The first decision to make when designing a sequencing experiment is which sequencing technology to use. Today there are two main varieties of next-generation sequencing: (1) sequencing by synthesis (SBS), employed by 454 sequencing http://www.454.com/; 454 Life Sciences/Roche, Branford, CT, USA) 77, Illumina (formerly called Solexa sequencing; http://www.illumina.com/; San Diego, CA, USA) 13, Helicos http://www.helicosbio.com/; Helicos Biosciences Corp., Cambridge, MA, USA) 7879 and the latest entrant into the market, small-molecule, real-time sequencing, or SMRT, sequencing introduced by Pacific BioSciences http://pacificbiosciences.com/; Menlo Park, CA, USA) 80; and (2) sequencing by ligation (SBL), used in SOLiD (Sequencing by Oligonucleotide Ligation and Detection; http://www.appliedbiosystems.com/; Applied Biosystems, Carlsbad, California, USA) 81 and Polonator sequencing http://www.polonator.org/; Dover Systems, Salem, New Hampshire, USA) 82. Table 1 shows the current efficiency statistics for each of these methods as provided by the product websites, but the sequencing depth, speed and accuracy of these technologies are constantly increasing. Most of these approaches can be implemented as paired-end runs, in which both ends of each clone are sequenced, increasing the amount of information gleaned per fragment, but single-end runs are sufficient for the short length of sRNA 838485.

The choice of sequencing method often comes down to cost, read length and sequencing depth. Because sRNA are in the range of approximately 18 to 30 nt and high sequencing depth is necessary to observe rare species, Illumina and SOLiD are currently the most appropriate methods for sRNA sequencing studies (Table 1). Illumina uses a four-color, reversible terminator sequencing-by-synthesis technology to sequence one base at a time. SOLiD uses 16 dinucleotide probes, each labeled with one of four fluorophores, to sequence by ligation two nucleotides of each clone at a time. This means that four dinucleotide pairs share the same label, making the analysis of SOLiD data a little more complicated. An algorithm generates the nucleotide sequence of a particular base n from this color space by examining the labels for the overlapping dinucleotides n - 1, n and n, n + 1 81. In this fashion, two different probes interrogate each base, which accounts for the reportedly high accuracy of this method. A single color call error, however, invalidates the sequence determination for all positions after this point. The read length and sequencing depth of Helicos sequencing make Helicos appropriate for sRNA sequencing as well, but this application has not been widely commercialized. For Helicos sequencing, cDNA molecules are polyadenylated and then annealed to immobilized oligo(dT) primers. Individual molecules are sequenced by sequential addition of each of the four nucleotides. One advantage of the Helicos method is that it allows for the sequencing of individual DNA molecules, eliminating the need for polymerase chain reaction (PCR) amplification and its inherent error rate. While Polonator sequencing allows for 26-nt reads at great sequencing depths, a 3- to 4-nt sequence gap remains in the middle of each read, which is not ideal for sRNA experiments.

Recent data have shown that the library preparation method, more than the sequencing technology, can significantly affect the diversity and abundance of the sRNA that are sequenced 86. For differential expression analyses comparing the relative abundance of the same sequence in different libraries, this is not a problem because all libraries will be affected equally by biases due to library preparation. Despite the digital nature of sequencing data, however, the relative levels of different sequences within the same library will be affected by these biases. Some sequences present in the biological samples may even be absent in the libraries because of preparation bias.

Illumina and SOLiD sRNA sequencing libraries are made by ligating RNA adapters of known sequence to the 5' and 3' ends of single molecules in a purified sRNA population. Alternatively, SOLiD sequencing can be performed by in vitro polyadenylation of the 3' end of the sRNA and addition of a 5' adapter 86. In either case, the adapter-ligated sequences are reverse-transcribed, amplified by PCR to increase the size of the library, applied to the platform and amplified again in situ to form millions of clusters of DNA of the same sequence. Then these clusters are sequenced in parallel.

Three steps in this process have the potential to influence the sequencing results: adapter ligation, reverse transcription and PCR amplification. Adapter ligation is the most important. The adapters have typically been ligated to each sRNA using T4 RNA ligase 1, which is capable of ligating two single-stranded oligoribonucleotides, where the acceptor nucleotide (≥3 nt long) has a free 3'-hydroxyl group and the donor (≥1 nt) has a 5'-monophosphate 87. The ligation efficiency of T4 RNA ligase 1 is very sensitive to nucleotide base composition at the ligation site and to sRNA modifications, however, and not all sRNA can act as donor substrates for the enzyme. Studies have suggested that the sequences of both the acceptor and the donor have an effect on ligation efficiency 868788899091, but the acceptor sequence is more important 87. The identity of at least the three 3'-most nucleotides of the acceptor affects ligation efficiency 8791, with a different base preference at each position (5'-nucleotide: A > G ≈ C > U; middle nucleotide: A > C > U > G; 3'-nucleotide: A > C > G > U when using a pUUUCp donor) 91. The donor sequence appears to be less important, but the bias for the 5' nucleotide is C > U ≥ A > G 8889.

Many sRNA are modified, and these modifications can also make them poor substrates for T4 RNA ligase 1. In particular, miRNA, siRNA, hc-siRNA, ta-siRNA and nat-siRNA in plants, siRNA and piRNA in insects and piRNA in animals are known to be 2'-O-methylated on the 3' end by the conserved methyltransferase HUA ENHANCER 1 (HEN1) (reviewed in 92), and this modification lowers ligation efficiency by T4 RNA ligase 1 by 30% to 72%, depending on assay conditions 939495. The 2'-O-methylation also introduces a sequence bias for the 3' nucleotide of the acceptor at the ligation site, such that the efficiency is G = C > A > U 95. Unlike previous studies, the study by Munafó et al. 95 did not find sequence bias at the acceptor site in unmethylated sRNA. Both of these issues are eliminated by using a truncated version of a closely related ligase, T4 RNA ligase 2, with a preadenylated 3'-RNA adapter 95, so this enzyme is being used more and more for library preparation. Illumina's first-generation sRNA library preparation kits used T4 RNA ligase 1 for the ligation of both the 5'- and 3'-adapters, but their Small RNA version 1.5 and TrueSeq™ RNA Sample Preparation kits use the truncated form of T4 RNA ligase 2 for the ligation of the 3'-adapter. T4 RNA ligase 1 is still required for the ligation of the 5'-adapter, however, because of the need by the truncated T4 RNA ligase 2 for a preadenylated donor, which in this case is the sample itself. Thus, sequence bias is eliminated in only one of the two ligation reactions. To test whether an sRNA is 3'-modified or to specifically clone 3'-modified products, sRNA can be oxidized with NaIO₄ followed by β-eliminated at an alkaline pH. This treatment removes the 3'-most nucleotide from all sequences with 2',3'-OH groups (that is, unmodified sRNA), but not from modified sRNA, leaving a 3'-phosphate 969798, which is not a substrate for T4 RNA ligase 1 or 2.

Because T4 RNA ligase 1 requires a 5'-monophosphate on the donor sequence, sRNA lacking this group are absent from standard libraries. A large population of 5'-ligation-resistant secondary siRNA was found in C. elegans 5152. These secondary siRNA are involved in the perpetuation of RNA interference (RNAi) and have a 5'-triphosphate, which is not a substrate for T4 RNA ligase 1. sRNA with 5'-diphosphate or 5'-triphosphate have also been found in the single-celled eukaryote Entamoeba histolytica 99. The 5'-caps similarly block ligation by the enzyme and have been seen on 18- to 25-nt sRNA associated with the human hepatitis delta virus and on some RNA under 200 nt in human cells 100101. Both of these ligase-resistant 5'-modifications can be removed by pretreatment with tobacco acid pyrophosphatase before ligation of a 5'-adapter 101. Alternatively, a 5'-adapter-independent method can be used 5199100; however, this approach is not compatible with Illumina and SOLiD sequencing technologies. The importance of considering such a method, however, is highlighted by a study by Pak et al. 51, who studied RNAi-induced C. elegans that used a 5'-adapter-independent library preparation protocol. In contrast to work that did not account for the possibility of 5'-ligation-resistant sRNA, which suggested that miRNA vastly outnumbered siRNA, they demonstrated that the two classes are actually found in similar degrees of abundance 51.

Because sRNA acts as the donor during the 5'-adapter ligation and as the acceptor during the 3'-adapter ligation, the best solution for avoiding this bias would be to use a ligation-independent library preparation. Such a method has been applied to the generation of Illumina sequencing libraries 10 and would be applicable to SOLiD sequencing as well. This method involves using Escherichia coli poly(A) polymerase (PAP) to polyadenylate the RNA molecules and then performing a reverse transcription reaction with an oligo(dT) primer having both 5'- and 3'-adapter sequences at the 5' end of the primer. The products are then circularized and cut with a restriction enzyme that cleaves between the 5'- and 3'-adapters, yielding the typical linear read of 5'-adapter, clone and 3'-adapter. Ligation-independent methods that rely on 3'-polyadenylation of the sRNA population, such as this technique and the one used for Helicos sequencing, may be better than ligation-dependent methods, but they are still not perfect. PAP has a bias for the 3'-nucleotide A = G > C > U, but the efficiencies of the different bases are within twofold of each other 95. As seen with T4 RNA ligase 1, 2'-O-methylation greatly reduces the efficiency of PAP by up to 10-fold, with the sequence bias altered to 2'-O-meG > 2'-O-meA = 2'-O-meU > 2'-O-meC 939495.

While adapter ligation is probably the largest potential source of bias, bias can also be introduced during reverse transcription and amplification. The 2'-O-methylation of sRNA reduces the efficiency of reverse transcription as well as adapter ligation 95102. The step of PCR amplification during library preparation can be a problem with sequences that have very low or very high guanine-cytosine (GC) content, reducing the likelihood that these sequences will be represented in the final population. Two techniques that do not require the initial library amplification and are compatible with Illumina sequencing have been used for DNA-seq and RNA-seq, and both methods provide a less biased library preparation for low GC sequences 103104. These approaches remain to be tried with sRNA libraries and still require the standard amplification within the Illumina flow cell to generate clusters of identical sequences. The Helicos system will provide a truly amplification-independent sequencing protocol because it does not require PCR in the library preparation and sequences only single molecules, not clusters of molecules.

High-throughput sequencing can be costly when loading only one sample per sequencing lane. To help improve cost efficiency, users can multiplex two or more samples in a single lane using bar coding 105106107108109110111112113. As the number of reads per run has increased (Table 1), sufficiently deep sequencing can be achieved even when running multiple samples in the same lane, with the number of multiplexed samples depending on the desired depth. Multiplexing either incorporates a unique sequence called a bar code into the 5'- or 3'-adapter of each library to be run in the same lane or adds the bar code during a PCR step after adapter ligation, an approach that minimizes ligation bias. All of the reads in a lane can be sorted into their respective libraries using their bar codes after sequencing has taken place. Because of the inherent error rate of sequencing, it is recommended that bar codes be long enough so that each pair varies by multiple substitutions, thereby reducing the likelihood that sequencing errors in the bar code will result in assigning reads to the wrong sample 107112. In particular, Illumina sequencing has a tendency to erroneously incorporate adenine more than the other bases 114, which should also be taken into account when designing your own bar codes. Multiplexing library preparation kits are now available for both Illumina and SOLiD. In both cases, the bar code is located within one of the adapters and separated by multiple bases from the ligation site, reducing the likelihood that the bar code will introduce any ligation bias. Helicos is also compatible with bar coding, though it requires a ligation step not in the original protocol. The one downside of using a bar code is that it may reduce the maximum length of the sRNA that can be sequenced, trimmed and assigned to a sample. However, the latest multiplexing systems for the Illumina and SOLiD machines incorporate the index into the 3' PCR primer and perform a second reaction specifically to sequence the bar code. This type of approach has numerous advantages, such as reducing or eliminating ligation bias, ensuring long reads across the sRNA and enabling multiplexing that reduces sequencing costs.

Several reports have used technical replicates, that is, the same library sequenced multiple times or independent libraries constructed from the same biological sample, to demonstrate the high reliability of Illumina 86115116117118 and SOLiD sequencing 86. Similar results are possible for biological replicates 115118119. Because of the high cost of deep sequencing, most experiments published to date have not used biological replicates, even though they can increase the statistical significance and reduce both false-positive and false-negative rates. With biological replicates, the significance analysis of microarrays (SAM) 115 and the Bioconductor program edgeR 118120 can be applied to differential expression analysis of sequencing data, as we discuss later in the section "Differential expression analysis". Standards for deep sequencing experiments remain to be agreed upon, but as sequencing costs go down, sequencing depths further increase and multiplexing becomes more widely adopted, the requirement for biological replicates in differential expression experiments will surely follow.

Once sRNA data have been preprocessed, it is common for researchers to verify the quality of the data before moving on to normalization and analysis. There are several ways to perform quality control on sRNA data. Each base of every Illumina sequenced read or each color call of every SOLiD sequenced read is given a quality score, which can be used to calculate an average error rate for each cycle of a sequencing run. While it is normal for the error rate to increase toward the end of a run, for a good run the average error rate throughout should be relatively similar and close to the expected rate for the technology. Creating size distribution graphs should reveal peaks of sequences corresponding to the dominant size classes. For example, in Arabidopsis, the dominant classes are 20 or 21 nt and 23 or 24 nt, which correspond to miRNA and hc-siRNA, respectively. Libraries made from high-quality RNA should have low levels of sRNA corresponding to highly abundant mRNA. Libraries made from green tissues of plants, for instance, should have low levels of sRNA for genes encoding the highly expressed photosynthetic proteins. Computing the levels of other RNA types, such as tRNA or rRNA, among different libraries in a data set may or may not be informative, as the relative level of tRNA can vary significantly. For example, from 51 public Arabidopsis sRNA libraries in our databases, tRNA represented from 4% to 40% of the total number of sequenced reads. Ideally, the level of nongenomic reads should also be similar between libraries to be compared.

The more than 20-year history of microarray experiments provides a good starting point for considering how to normalize next-generation sequencing data. While there are many technology-specific issues involved when handling raw microarray and sequencing data, the basic problem is still the same: how to convert raw data, in the form of image files, to numerical data, such that any expression differences between samples are due solely to biological variation, not to technical, experimentally introduced variation. In the case of microarrays, technical bias can be introduced during sample preparation (differences in RNA isolation, quality and amplification; target labeling; total amount of target; dye biases for spotted arrays; and so on), array manufacture (array surface chemistry, sequences used for the probes, locations of the probes within a gene, array printing for spotted arrays, scratches and so on) and array processing (hybridization conditions and scanning intensity and settings). Failing to properly remove these biases can lead to false conclusions when making comparisons within a single array or between two different arrays. Normalization attempts to remove technical bias without introducing noise.

Normalization requires two basic decisions: (1) which subset of genes (also called the normalization baseline or reference population) to use to determine the normalization factor and (2) which normalization method to employ 130. These two choices are independent, such that a given reference population can be used in combination with any of the different normalization methods. A good reference population is invariant in expression, meaning that the true expression levels are constant across biological treatments and span the entire expression range. Reference populations that have been used previously for microarray normalization include housekeeping genes 131, spike-ins of nonendogenous RNA or genomic DNA, an algorithmically identified set of invariant genes 29132133134135 and all genes 130. Housekeeping genes are typically used for normalizing northern blot analysis results and quantitative reverse transcription PCR (qRT-PCR) because of their supposedly constant expression level, but it has become ever more apparent that even these genes can vary in their expression 136137138139140141. Commercial arrays typically have probes for nonendogenous genes, and in vitro transcribed RNA from these genes can be used as spike-ins at various steps in the target preparation and array hybridization procedure. The point chosen will determine how much and what kind of technical variation will be corrected by the normalization. Genomic DNA has also been used for normalization because the concentration of a control sequence is readily known. In the absence of knowledge regarding invariant genes, algorithms have been developed that identify a set of invariant genes from the set of arrays themselves. These genes are discovered by comparing expression-ranked lists of all of the probes in each array to find the most rank-invariant genes 29132133134135. This method is advantageous because it makes no assumptions about the expression patterns of individual genes. Normalization is generally improved by increasing the size of the reference population, which has been a disadvantage of spike-ins because only a few sequences are typically added. As an alternative to using a subset of probes for normalization, all probes can be used. This type of normalization assumes that because the RNA content is constant between treatments and most of the genes do not change in expression between treatments, the median or mean expression across all of the genes is unchanged.

There are many different algorithms for normalizing microarray data on the basis of the chosen reference population, but they fall into four main categories: linear scaling (as in the MAS5.0 algorithm), nonlinear scaling (as in locally weighted linear regression (LOWESS), cyclic LOWESS), quantile normalization (as in robust multi-array average (RMA), GC-RMA (a variation of RMA), dChip) and variance stabilization normalization (VSN), two of which (linear and nonlinear scaling) have been applied to sRNA sequencing data as we will see later in the section "Normalization methods". Linear scaling uses the reference population to determine a single factor by which the population varies when compared to a set target, such as a predetermined mean or median expression value. The expression of each probe or gene on the array is multiplied by this factor to achieve the normalized expression value. The advantage of using linear scaling is that the scaling factor is determined independently for each sample, unlike the other approaches, which normalize the data with reference to the other arrays in the data set. Linear normalization of microarray data has been largely abandoned, though, because expression values are not necessarily linear, particularly at the extremes 142. In attempt to overcome this problem, nonlinear scaling methods have been developed that, for a given pair of arrays or for an individual array and the mean or median data derived from all of the arrays in question, first fit a curve to the expression values of the reference using LOWESS or splines and then normalize the data such that the average fold change when comparing any two arrays is 1 (that is, no change) across the expression range. Thus, a scaling factor is determined independently for small windows across the entire expression range. Quantile normalization uses a nonscaling approach that assumes that most genes are not differentially expressed and that the true expression distribution is similar between different samples 142. The average distribution of the reference population is determined from all of the arrays in question, and then each array is normalized to have this same distribution. Variance stabilization normalization likewise assumes that most genes are not differentially expressed. Using a generalized logarithmic transformation, VSN methods fit the data such that the variance is equal across the expression range, allowing for greater precision for low expression values, which are generally subject to greater variance 143144145. Many studies have been performed comparing these different normalization methods, but beyond the opinion that linear scaling is not as ideal because of the analog nature of microarray data, the general conclusion is that there is no single "best" normalization method 31131142146147148149. Even though the data are digital, the same is likely to be true in the case of RNA sequencing experiments as discussed below in the section "Normalization methods".

There are a number of nonbiological sources of variation that can add noise to sRNA sequencing experiments. RNA quality is a major issue because low quality can result in an increase in sequencing of degradation products. As discussed above in the section "Library preparation and inherent biases", the choice of library preparation methods has a significant impact on the makeup of the library because of biases in ligation, reverse transcription, PCR amplification or polyadenylation efficiency. While not currently done, it may be possible to develop methods to correct for these biases. One issue that can be dealt with to some extent by normalization is differences in sequencing depth between libraries. More total reads equate to a higher likelihood of any particular sequence's appearing in a library, and standardizing the total number of reads per library or sequence run is not a realizable goal. One way to reduce the impact of this kind of variation (or other technical variations encountered as a result of the sequencing procedure itself) is to sequence all of the libraries to be compared at the same time or to use multiplexing to run the samples in the same lane or at least on the same flow cell.

Microarray and sequencing experiments start with equal amounts of total RNA when constructing a library or a labeled target. When performing differential expression analyses using such data, an inherent assumption is that a set amount of starting RNA comes from the same number of cells in each sample. It is well known, though, that transcription rates change depending on the stage of growth, development or environment of the cell, tissue, organ or organism. Thus, this assumption can result in over- or underestimation of differences between samples. This issue is probably most significant when comparing different stages of growth or development. Studies of the per-cell abundance of sRNA in different experimental conditions have not been performed, but such studies might help improve our estimates of differential expression as well as our knowledge of the biology of sRNA.

Three reference populations for normalization have been used with sRNA sequencing experiments: spike-ins, all "good reads" and all reads. As discussed earlier in the section "Lessons from microarrays", housekeeping genes have been shown to be nonideal for normalizing microarray data because of their variable expression 136137138139140141. In the case of sRNA, few "housekeeping" sequences have been delineated. The identification of rank-invariant sRNA sequences would help to establish a statistically significant baseline for normalization, but this has not been done to date. RNA spike-ins of foreign sequences have proven useful, however, to account for multiple sources of variation in sequencing experiments, particularly when the spike-in RNA have been added to the total sample RNA prior to library preparation 115. Fahlgren et al. 115 added multiple spike-ins at different concentrations to cover a range of abundances. Some sequences were more likely sequenced than others even when added at the same concentration, possibly as a result of sequence biases, so it is probably best to include multiple spike-ins of varying base compositions for each of the concentrations to be tested. Spike-ins also have proven useful in demonstrating the accuracy of some downstream data analyses 126150.

Many other studies have used all reads or, more often, all "good reads" for the normalization baseline, which is comparable to using all probe sets when normalizing microarrays. Good reads are defined as all tags that map to a reference genome, except those associated with tRNA, rRNA, snRNA, snoRNA or other structural RNA 124151. This approach helps to mitigate the effects of bad sequencing runs and contamination with foreign RNA, both of which result in higher numbers of sequences that do not map to the reference genome. Experiments focusing on a specific RNA type, such as miRNA, may choose to use only these sequences for the normalization baseline 152153.

In sRNA sequencing experiments, the majority of distinct reads will be sequenced in only one copy and often will be observed in only a single library. Because these sequences can act as outliers, it is sometimes best to eliminate them from the normalization baseline as discussed in the next section.

Once a normalization baseline has been chosen, there is still the decision which normalization method to use. Existing methods can be classified as either linear or nonlinear. Linear total count scaling is perhaps the simplest of all existing methods. It involves using the summation of all reads belonging to the normalization baseline as a "library size," choosing an appropriate "control" library size (either the actual size of a control library or the average size of all libraries in the experiment) and then multiplying the abundance of each individual read by the normalization value (control divided by library size). This method has been widely applied to different types of data, including sRNA Illumina data, mRNA Illumina data 154 and PARE Illumina data 151. Linear total count scaling has been shown to be no better than the analog data of microarray experiments for detecting differentially expressed genes 154. A slight variation of this method is to use the number of distinct sequences, rather than the total abundance, as the size of each library 155.

Total count scaling is computationally simple but, for some experiments, biologically naïve. Consider this hypothetical scenario in which total count scaling fails: If sample A contains all reads from sample B, as well as a novel set of reads equal in size to the first set, total count scaling will result in underrepresenting reads from sample A and overrepresenting reads from sample B 120. Total count scaling is particularly inefficient in the context of sRNA sequencing because it ignores the number of distinct reads within each sample. One proposed method that incorporates this number is quantile-based normalization, which uses the upper quartile of expressed genes (after excluding genes not expressed in any library) as a linear scaling factor 154. (Note that this differs from quantile normalization, which scales data within each quantile separately.) The quantile-based method has been shown to yield better concordance with qRT-PCR results (with a bias near zero) than linear total count scaling, making quantile-based normalization better at detecting differentially expressed genes 154. This quantile-based method has been used with RNA-seq data, where all reads per gene have been grouped together to yield one total per gene, but it has not been used with sRNA sequencing data. Our attempts to apply this approach to sRNA sequencing data (about 0.5 to 2 million distinct reads per library) found that the 75th-percentile sRNA were found at only one or two copies per library. Even grouping sRNA by gene or by 500-bp sliding window found very low copy numbers at this percentile. As a result, this method may need further modification to be applied to sRNA data, such as not considering distinct reads sequenced only one time or raising the percentile used for the normalization.

Even quantile-based normalization has its limitations, because it assumes a similar distribution of abundances per distinct read among all libraries being normalized. It is not yet known how accurate next-generation sequencing is with regard to read distribution. It is possible, however, to properly normalize libraries that may not have similar abundance distributions by using linear regression 123. This method involves performing linear regression by comparing the abundance of each baseline element between two samples or between one sample and the mean or median of all samples, and then using the slope of the regression line as a linear scaling factor.

Because the total RNA output of each sample is unknown, linear total count scaling and other naïve methods can lead to underrepresentation of counts from high-output samples. Highly expressed genes (or other genomic elements) can sometimes take up too much "sequencing real estate" in a sample. The number of reads that map to a particular gene depends not only on gene length and expression level but also on the composition of the RNA population being sampled 120. In some studies, it is assumed that most genes are not differentially expressed and thus that their true relative expression levels should be pretty similar. The trimmed mean of M value (TMM) normalization method exploits this fact by calculating, for each baseline element, the log expression ratio (M values) of the experimental sample to a control sample (or the mean or median of all samples) and using their trimmed mean as a linear scaling factor. Although Robinson and Oshlack 120 applied this method to genes using RNA-seq data, it could be applied to individual sRNA sequence counts as well.

All of the normalization methods discussed thus far are linear scaling methods, and they suffer from an inherent flaw in assuming that the level of noise in an sRNA library is directly proportional to the size of the library. A two-step nonlinear regression method can be used to eliminate nonlinear noise without making any assumptions about its shape 156. A previously published implementation of this method is shown in Figure 5. This method uses the number of sequences mapping to each genomic window as well as the averages of these counts across the set of libraries. While this particular normalization method assumes that the data include only uniquely mapping sequences, multireads could be included by using probability mapping (described above in the section "Preprocessing of sRNA data") to estimate the total number of transcripts originating from within each genomic window. The first step is to regress observed counts of differences (control minus sample) on the mean to estimate fitted values and then subtract these fitted values from the observed difference counts. This results in each observed count's being transformed into a mean normalized difference. The second step is to estimate the moving mean absolute deviation (by regressing the absolute value of mean normalized differences on absolute mean counts) and then divide the mean normalized difference counts by the estimated mean of absolute deviation.

A summary of the normalization methods discussed here is given in Table 2. Because modern computational standards make most of the more advanced normalization methods relatively trivial, especially when compared to the task of genome mapping, we recommend that researchers not hesitate to use the more sophisticated approaches described herein. In particular, the methods implemented by Robinson et al. 120 (TMM) and Taslim et al. 156 (two-step nonlinear regression) seem to account for many flaws inherent in total count linear scaling, which has been the predominant normalization method of choice. A study comparing these two methods, as well as others, with each other would help to provide a much-needed "gold standard" for normalizing sRNA data. We also recommend using absolute counts, rather than log ratios, when performing normalization, as log ratios fail to account for the vast differences in magnitude evident in many sRNA data sets but absent from microarray experiments.