Methods

3.5 Discussion

4.1.1 Methods

4.1.1.1 Data Preprocessing:

The microarray dataset measuring expression levels of nearly every gene in yeast through- out two cell cycles was obtained from the cited authors of Cho et al. (1998). These data were collected by Cho and colleagues from yeast cells synchronized using a cdc28TS ar- rest. RNA was extracted from the cells every 10 minutes for 170 minutes. Labeled target was synthesized from the extracted RNA and then hybridized to Affymetrix arrays. The resulting data processing was the same as in section 3.2.1. Briefly, any gene that did not show a sustained absolute expression level of at least 8 for 30 consecutive minutes was removed from the analysis. For each of the remaining 6174 gene vectors we divided each timepoint measurement by the median expression value across all time points for the gene.

Thelog2 of each ratio was then used to create the expression matrices that we used. Much of our analysis focuses on a set of 384 “cycling” genes in which Cho et al., 1998 identified

All Regulators ABF1 ABT1 ACA1 ADR1 ZAP1 ZMS1YRR1

0 5 10 15

−2 0 2

0 5 10 15

−2 0 2

0 5 10 15

−3

−2

−1 0 1

0 5 10 15

−2 0 2

0 5 10 15

−3

−2

−1 0 1

Expression Classes

Weights A)

ABF1

ABT1

ACA1

ADR1

ZAP1

ZMS1

EM1

EM2

EM3

EM4

EM5 YRR1

B)

EM4 EM3 EM1

EM2

EM5

Weights Matrix

Figure 4.1: The Artificial Neural Network Architecture (ANN) A) Shown is the sim- ple single layer network we trained to predict expression behavior based on the in vivo binding activity of 75% of the transcription regulators in yeast. A 204 dimension vec- tor containing the measured binding data from [Harbison et al., 2004] is used as the input vector. Given this binding vector the ANN was trained to predict during which of the five canonical cell cycle expression groups it is likely to be expressed. These expression classes were determined using EM MoDG (section 2.4.6) B) Matrix representation of the ANN.

Each matrix cell,W_c;r, represents the real-valued connection strength, or weight, between a regulator (r) and an expression class (c) and is shown in A as an edge between a regulator and an expression class. These weights represent the importance of a regulator’s binding activity or inactivity in the associated expression class

to show cell cycle dependent expression and which also passed our thresholds for being significantly expressed.

The protein:DNA interaction dataset (ChIP/chip) was collected from the cited authors of Harbison et al. (2004). No further processing was necessary with these data and the reported p-values were used for all of our analyses. Briefly, for each of the 204 assayed transcriptional regulators, Harbison and colleagues labeled targets synthesized from DNA that were enriched through chromatin immunoprecipitation (ChIP) using an affinity tag directed against the specific transcriptional regulator being measured. The targets synthe- sized from the ChIP enriched DNA was then co-hybridized along with targets synthesized and differently labeled from control DNA. Nearly every intergenic sequence in yeast was represented as a single feature on the microarrays. A binding ratio was then calculated based on the relative hybridization signal for targets synthesized from ChIP enrichment vs control DNA. Three biological replicates, starting from fresh yeast cultures each time, were performed. Based on an error model first described in [Hughes et al., 2000] and the three replicate binding ratios for each intergenic sequence, a p-value was calculated for each in- tergenic sequence. This p-value estimates the probability that a given transcription factor was bound to it.

4.1.1.2 Neural Network Implementation and Training:

Figure 4.1 illustrates the overall structure of the artificial neural networks (ANN) that we trained. We used backpropagation implemented by the UWBP package [Maclin et al., 1992]

to train a simple single layer network with no hidden units. The “cycling” genes from the yeast microarray dataset were clustered using an expectation maximization algorithm fit- ting the data to a mixture of diagonal covariance Gaussians probability distributions (EM MoDG, section 2.4.6). We then trained artificial neural networks to predict the cluster membership of each gene based on the input vector of the binding probabilities for the 204 measured regulators. A best average network was created by iteratively splitting the data into testing and training datasets in which the training dataset contained 80% of the data and the testing dataset contained the remaining 20%. For each dataset split, ten neural net- works were trained using different random seeds for each network. The network with the

best prediction accuracy on the testing dataset was then selected. This process was then repeated 40 times splitting the dataset into different testing and training datasets. The net- work weights from the resulting 40 selected “best” networks were then averaged together to create the average-of-bests neural network. We focused on this network for subsequent biological interpretation. The main goal was to identify regulatory connections between transcription factors and their target genes.

4.1.1.3 Consensus Site Enrichment Calculations:

In order to determine whether an expression cluster showed an enrichment in genes that contain a particular consensus site we calculated the likelihood of the observed enrich- ment, or depletion, being a chance occurrence according to a binomial model of occurrence probabilities. We count the observed number of genes that have at least one instance of a consensus sequence within the 1KB directly upstream of the coding sequence for all genes in an expression cluster versus the number of genes that would be expected by chance. As no known background sequence model is completely provably correct, for each consen- sus sequence we calculate the expected background frequency ( ^f) using a bootstrapping method. We randomly selected 1000 different sets of genes the same size as the cluster being compared (n). These randomly selected background sets are drawn from either the entire genome or from only the “cycling” genes which were used in training the ANNs.

The number of genes that contain at least a single instance of the consensus is counted for each randomly selected set. The average count across the 1000 samples is normalized and used as our estimate of the expected number of genes within a cluster that have a sin- gle occurrence within 1KB upstream (Ec). Since the chances of any given gene within a cluster having a given consensus sequence within the 1KB upstream can be assumed to be independent, we can estimate the probability of finding the observed number of counts (Oc) using a standard binomial distribution (4.1). If the site is enriched we estimate the p-value for the likelihood of finding at least the observed count, but if the site is depleted we calculate likelihood of finding at most the observed count (equation 4.2).

P (ijc; n) = n

i c

n _i

1 c

n _{n i}

(4.1)

p = 8<

: P_n

i=0cP (ijE_c; n) ifO_c > E_c 1 P_n

i=0cP (ijEc; n) if Oc Ec

(4.2)