group 'IDH2':
  |======================================================================| 100%

Time difference of 123.6 secs

Selecting the most common primer sequences:
  |======================================================================| 100%

Time difference of 15.89 secs

Determining PCR products from each group:
  |======================================================================| 100%

Time difference of 131.86 secs

Scoring primer pair combinations:
  |======================================================================| 100%

Time difference of 1.76 secs

Choosing optimal forward and reverse pairs:
  |======================================================================| 100%

Time difference of 2.27 secs

Finding the best restriction enzyme:
  |======================================================================| 100%

Time difference of 8.69 secs
\end{Sinput}
\end{Schunk}

The output \code{data.frame} is sorted by the sum of \code{"score"} and \code{"digest_score"}, because it is sometimes possible to obtain both signatures experimentally.  However, we can separately look at the top scoring primers with and without using restriction enzymes.

<<expr8,eval=FALSE>>=
primers[which.max(primers$score),] # best primers without digestion
@

\begin{Schunk}
\begin{Sinput}
       forward_primer       reverse_primer        score coverage products
70 TGGCTGGACCAAGCCCAT GCCTTGTACTGGTCGCCATG 0.049074....        1        4
   enzyme digest_score fragments
70   MslI            0         2
\end{Sinput}
\end{Schunk}

<<expr9,eval=FALSE>>=
primers[which.max(primers$digest_score),] # best primers with digestion
@

\begin{Schunk}
\begin{Sinput}
       forward_primer       reverse_primer        score coverage products
1 AGTCCCTGGCTGGACCAAG CTGTGGCCTTGTACTGGTCG 0.037037....        1        4
  enzyme digest_score fragments
1   MslI    0.1618056        13
\end{Sinput}
\end{Schunk}

The PCR products digested with \textit{MslI} are substantially high scoring (\code{digest_score}) than the undigested primers (\code{score}).

%------------------------------------------------------------
\section{Assessing the Results}
%------------------------------------------------------------

\subsection{View the Target Sites}

We can now look at the target sites of the top scoring primers and restriction enzyme.

<<expr9,eval=FALSE>>=
PSET <- 1 # examine the top scoring primer set overall

# select the first sequence from each group
dna <- SearchDB(dbConn,
                remove="all",
                nameBy="id",
                clause="where row_names =
                        (select min(row_names)
                         from DNA as S
                         where S.id = DNA.id)",
                verbose=FALSE)

f_primer <- DNAStringSet(primers$forward_primer[PSET])
r_primer <- DNAStringSet(primers$reverse_primer[PSET])
patterns <- c(f_primer,
              reverseComplement(r_primer),
              DNAStringSet(gsub("[^A-Z]", "", ENZYMES)))

BrowseSeqs(dna,
           patterns=patterns)
@

\begin{figure}
\begin{center}
\includegraphics{BrowseSignaturesOutput}
\caption{\label{f1} The forward (magenta) the reverse (green) primers situated around the SNP, with internal restriction site(s) (blue)}
\end{center}
\end{figure}

We can see in Figure \ref{f1} that the forward and reverse primers target sites on both sides of the SNP, which is located approximately in the center of the amplicon.  There are restriction sites next to the SNP, which will shorten the amplicons and further spread their melting curves.  Furthermore, the final allele has two adjacent restriction sites, whereas the others all have one.

\subsection{Plot the Signatures}

Next we will compare the signatures of the top scoring primers with and without digestion.  The simplest way to accomplish this is to use the \Rpackage{Biostrings} function \Rfunction{matchLRPatterns} to find the amplicons.  This requires a fair amount of code, much of which depends on the type of experiment (HRM, FLP, or sequencing):

<<expr10,eval=FALSE>>=
PSET <- which.max(primers$score) # top scoring without digestion

f_primer <- DNAString(primers$forward_primer[PSET])
r_primer <- DNAString(primers$reverse_primer[PSET])
r_primer <- reverseComplement(r_primer)

ids <- dbGetQuery(dbConn, "select distinct id from DNA")$id

if (TYPE=="sequence") {
    signatures <- matrix(0, nrow=4^RESOLUTION, ncol=length(ids))
} else if (TYPE=="melt") {
    signatures <- matrix(0, nrow=length(RESOLUTION), ncol=length(ids))
} else { # TYPE=="length"
    signatures <- matrix(0, nrow=length(RESOLUTION) - 1, ncol=length(ids))
}

for (i in seq_along(ids)) {
    dna <- SearchDB(dbConn, identifier=ids[i], remove="all", verbose=FALSE)
    amplicons <- matchLRPatterns(f_primer, r_primer,
                                 MAX_SIZE, unlist(dna),
                                 max.Lmismatch=1, max.Rmismatch=1,
                                 Lfixed="subject", Rfixed="subject")
    amplicons <- as(amplicons, "DNAStringSet")
    if (length(amplicons)==0)
        next
    
    if (TYPE=="sequence") {
        signature <- oligonucleotideFrequency(amplicons, RESOLUTION)
        signatures[, i] <- colMeans(signature)
    } else if (TYPE=="melt") {
        signature <- MeltDNA(amplicons, "melt curves", RESOLUTION)
        # weight melting curves by their amlicon's width
        signature <- t(signature)*width(amplicons)
        signatures[, i] <- colSums(signature)/sum(width(amplicons))
    } else { # TYPE=="length"
        signature <- .bincode(width(amplicons), RESOLUTION)
        for (j in signature[which(!is.na(signature))])
            signatures[j, i] <- signatures[j, i] + 1/length(signature)
    }
}

if (TYPE=="sequence") {
    d <- dist(t(signatures))
    h <- hclust(d)
    plot(h, labels=ids, cex=0.7, ann=FALSE)
} else if (TYPE=="melt") {
    matplot(RESOLUTION, signatures, type="l",
        xlab="Temperature (degrees Celsius)", ylab="Average Helicity")
} else { # TYPE=="length"
    plot(NA, xlim=c(1, length(ids)), ylim=range(RESOLUTION),
        xlab="Group Index", ylab="Amplicon Length", yaxs="i", xaxs="i")
    xaxs <- RESOLUTION[-1] - diff(RESOLUTION)/2 # average lengths
    for (i in seq_along(ids)) {
        w <- which(signatures[, i] > 0)
        if (length(w) > 0)
            segments(i, xaxs[w], i + 1, xaxs[w], lwd=2)
    }
}
@

\begin{figure}
\begin{center}
\includegraphics[width=.8\textwidth]{AmpliconSignatures}
\caption{\label{f2} Melting curves for the amplicons without digestion}
\end{center}
\end{figure}

Figure \ref{f2} shows that two alleles will be indistinguishable when using these primers because their melting curves are nearly overlapping.  We will now compare the result after using a restriction enzyme.  Note that this is only possible because we previously specified a restriction enzyme in the input to \Rfunction{DesignSignatures}.

<<expr11,eval=FALSE>>=
PSET <- which.max(primers$digest_score) # top scoring with digestion

f_primer <- DNAString(primers$forward_primer[PSET])
r_primer <- DNAString(primers$reverse_primer[PSET])
r_primer <- reverseComplement(r_primer)
enzyme <- RESTRICTION_ENZYMES[primers$enzyme[PSET]]

signatures[] <- 0 # initialize the results matrix used previously
for (i in seq_along(ids)) {
    dna <- SearchDB(dbConn, identifier=ids[i], remove="all", verbose=FALSE)
    amplicons <- matchLRPatterns(f_primer, r_primer,
                                 MAX_SIZE, unlist(dna),
                                 max.Lmismatch=1, max.Rmismatch=1,
                                 Lfixed="subject", Rfixed="subject")
    amplicons <- as(amplicons, "DNAStringSet")
    if (length(amplicons)==0)
        next
    digested <- DigestDNA(enzyme, amplicons, strand="top")
    digested <- unlist(digested) # convert to DNAStringSet
    
    if (TYPE=="melt") {
        signature <- MeltDNA(digested, "melt curves", RESOLUTION)
        # weight melting curves by their fragment's width
        signature <- t(signature)*width(digested)
        signatures[, i] <- colSums(signature)/sum(width(digested))
    } else { # TYPE=="length"
        signature <- .bincode(width(digested), RESOLUTION)
        for (j in signature[which(!is.na(signature))])
            signatures[j, i] <- signatures[j, i] + 1/length(signature)
    }
}

if (TYPE=="melt") {
    matplot(RESOLUTION, signatures, type="l",
        xlab="Temperature (degrees Celsius)", ylab="Average Helicity")
} else { # TYPE=="length"
    plot(NA, xlim=c(1, length(ids)), ylim=range(RESOLUTION),
        xlab="Group Index", ylab="Amplicon Length", yaxs="i", xaxs="i")
    xaxs <- RESOLUTION[-1] - diff(RESOLUTION)/2 # average lengths
    for (i in seq_along(ids)) {
        w <- which(signatures[, i] > 0)
        if (length(w) > 0)
            segments(i, xaxs[w], i + 1, xaxs[w], lwd=2)
    }
}
@

\begin{figure}
\begin{center}
\includegraphics[width=.8\textwidth]{DigestedSignatures}
\caption{\label{f3} Melt curves for the amplicons after digestion}
\end{center}
\end{figure}

Figure \ref{f3} shows that the two amplicons which had nearly identical melt curves can be easily distinguished after restriction digest.

\subsection{Finishing Up}

Finally, we can order the top scoring forward and reverse primers for synthesis and try them out in a PCR reaction!  The primers should be synthesized in the same orientation and sense that they are listed in the output (\code{primers}).

\section{Session Information}
All of the output in this vignette was produced under the following conditions:

<<sessinfo,echo=FALSE,results=tex>>=
zzz <- dbDisconnect(dbConn)
toLatex(sessionInfo(), locale=FALSE)
@

\end{document}
