This section summarizes the steps for the generation of sites corresponding to RNA or modified histone and/or RNA PolII binding.

i) Probe-level normalization: This includes median scaling and quantile normalization 4142 of all PM and MM probes. The former is a linear operation, where fluorescence data from the arrays are scaled relative to the median intensity distributions of all arrays. The quantile normalization accounts for linear and non-linear effects.

ii) RNA profiling experiments: The pp signal intensity (SI) distribution is computed based on PM-MM intensity; regions of detected RNA referred to as transfrags (transcribed fragments) are then estimated against a baseline transcription signal derived from both positive and negative bacterial controls on the same microarray. For the data presented here, the intensity threshold for transcriptionally positive probes is set based on a 5 percent FPR 232425.

iii) ChIP on chip experiments: The probe-level signal enrichment (SE) profiles are generated based on a comparison of the signal intensity of the treatment and control probe pairs (Eqn. 10). Putative transcriptional regulatory elements (TREs) are generated per factor on a per time point basis using the Rank Statistics based site prediction algorithm 43. In general, the enriched fragments exhibit the following types of bias 31:

a) Canonical regulatory sites have a 5'end bias;

b) Non-canonical sites are distal to the annotated 5'ends223144;

S E p p = max ⁡ ( 1 , log ⁡ ( P M − M M ) T r e a t m e n t ) p p max ⁡ ( 1 , log ⁡ ( P M − M M ) C o n t r o l ) p p MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=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@7526@

This section provides a rationale for the choice of pair-wise conditions at which the cellular responses are profiled and analyzed.

Cellular response to an exogenous stimulus is not necessarily synchronized; however the reaction is on a very short time-scale – essentially continuous. In capturing events over time-points separated on the order of hours, a discrete time-differential response is generated by sampling a continuous time-signal. The sampling process is analogous to an accumulator system45 where the output state of the system (y) at any given time n is essentially a summation/accumulation of the response of all its states (x) up to the present state x[n] (Eqn. 11). Although the superimposed cellular states measured by the experiment cannot be de-convoluted, fundamentally because of the mentioned system characteristic, there is information loss when the states are profiled at large time intervals. Temporal resolution therefore is a critical component of the experimental design. The optimal resolution varies for different responding functional elements, conditions of cell growth and cell/tissue/organism type, with a likelihood of non-linear increments in the time-series. In this particular study, the choice of 0-2-8-32 hours represents the undifferentiated state, an early time point (2 hours), a midway time point (8 hours) and a moderately late time point (32 hours) based on the previously published profiles of HL60 differentiation 4647.

The associated property that needs to be appreciated is that the differential response follows a cascade connection model 45. Here the un-stimulated(baseline) state at the 0 hour serves as the original input to the system; the output(response) at the 2 hour serves as the input to the 8 hour with the output of the 32 hour (latest) being the overall output. Thus any measurement performed at any state other than the baseline has a memory of the system even prior to its current state.

y [ n ] = ∑ t = 0 n x [ t ] MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWG5bqEcqGGBbWwcqWGUbGBcqGGDbqxcqGH9aqpdaaeWbqaaiabdIha4jabcUfaBjabdsha0jabc2faDbWcbaGaemiDaqNaeyypa0JaeGimaadabaGaemOBa4ganiabggHiLdaaaa@3F88@

Δ y = y [ T ] − y [ T − n ] = ∑ t = 0 T x [ t ] − ∑ t = 0 n < T x [ t ] = ∑ t = 0 n < T x [ t ] + ∑ t = n < T T x [ t ] − ∑ t = 0 n < T x [ t ] Δ y = y [ T ] − y [ T − n ] = ∑ t = n < T T x [ t ] MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=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@ABD3@

These two properties, motivates the quantification of the temporal differential response as a pairwise time-forward system encompassing very specific reference and target time-points; Eqn. 12 generalizes this concept. A time-forward analysis implies that samples obtained at (T-n)^th and T^th(where n<T) time-points comprise the reference and target respectively. Here the reference precedes the target time-point, and may or may not represent the un-stimulated condition. While measurement of a response between two time-points might seem trivial, given the underlying accumulator and cascade connection properties, the choice of these time-points is critical; a pairwise combination at random, without appropriate de-convolution will result in erroneous interpretation of the underlying biology. Measurement of first order effects, which is the difference between two contiguous time-points profiled, is simpler to interpret than higher order effects, which include differential profiling across non-contiguous time-points potentially involving non-linear effects.

For the described time-series experiment, a measurement of an increased differential response from 0 to 8 hours, without knowledge of the 2 hour time-point, does not uniquely characterize the underlying differential mechanism. Any of the following are equally probable for a given locus:

i) Between 0 and 8 hours, there is a steady increase in response to ATRA stimulus;

ii) There is an initial decrease in the response between 0 and 2 hours, with a subsequent increase between 2 and 8 hours;

iii) There is a rapid increase in response between 0 and 2 hours with a significantly slower decrease in response between 2 and 8 hours;

Quantification of the first order response slopes significantly reduces the complexity of interpretation. All results presented here comprise the first order differential analysis. Although, gSAM is presented in a temporal context, it is equally applicable in a spatial one; this facilitates quantification of differential response across tissue-types derived from normal (reference) and diseased (target) sites, for example.

This section summarizes the logical segmentation of the enrichment regions which constitutes the input model for gSAM.

Based on published research 232425484950, presumed non-coding transcripts of yet unknown functionality are widespread in the genome. Thus the analysis of differential response should not be biased toward protein-coding genes but be based on a generalized framework. The generalization in gSAM arises primarily from the piece-wise modeling of the input, which simultaneously accommodates for responses from genic and inter-genic regions.

The gSAM piece-wise model introduced in Eqn. 8–9 is elaborated in Eqn. 13–14. Fragmented enrichment sites – histone/RNA PolII binding sites, transfrags of canonical and/or non-canonical origin, emanating from the coding and/or non-coding regions of the genome, independent of annotation, serve as the input. Eqn. 13 defines the probe-specific input, where the atomic entity is a probe-pair; the differential response is estimated individually for each pp encompassing an enrichment site (ε).

Input = {pp | pp ∈ ε}

I n p u t = ∑ g G e n i c g + ∑ i g I n t e r g e n i c i g G e n i c [ g ] = ∑ α p p α ; I n t e r g e n i c [ i g ] = ∑ β p p β ;   p p ∈ ε G e n i c = { E x o n , I n t r o n , U T R } I n t e r g e n i c = { F u n c t i o n a l C o m p l e x i t y , S e q u e n c e C o m p l e x i t y , ... } MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=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j7aIbqab0GaeyyeIuoakiabcUda7iabbccaGiabdchaWjabdchaWjabg2da9iab=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@F4C3@

Eqn. 14 defines a probe-set specific input; here, a probe-set (α/β), which is a cluster of probe-pairs, interrogates a sequence of nucleotides spanning ε. This suggests a heterogeneous model which at the most generalized level is a superposition of genic (g) and inter-genic (ig) states. The genic state can be further partitioned, based on annotations, into elements such as exons, introns and UTRs. Analysis can be performed independently on each element or on the cumulative elements. The flexibility of selective inclusion of genic elements enhances the localization and specificity of estimation of gene-expression effects in various pathways. For example, this enables the localization of activity in regulatory elements with a 3'UTR bias 51. A response aggregated over the entirety of the genic components would not elucidate this. The inter-genic state is a mixture model as well, encompassing variants in terms of functional and sequence complexity. It can be partitioned based on regulatory potential, for example presence of CpG islands associated with gene expression, regions of sequence conservation, or sequence motifs for transcription factor(s). The framework to selectively integrate elements in the model, solely driven by co-regulation effects, highlights the adaptability and power of gSAM.

This section details the probe-specific summarization of signal intensity/enrichment, for pair-wise sample (s).

Subsequent to the setup of the gSAM model, a probe-specific or probe-set specific log transformed SI or SE is computed per replicate(r ∈ s) and time-point (t ∈ s). This constitutes the input value in gSAM. For a probe-set based system, the transfrags/binding sites are used to define the domain over which the intensity/enrichment summary is computed. Frequently, the enrichment sites as determined in the reference and target pairs have non-identical spatial bounds. This might be because of biological reasons: the same locus might not be enriched (expressed) at two different time-points; alternatively, this might be due to edge artifacts in the definition of enrichment sites 43, or a combination of both. This incongruity of bounds requires a formal definition of domains based on the segmentation of enriched fragments that are unique to, versus common in both the reference and target samples. Once the domains are defined for a pair-wise sample, they are held constant across all replicates in the relevant reference and target. The following describes the definition of domains and estimation of domain-specific summaries:

i) The first step involves outlier removal. The low complexity filter (LCF) estimates the median absolute deviation (MAD) of the SE/SI of all pp belonging to a fragment. All fragments with a MAD value of zero are assumed to represent signal from low complexity repeat probes and are therefore eliminated. It is possible that this step introduces a false negative bias, by eliminating enriched fragments composed of a shorter run of probes; this is not detrimental, since the statistical confidence obtained from less than three contiguous probes(66 nucleotides) – is low (data not shown). Independent of LCF enriched fragments with a minimum of three probe-sets is retained. Since these filters address a tiling design and/or sequence specific properties, their effect is assumed to be equivalent for all replicates and is therefore assessed based on a single replicate. Additionally, the MAD serves as a metric of co-regulation. Based on the cumulative MAD distribution, as estimated across all enriched fragments, a user defined threshold can be determined and only fragments with less than the MAD cutoff can be retained for analysis. This filter is replicate quality dependent and should be used with caution, since it can introduce incongruity of bounds.

ii) In this step, the enriched fragments are ordered and labeled – independently in the reference and target – based on their genomic location. It is probable that the bounds of a single enrichment site in the reference might overlap with multiple sites in the target (or vice-versa). In this case, the single reference site (R) has n associated target labels, where n corresponds to the number of distinct target sites (T₁...T_n) it overlaps with. This labeling scheme identifies the membership of fragments and their relationship across the reference and target.

iii) This step entails identification of genomic segments with overlapping (including partial overlaps) spatial bounds of enrichment between the reference and target. A union of the bounds of the overlapping regions is created. This is referred to as the overlapping enrichment domain (OED) distribution for a given sample(s) (Eqn. 15). The OED therefore comprises a mixture of enriched segments: a common enrichment fraction between reference and target, and a unique fraction with evidence of enrichment in either the reference or target.

iv) In a given OED, the probes interrogating the intersecting and unique enrichment fractions comprise the FragmentDomainI (FDI) and FragmentDomainU (FDU), respectively (Eqn. 17–18).

v) This step localizes genomic segments with non-overlapping bounds of enrichment between the reference and target. By definition, these segments have no enriched probes in their counterpart samples and these are referred to as null probes. This is referred to as the non-overlapping enrichment domain (NOED) (Eqn. 18).

vi) Subsequent to the segmentation, there exist three distinct types of enrichment domains: FDI, FDU and NOED. Elements of each domain are denoted by start and stop coordinates to specify their bounds (Eqn. 15) and their reference and target specific labels. For a pair-wise analysis these domains are uniquely labeled and ordered based on their genomic location. A comparison of the labels across the domains – FDI and FDU – potentially identifies differential response from alternative isoforms and/or provides a tool to isolate differential signal from selective genic elements, for example UTRs. Since the enrichment sites are generated in the first-place via a multi-replicate analysis, the spatial bounds of the above domains are held constant across all replicates within a given reference or target.

OED_s = (Enrichment_R ⋃ Enrichment_T)_s where Enrichment_R ∩ Enrichment_T > 0

FDI_s = (Enrichment_R ⋂ Enrichment_T)_s where FDI_s ⊂ OED_s

FDU_s = OED_s - FDI_s

NOED_s = (Enrichment_R ∩ Enrichment_T = Φ)_s where Φ : nullset

vii) RNA transcription: The gSAM test-statistic operates on the log transformed probe-pair signal intensity (SI_pp). For a domain-specific input, a trimmed mean signal intensity(TRSI_drt) estimate (Eqn. 19) is generated for each of the domain elements on a per replicate(r), per time-point (t) basis. This estimate considers all probes belonging to an element in a given domain and uses an optimal trim factor of κ = 0.2.

viii) ChIP on chip: gSAM operates on the winsorized mean (robust estimator) (Eqn. 20) of the SE of all probe-pairs per element per labeled domain; these estimates are also computed per replicate and per time-point. In Eqn. 20, n refers to the number of probe-pairs in an element of a given domain and k refers to the number of smallest and largest observations that are replaced with (k+1)^th smallest and largest observations respectively.

ix) The null probes in NOED are not set to zero, but their true signal intensities considered. This obviates the missing data problem in gSAM.

TRSI_drt = TrimmedMean((log(SI₁...SI_pp)),0.2)_drt

x ¯ k = 1 ( n − 2 k ) ∑ i = k + 1 n − k x i x w = k x ( k + 1 ) + x ¯ k ( n − 2 k ) + k x ( n − k ) n MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=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@6802@

Fig. 1(A–B) presents the schematics of input bounds to gSAM. In this example, 0 and 2 hours constitute the reference and target, respectively. In panel A the probes and enrichment regions are represented by red and light blue bars, respectively; panel B demonstrates the domains defined in Eqn. 15–18; FDU: 1, 3, 5, 7; FDI: 2, 6, NOED: 4. Fig. 1C applies the domain definition to biological data, where the top five SE graphs (blue) are representative of five replicates for the reference and the bottom five graphs (yellow) are representative of the target; all graphs have been scaled identically. Additionally, there are three levels of annotation between the reference and target graphs; the annotations in blue and yellow are representative of enrichment fragments unique to the reference and target, respectively; the annotation in red is representative of the intersecting enrichment fragments. Peaks representative of the binding of putative TREs are evident upstream of and at the 5'end of the HIC gene as well as in the first few exons and in the introns. This data is visualized in the Integrated Genome Browser (IGB) 52.

The sample-size can be improved by considering probe-specific as opposed to domain-specific input values. This comes at the cost of computational time and potential increase in noise; it requires a post-differential analysis data clustering, followed by the application of a more conservative FDR-based significance threshold for downstream significance analysis. Alternatively, gaussian smoothing of the probe-level data can also enhance the SNR. Finally, it has been validated that the differential transcription/regulation outcome under the probe and domain-specific inputs are consistent with one another (R²~0.91). All data presented here, unless specifically noted is generated using domain-specific input. For either types of input, no probe-specific correction is required, since in a pair-wise analysis, signal from identical probes are summarized for both the reference and target samples.

This section summarizes the differential response of a pair-wise system. This is encapsulated by the four elements in Eqn. 21:

Γ = (d - statistic,δ,FDR,FC)

i) D-statistic: A variant on the t-statistic, it is a standardized differential change index. Fig. 2A presents a comparison of the t-statistic (green) and d-statistic (black) distributions. The additional variance term in the latter is responsible for the shrinkage in the tails, consequently boosting the peak centered about zero. Use of the t-statistic as an estimator of differential change potentially increases the FPR; the d-statistic essentially controls it, thereby optimizing the sensitivity and specificity for differential detection. In the original SAM publication 5, the core bootstrapping step to generate the null d-statistic distribution is carried out across untreated controls and samples treated with ionizing radiation. For ChIP on chip experiments, the labels on the treatment and control replicates are shuffled across the time-pairs in a balanced manner -with equal number of replicates and entries in the reference and target time-pairs – to generate a null (expected) distribution. For RNA transcription the signal intensity across the time-points are permuted to generate the null. Fig. 2B presents the observed (y-axis) versus expected (x-axis) d-statistic distribution.

ii) δ: The direction of differential change, often referred to as up or down regulation in the gene expression terminology, is also referred to as positive/negative/null differential shift in gSAM.

iii) FDR: Significance of the differential change is quantified via the FDR or q-value 1819. Analogous to the p-value, a measure of significance in terms of the FPR, the q-value is a measure of significance in terms of the FDR. Q-value is the minimal FDR at which a differential change is deemed significant.

iv) FC: Microarray-based FC is a commonly used discriminator for differential change. This essentially estimates true biological change over background by comparing signal intensity/enrichment between the reference and target pair.

Theoretically, any/combination of the output metrics (Γ) can be used for the segmentation of significant versus non-significant differential response. An early method suggested by Tusher et al 5 is that of using a delta (±Δ) envelope about a d-statistic of zero, to define a null domain – such that regions above and below the positive and negative Δ cutoff indicate up-regulation and down-regulation, respectively. This is elucidated in Fig. 2B, where the Δ envelope is shown in green. This is a symmetric approach about the d-statistic but does not guarantee symmetric FDR bounds for both up and down regulated regions. Researchers 53 have discussed the dependence of the outcome of SAM, specifically, the variation in the list of significant genes, as a function of the initial threshold. The Results discusses the inter-relationship amongst the output metrics, and contrasts the biases introduced by each in the context of transcriptome data.