Learning probabilistic networks of condition-specific response:

Digging deep in yeast stationary phase

Sushmita Roy∗, Terran Lane∗, and Margaret Werner-Washburne+

∗Department of Computer Science, University of New Mexico+Department of Biology, University of New Mexico

Abstract

Condition-specific networks are functional networks of genes describing molecular behavior un-

der different conditions such as environmental stresses, cell types, or tissues. These networks

frequently comprise parts that are unique to each condition, and parts that are shared among

related conditions. Existing approaches for learning condition-specific networks typically iden-

tify either only differences or similarities across conditions. Most of these approaches first learn

networks per condition independently, and then identify similarities and differences in a post-

learning step. Such approaches have not exploited the shared information across conditions

during network learning.

We describe an approach for learning condition-specific networks that simultaneously identi-

fies the shared and unique subgraphs during network learning, rather than as a post-processing

step. Our approach learns networks across condition sets, shares data from conditions, and leads

to high quality networks capturing biologically meaningful information.

On simulated data from two conditions, our approach outperformed an existing approach

of learning networks per condition independently, especially on small training datasets. We

further applied our approach to microarray data from two yeast stationary-phase cell popu-

lations, quiescent and non-quiescent. Our approach identified several functional interactions

that suggest respiration-related processes are shared across the two conditions. We also iden-

tified interactions specific to each population including regulation of epigenetic expression in

the quiescent population, consistent with known characteristics of these cells. Finally, we found

several high confidence cases of combinatorial interaction among single gene deletions that can

be experimentally tested using double gene knock-outs, and contribute to our understanding of

differentiated cell populations in yeast stationary phase.

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1 Introduction

Although the DNA for an organism is relatively constant, every organism on earth has the po-

tential to respond to different environmental stimuli or to differentiate into distinct cell-types or

tissues. Different environmental conditions, cell-types or tissues can be considered as different in-

stantiations of a global variable, the condition variable, which induces condition-specific responses.

These condition-specific responses typically require global changes at the transcript, protein and

metabolic levels and are of interest as they provide insight into how organisms function at a systems

level. Condition-specific networks describe functional interactions among genes and other macro-

molecules under different conditions, providing a systemic view of condition-specific behavior in

organisms.

Analysis of condition-specific responses has been one of the principal goals of molecular biology,

and several approaches have been developed to capture condition-specific responses at different

levels of granularity. The most common approach is the identification of differentially expressed

genes in a condition of interest using genome-wide measurements of gene, and often protein expres-

sion [20]. More recent approaches are based on bi-clustering, which cluster genes and conditions

simultaneously [5,7,9,29], and identify sets of genes that are co-regulated in sets of conditions. How-

ever, these approaches do not provide fine-grained interaction structure that explains the condition-

specific response of genes. More advanced approaches additionally identify transcription modules

(set of transcription factors regulating a set of target genes) that are co-expressed in a condition-

specific manner [11,13,26,31], but these too do not provide detailed interaction information among

genes for each condition.

In this paper, we describe a novel approach, Network Inference with Pooling Data (NIPD), for

condition-specific response analysis that emphasizes the fine-grained interaction patterns among

genes under different conditions. The main conceptual contribution of our approach is to learn

networks for any subset of conditions. This subsumes existing approaches that find either only

patterns that are specific to each condition, or only patterns that are shared across conditions.

To make this clear, let us consider a simple example of two environmental starvation conditions:

Carbon and Nitrogen starvation. Using our approach we can simultaneously find patterns that are

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specific only to Carbon starvation, only to Nitrogen starvation, and those that are shared across

these two conditions. From the methodological stand-point our work is similar to Bayesian multi-

nets [10], which we extend by allowing data to be pooled across conditions and learning networks

for any subset of conditions.

NIPD is based on the framework of probabilistic graphical models (PGMs), where edges rep-

resent pairwise and higher-order statistical dependencies among genes. Similar to existing PGM

learning algorithms, NIPD infers networks by iteratively scoring candidate networks and selecting

the network with the highest score [12]. However, NIPD uses a novel score that evaluates candidate

networks with respect to data from any subset of conditions, pooling data for subsets with more

than one conditions. This subset score and search strategy of NIPD incorporates and exploits the

shared information across the conditions during structure learning, rather than as a post-processing

step. As a result, we are able to identify sub-networks not only specific to one condition, but to mul-

tiple conditions simultaneously, which allows us to build a more holistic picture of condition-specific

response.

The data pooling aspect of NIPD makes more data available for estimating parameters for

higher-order interactions, i.e., interactions among more than two genes. This enables NIPD to

robustly estimate higher-order interactions, which are more difficult to estimate due to the high

number of parameters relative to pairwise dependencies.

By formulating NIPD in the framework of PGMs we have additional benefits: (a) PGMs are

generative models of the data, providing a system-wide description of the condition-specific behavior

as a probabilistic network, (b) the probabilistic component naturally handles noise in the data,

(c) the graph structure captures condition-specific behavior at the level of gene-gene interactions,

rather than coarse clusters of genes, (d) the PGM framework can be easily extended to more

complex situations where the condition variable itself may be a random variable that must be

inferred during network learning. We implement NIPD with undirected, probabilistic graphical

models [14]. However, the NIPD framework is applicable to directed graphs as well.

We are not the first to propose networks for capturing condition-specific behavior [24, 34].

Several network-based approaches have been developed for capturing condition-specific behavior

3

such as disease-specific subgraphs in cancer [8], stress response networks in yeast [21], or networks

across different species [4,28]. However, these approaches are not probabilistic in nature, often rely

on the network being known, and are restricted to pairwise co-expression relationships rather than

general statistical dependencies. Other approaches such as differential dependency networks [34],

and mixture of subgraphs [24], construct probabilistic models, but focus on differences rather

than both differences and similarities. The majority of these approaches infer a network for each

condition separately, and then compare the networks from different conditions to identify the edges

capturing condition-specific behavior.

We compared NIPD against an existing approach for learning networks from the conditions

independently. We refer to this approach as INDEP, which represents a general class of existing

algorithms that learn networks per condition independently. On simulated data from networks

with known ground truth, NIPD inferred networks with higher quality than did INDEP, especially

on small training datasets. We also applied our approach to microarray data from two yeast

(Saccharomyces cerevisiae) cell types, quiescent and non-quiescent, isolated from glucose-starved,

stationary phase cultures [2]. Networks learned by NIPD were associated with many more Gene

ontology biological processes [3], or were enriched in targets of known transcription factors (TFs)

[17], than networks learned by INDEP. Many of the TFs were involved in stress response, which

is consistent with the fact that the populations are under starvation stress. NIPD also identified

many more shared edges, which represent biologically meaningful dependencies than the INDEP

approach. This suggests that by pooling data from multiple conditions, we are able to not only

capture shared structures better, but also to infer networks with higher overall quality.

2 Results

The goal of our experiments was three fold: (a) to examine the quality of condition-specific net-

works inferred by our approach that combines data from different conditions (NIPD) versus an

independent learner (INDEP), (b) to evaluate the algorithmic performance (measured by network

structure quality) as a function of training data size, (c) analyze how two different cell populations

behave, at the network level, in response to the same starvation stress. We address (a) and (b)

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on simulated data from networks with known topology, giving us ground truth to directly validate

the inferred networks. We address (c) on microarray data from two yeast cell populations isolated

from glucose-starved stationary phase cultures [2].

2.1 NIPD had superior performance on networks with known ground truth

We simulated data from two sets of networks, each set with two networks, one network per condition.

In the first, HIGHSIM, the networks for the two conditions, shared a larger portion (60%) of the

edges, and in the second, LOWSIM, the networks shared a smaller (20%) portion of the edges.

We compared the networks inferred by NIPD to those inferred by INDEP by assessing the match

between true and inferred node neighborhoods (See Supplementary Methods). Briefly, the data were

split into q partitions, where q ∈ {2, 4, 6, 8, 10}, and networks learned for each partition. The size of

the training data decreased with increasing q. We first evaluated overall network structure quality

by obtaining the number of nodes on which one approach was significantly better (t-test p-value,

< 0.05) in capturing its neighborhood as a function of q. On LOWSIM, NIPD was significantly

better for smaller amounts of training data. On HIGHSIM, NIPD performed significantly better

than INDEP for all training data sizes (Fig 1).

Next, we evaluated how well the shared edges were captured as a function of decreasing amounts

of training data (Supplementary Fig 1). NIPD captured shared edges better than INDEP on

LOWSIM as the amounts of training data decreased. NIPD was better than INDEP on HIGHSIM

regardless of the size of the training data.

Our results show that when the underlying networks corresponding to the different conditions

share a lot of structure, NIPD has a significantly greater advantage than INDEP, which does not do

any pooling. Furthermore, as training data size decreases, NIPD is better than INDEP for learning

both overall and shared structures, independent of the extent of sharing in the true networks.

2.2 Application to yeast quiescence

We applied NIPD to microarray data from two yeast cell populations, quiescent (QUIESCENT)

and non-quiescent (NON-QUIESCENT), isolated from glucose starvation-induced stationary phase

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cultures [2]. The two cell populations are in the same media but have differentiated physiologically

and morphologically, suggesting that each population is responding differently. We learned networks

using NIPD and INDEP treating each cell population as a condition. Because each array in the

dataset was obtained from a single gene deletion mutant, the networks were constrained such that

genes with deletion mutants connected to the remaining genes1.

The inferred networks from both methods were evaluated using information from Gene Ontology

(GO) process, GO Slim [3] and transcriptional regulatory networks [17]. Gene Ontology is a

hierarchically structured ontology of terms used to annotate genes. GO slim is a collapsed single

level view of the complete GO terms, providing high level information of the processes, functions

and cellular locations involving a set of genes. Finally, we analyzed combinations of genes with

deletions that were in the neighborhood of other non deletion genes.

2.2.1 NIPD identified more biologically meaningful dependencies

To determine if one network was more biologically meaningful than the other, we examined the net-

works based on Gene Ontology (GO) slim category (process, function and location), transcription

factor binding data and GO process, referred as GOSLIM, TFNET and GOPROC, respectively

(Fig 2). Network quality was determined by the number of GOSLIM categories (or TFNET or

GOPROC) with better coverage than random networks (See Methods). Both approaches were

equivalent for GOSLIM, with INDEP outperforming NIPD in QUIESCENT and NIPD outper-

forming INDEP on NON-QUIESCENT. NIPD outperformed INDEP with a larger margin than

was outperformed on TFNET categories from NON-QUIESCENT. NIPD was consistently better

than INDEP on GOPROC categories.

The networks learned by NIPD had many more edges than the networks learned by INDEP

(Supplementary Table 1). To estimate the proportion of the edges capturing biologically meaningful

relationships, we computed semantic similarity of genes connected by the edges [16]. Although both

INDEP and NIPD had significantly better semantic similarity than random networks, INDEP

degraded in p-value for QUIESCENT at the highest value of semantic similarity (Fig 3). NIPD-1This is not a bi-partite graph because the genes with deletion mutants are allowed to connect to each other.

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inferred networks had many more edges with high semantic similarity than INDEP, while keeping

the proportion of edges satisfying a particular semantic similarity threshold close to INDEP. This

suggests that NIPD identifies more dependencies that are biologically relevant than INDEP without

suffering in precision.

2.2.2 NIPD identified more shared edges representing common starvation response

We performed a more fine-grained analysis of the inferred networks by considering each gene and

its immediate neighborhood and tested whether these gene neighborhoods were enriched in GO

biological processes, or in the target set of transcription factors (TFs) (See Methods). Using a false

discovery rate (FDR) cutoff of 0.05, we identified many more subgraphs in the networks inferred

by NIPD than by INDEP to be enriched in a GO process or in targets of TFs (Figs 4, 5). NIPD

identified more processes and larger subgraphs in both populations (oxidative phosphorylation,

protein folding, fatty acid metabolism, ammonium transport) than did INDEP.

NIPD identified subgraphs involved in aerobic respiration and oxidative phosphorylation were

enriched in targets of HAP4, a global activator for respiration genes. The presence of HAP4 targets

in both cell populations makes sense because both populations are experiencing glucose starvation

and must switch to respiration for deriving energy. We also found the TFs, MSN2, MSN4, and

HSF1, regulating subgraphs involved in protein folding. These TFs activate stress responses and

are known to activate genes involved in heat, oxidative and starvation stress. We also found

targets of SIP4 in both populations. SIP4 is a transcriptional activator of gluconeogenesis [32],

expressed highly in glucose repressed cells [15], and therefore would be expected to be present in

both quiescent and non-quiescent cells. In contrast, the only shared regulatory connection found

by INDEP was HAP4. We conclude that the NIPD approach identified more networks that were

biologically relevant and informative about glucose starvation response than did INDEP.

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2.2.3 Wiring differences in NIPD-inferred networks exhibit population-specific star-

vation response

NIPD identified several processes associated exclusively with quiescent cells. This included regu-

latory processes (regulation of epigenetic gene expression, and regulation of nucleobase, nucleoside

and nucleic acid metabolism) and metabolic processes (pentose phosphate shunt). These were

novel predictions that highlight differences between these cells based on network wiring. INDEP

identified only one population-specific GO process (response to reactive oxygen species in NON-

QUIESCENT). An INDEP identified subgraph specific to quiescent (protein de-ubiquitination), was

actually a subset of the NIPD-identified subgraph involved in epigenetic gene expression regulation,

indicating that NIPD subsumed most of the information captured by INDEP.

NIPD QUIESCENT networks contained subgraphs enriched exclusively in targets of SKO1, and

AZF1. Both of these are zinc finger TFs, with AZF1 protein expressed highly under non-fermentable

carbon sources [27], and SKO1 which regulates low affinity glucose transporters [30], and are both

consistent with the condition experienced by these cells. Unlike NIPD, which identified SIP4 to

be associated with both populations, INDEP identified SIP4 only in QUIESCENT. However, as

we describe in the previous section, it is more likely that SIP4 is involved in both QUIESCENT

and NON-QUIESCENT populations. INDEP also found the TFs YAP7 and AFT2 exclusively in

QUIESCENT and NON-QUIESCENT, respectively. YAP7 is involved in general stress response

and would be expected to have targets in both QUIESCENT and NON-QUIESCENT. AFT2 is

required under oxidative stress and is consistent with the over-abundance of reactive oxygen species

in NON-QUIESCENT population [1].

NIPD also identified wiring differences in the subgraphs involved in shared processes. For ex-

ample in addition to HAP4, NIPD identified HAP2 as an important TF in QUIESCENT. The

presence of both HAP2 and HAP4 makes biological sense because they are both part of the

HAP2/HAP3/HAP4/HAP5 complex required for activation of respiratory genes. The presence

of both HAP2 and HAP4 in QUIESCENT, but not NON-QUIESCENT, suggests that the QUI-

ESCENT population maybe better equipped for respiration and long term survival in stationary

phase.

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Overall, the NIPD inferred networks captured key differences and similarities in metabolic and

regulatory processes, which are consistent with existing information about these cell populations

[1,2], and also include novel findings that can provide new insight into starvation response in yeast.

2.2.4 NIPD identified several knock-out combinations

The microarrays used in this study measured expression profile of single gene deletions that were

previously identified to be highly expressed at the mRNA level in stationary phase. We constrained

the inferred networks to identify neighborhoods of genes comprising only the genes with deletion

mutants, allowing us to identify combinations of such deletion mutants and their targets. Such com-

binations can be validated in the laboratory to verify cross-talk between pathways. We found that

NIPD-inferred networks contained significantly more deletion combinations compared to random

networks for both the quiescent and non-quiescent populations (p-value < 3E-10, Supplementary

Tables 3, 4, 5), which was not the case for the INDEP-identified networks (Supplementary Tables 6,

7).

A more stringent analysis of the knock-out combinations using GO process semantic similar-

ity identified several double knock-out and target gene candidates (Supplementary Table 2). We

also found more deletion combinations in NON-QUIESCENT compared to QUIESCENT. This is

consistent with the identification of many more mutants affecting non-quiescent than quiescent

cells [2]. In QUIESCENT, we found three genes that were all likely down-stream targets of a

COX7-QCR8 double knock-outs, all involved in the cytochrome-c oxidase complex of the mito-

chondrial inner membrane. Other deletion mutant combinations were involved in mitochondrial

ATP synthesis and ion transport. Many of these genes have been shown to be required for qui-

escent non-quiescent cell function, viability and survival [2, 18]. In NON-QUIESCENT, we found

several knock-out combinations involved in oxidative phosphorylation, aerobic respiration etc, in-

cluding a novel combination, YMR31 and QCR8, connected to TPS2. All three genes are found in

the mitochondria, which play a critical and complex role in starved cells, but the exact mechanisms

are not well-understood. Experimental analysis of this triplet can provide new insights into the role

of mitochondria in glucose-starved cells. In summary, these results demonstrated another benefit

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of data pooling in NIPD: learning more complex, combinatorial relationships among genes.

3 Discussion

Inference and analysis of cellular networks has been one of the cornerstones of systems biology.

We have developed a network learning approach, Network Inference with Pooling Data (NIPD) to

capture a systemic view of condition-specific response. NIPD is based on probabilistic graphical

models and infers the functional wiring among genes involved in condition-specific response. The

crux of our approach is to learn networks for any subset of conditions capturing fine-grained gene

interaction patterns not only in individual conditions but in any combination of conditions. This

allows NIPD to robustly identify both shared and unique components of condition-specific cellular

networks. In comparison to an approach that learns networks independently (INDEP), NIPD

(a) pools data across different conditions, enabling better exploitation of the shared information

between conditions, (b) learns better overall network structures in the face of decreasing amounts

of training data, and (c) learns structures with many more biologically meaningful dependencies.

Small training data sets, which are especially common for biological data, present significant

challenges for any network learning approach. In particular, approaches such as INDEP may learn

drastically different networks due to small data perturbations leading to differences that are not

biologically meaningful. NIPD is more resilient to small perturbations because by pooling data

from different conditions during network learning, NIPD effectively has more data for estimating

parameters for the shared parts of the network.

Another challenge in the analysis of condition-specific networks is to extract patterns that

are shared across conditions. Approaches such as INDEP that learn networks for each condition

independently, and then compare the networks, are more likely to learn different networks making

it difficult to identify the similarities across conditions. Application of both NIPD and INDEP

approaches to microarray data from two yeast populations showed that many of subgraphs that

would be considered specific to each population by INDEP, were actually shared biological processes

that must be activated in both populations irrespective of their morphological and physiological

differences.

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One of the strengths of NIPD in comparison with INDEP was its ability to identify pairs of gene

deletions and downstream targets using data from individual gene deletions. Amazingly, several

of these gene deletions are already known to have a phenotypic effect on stationary phase cultures

and often on quiescent or non-quiescent cells (Supplementary Table 2) [2,18]. These predictions are

therefore good candidates for future experiments using double deletion mutants, and are a drastic

reduction of the space of possible combinations of sixty-nine single gene deletions. Identification of

population-specific malfunctions in signaling pathways via experimental analysis of these multiple

deletions can provide new insight into aging and cancer studies using yeast stationary phase as a

model system.

The NIPD approach establishes ground-work for important future enhancements, including the

ability to efficiently learn networks from many conditions. The probabilistic framework of NIPD can

be easily extended to automatically infer the condition variable to make NIPD widely applicable to

datasets with uncertainty about the conditions. The NIPD approach can also integrate novel types

of high-throughput data including RNASeq [33] and ChipSeq [25]. These extensions will allow

us to systematically identify the parts, and the wiring among them that determine stage-specific,

tissue-specific and disease specific behavior in whole organisms.

4 Methods

4.1 Independent learning of condition-specific networks: INDEP

Existing approaches of learning condition-specific networks [4, 21, 28] can be considered as spe-

cial cases of a general independent learning approach, INDEP, where networks for each condition

are learned independently and then compared to identify network parts unique or shared across

conditions.

Let {D1, · · · ,Dk} denote k datasets from k conditions. In the INDEP approach, each network

Gc, 1 ≤ c ≤ k, is learned independently using data from Dc only. Our implementation of the

INDEP framework considered each Gc as an undirected probabilistic graphical model, or a Markov

random field (MRF) [14], which like Bayesian networks, can capture higher-order dependencies,

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but additionally captures cyclic dependencies. We use a pseudo-likelihood framework with an

MDL penalty to learn the structure of the MRF [6]. The pseudo-likelihood score for a network

Gc describing data Dc is PLL(Gc) =∑N

i=1 PLLV(Xi,Mci, c) where X1, · · · , XN are the random

variables (one for each gene), encoding the expression value of a gene. PLLV is Xi’s contribution to

the overall pseudo-likelihood and is defined, including a minimum description length (MDL) penalty,

as PLLV(Xi,Mci, c) =∑|Dc|

d logP (Xi = xdi|Mci = mcdi) + |θci|log(|Dc|)2 . Here Mci is the Markov

blanket (MB) of Xi in condition c and xdi and mcdi are assignments to Xi and Mci, respectively

from the dth data point. θci are the parameters of the conditional distribution P (Xi|Mci). We

assume the conditional distributions to be conditional Gaussians. The structure learning algorithm

for each graph is described in [22].

4.2 Network Inference with Pooling Data: NIPD

The NIPD approach that we present extends the INDEP approach by incorporating shared infor-

mation across conditions during structure learning. In this framework, we do not learn networks

for each condition c separately. Instead, we devise a score for each edge addition that considers

networks for any subset of the conditions. Let C denote the set of k conditions. For a non-singleton

set, E ⊆ C, we pool the data from all conditions e ∈ E and evaluate the overall score improve-

ment on adding an edge to networks for all e ∈ E. To learn {G1, · · · ,Gk} for the k conditions

simultaneously, we maximize the following MDL-based score:

S(G1, · · · ,Gk) = P (D1, · · · ,Dk|θ1, · · · , θk)P (θ1, · · · , θk|G1, · · · ,Gk) + MDL Penalty (1)

Here θ1, · · · , θk are the maximum likelihood parameters for the k graphs. We assume P (Dc|θ1, · · · , θk) =

P (Dc|θc). That is, if we know the parameters θc, the likelihood of the data from condition, Dc, given

θc can be estimated independently. Thus, P (D1, · · · ,Dk|θ1, · · · , θk) =∏kc=1 P (Dc|θc). Because our

networks are MRFs, we use pseudo-likelihood PLL(Dc). We expand the complete condition-specific

parameter set θc, to {θc1, · · · , θcN}, which is the set of parameters of each variable Xi, 1 ≤ i ≤ N ,

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in condition c. Using the parameter modularity assumption for each variable, we have:

P (θ1, · · · , θk|G1, · · · ,Gk) =N∏i=1

P (θ1i, · · · , θki|M1i, · · · ,Mki) (2)

Note the parameters of conditional probabilities of individual random variables are independent, but

the parameters per variable are not independent across conditions. To enforce dependency among

the θci, we make Mci depend on all the neighbors of Xi in condition c and all sets of conditions

that include c. To convey the intuition behind this idea, let us consider the two condition case

C = {A,B}. A variable Xj can be in Xi’s MB in condition A, either if it is connected to Xi only

in condition A, or if it is connected to Xi in both conditions A and B. Let M∗Ai be the set of

variables that are connected to Xi only in condition A but not in both A and B. Similarly, let

M∗{A,B}i denote the set of variables that are connected to Xi in both A and B conditions. Hence,

MAi = M∗Ai ∪M∗

{A,B}i. More generally, for any c ∈ C, Mci =⋃

E∈powerset(C) : c∈E M∗Ei, where M∗

Ei

denotes the neighbors of Xi only in condition set E. To incorporate this dependency in the structure

score, we need to define P (Xi|Mci) such that it takes into account all subsets E, c ∈ E. We assume

that the MBs, M∗Ei, independently influence Xi. This allows us to write P (Xi|Mci) as a product:

P (Xi|Mci) ∝∏

E∈powerset(C) : c∈E P (Xi|M∗Ei). To learn the k graphs, we exhaustively enumerate

over condition sets, E, and estimate parameters θEi by pooling the data for all non-singleton E.

Our structure learning algorithm maintains a conditional distribution for every variable, Xi for

every set E ∈ powerset(C). We consider the addition of an edge {Xi, Xk} in every set E. This addi-

tion will affect the conditionals of Xi and Xj in all conditions e ∈ E. Because the MB per condition

set independently influence the conditional, the pseudo-likelihood PLLV(Xi,Mei, e) decomposes as∑E s.t: e∈E PLLV(Xi,M∗

Ei, e) (Supplementary information). The net score improvement of adding

an edge {Xi, Xj} to a condition set E is given by:

∆Score{Xi,Xj},E =∑e∈E

|De|∑d=1

PLLV(Xi,Mei ∪ {Xj}, e)− PLLV(Xi,Mei, e) +

PLLV(Xj ,Mej ∪ {Xi}, e)− PLLV(Xj ,Mej , e) (3)

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Because of the decomposability of PLLV(Xi|Mei), all terms other than those involving the Markov

blanket variables in condition set E remain unchanged producing the score improvement:

∆Score{Xi,Xj},E = PLLV(Xi|M∗Ei ∪Xj)− PLLV(Xi|M∗

Ei)

This score decomposability allows us to efficiently learn networks over condition sets. Our structure

learning algorithm is described in more detail in Supplementary material.

4.3 Simulated data description and analysis

We generated simulated datasets using two sets of networks of known structure, HIGHSIM and

LOWSIM. All networks had the same number of nodes n = 68 and were obtained from the E. coli

regulatory network [23]. We used the INDEP model for generating the eight simulated datasets.

The parameters of the INDEP model were initialized using random partitions of an initial dataset

generated from a differential-equation based regulatory network simulator [19].

4.4 Microarray data description

Each microarray measures the expression of all yeast genes in response to genetic deletions from

quiescent (85) and non-quiescent (93) populations [2], with 69 common to both populations. The

arrays had biological replicates producing 170 and 186 measurements per gene in the quiescent

and non-quiescent populations, respectively. We filtered the microarray data to exclude genes with

> 80% missing values, resulting in 3,012 genes. We constrained the network structures such that a

gene connected to only the 69 genes with deletion mutants and no gene had more than 8 neighbors.

4.5 Validation of network edges using coverage of annotation categories

The coverage of an annotation category A is defined as the harmonic mean of a precision and

recall. Let L denote the complete list of genes used for network learning, LA ⊆ L denote the genes

annotated with A. Let lA denote the number edges in our learned network among two genes gi

and gj , such that gi ∈ LA and gj ∈ LA. Let tA be the total number of edges that are connected to

genes in LA (note tA > lA). Let sA denote the total number of edges that could exist among the

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genes in LA, which is(|LA|

2

)if |LA| < 8 and |LA| ∗ 8 if |LA| > 8. Precision for category A is defined

as pA = lAtA

and recall is defined as rA = lAsA

. These are used to define the coverage of category A,

2pArApA+rA

. We compute this coverage score for all categories using each inferred network, and compare

the score against an expected coverage from random networks with the same degree distribution.

To compare of NIPD against INDEP, assume we were comparing the inferred quiescent networks.

Let AINDEP and ANIPD denote the categories better than random in the INDEP and NIPD quiescent

networks, respectively. To determine how much better INDEP is than NIPD, we obtain the number

of categories in AINDEP ∪ANIPD on which INDEP has a better coverage than NIPD. We similarly

assess how much better NIPD is than INDEP. We repeat this procedure for the non-quiescent

networks. We also compared the semantic similarity of edges in inferred and random networks [16]

(Supplementary material).

4.6 Evaluation of gene deletion combinations

We identified combinations of genes with deletion mutants from Markov blankets comprising > 1 of

these deletion genes. We evaluated each algorithm’s ability to capture gene deletion combinations

by comparing the number of such combinations in random networks with the same number of

edges. This random network model provided a rough significance assessment on the number of

inferred knock-out combinations (Supplementary Table 3). We then performed a more stringent

analysis based on semantic similarity, using the sub-network spanning only the genes with deletion

combinations. We generated random networks with the same degree distributions as this sub-

network and computed the semantic similarity of each gene with the set of deletion genes connected

to it, in the inferred and random networks. We then selected genes with significantly higher semantic

similarity than in random networks (ztest, p-value <0.05).

5 Acknowledgements

This work is supported by grants from NIMH (1R01MH076282-03) and NSF (IIS-0705681) to

T.L., from NIH (GM-67593) and NSF (MCB0734918) to M.W.W. and from HHMI-NIH/NIBIB

(56005678).

15

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Figure 1: Number of variables (y-axis) on which one method was significantly better than the otheras function of the size of the training data (x-axis). Left is for the two networks (HIGHSIM) thatshare 60% edges and right is for the two networks (LOWSIM) that share 20% of their edges. Thetop and bottom graphs are for networks from the individual conditions.

0 

4 

8 

12 

16 

QUIESCENT  NON‐QUIESCENT 

# of Categories 

GOSLIM INDEP>NIPD 

NIPD>INDEP 

0 

4 

8 

12 

16 

QUIESCENT  NON‐QUIESCENT 

# of Categories 

TFNET INDEP>NIPD 

NIPD>INDEP 

0 

20 

40 

60 

80 

QUIESCENT  NON‐QUIESCENT # of Categories 

GOPROC INDEP>NIPD 

NIPD>INDEP 

Figure 2: Network quality comparison based on coverage of GOSlim (GOSLIM), targets of tran-scription factors (TFNET) and GO process (GOPROC). Each bar represents the number of cat-egories on which INDEP had better coverage than NIPD (INDEP>NIPD) or NIPD had bettercoverage than INDEP (NIPD>INDEP).

References

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16

‐1 

0 

1 

2 

3 

4 

5 

6 

7 

0  0.2  0.4  0.6  0.8  1  1.2  1.4 

log(# of Edges) 

Seman1c Similarity 

QUIESCENT  RAND (NIPD) NIPD RAND (INDEP) INDEP 

‐1 

0 

1 

2 

3 

4 

5 

6 

7 

0  0.2  0.4  0.6  0.8  1  1.2  1.4 

log(# of Edges) 

Seman1c Similarity 

NON‐QUIESCENT  RAND (NIPD) NIPD RAND (INDEP) INDEP 

Figure 3: Network quality comparison based on semantic similarity. The dashed lines representsthe background distribution generated from random networks and the solid lines represents thedistribution of the semantic similarity in the inferred networks.

YMR144W ADH2YMR187C

MUQ1

CAT2SIP18

ethanol metabolic process

ALD4

YMR090WEMP46

ALD2

SWP1

UTR1

YDR154C

GDH3

YJL016W

ALD3

FDH1

regulation of nucleobase, nucleoside, nucleotide and nucleic acid metabolic process

LSC2

ACS1

regulation of gene expression, epigenetic

carboxylic acid biosynthetic process

FMP37

AYR1

ADY2

REG2 FOX2

ATO3

nitrogen utilization ammonium transport

CTA1

PXA1

CUP2

SFA1

MAP1

CRS5

response to metal ion

FTH1ETR1

MDH3

fatty acid metabolic process

NADH regeneration

PEX11

MSS18

PAT1

PAI3

PUF4

DOA4

UBP10SBE22

GAC1

PDC5

ISW2

PDC1

TKL2YDL218W

YMR118CRPL2A

pentose-phosphate shunt

FYV7

GND2

SOD1

pentose metabolic process

beta-alanine biosynthetic process

YJR096W

polyamine catabolic process

RDH54

SOL4

HSP26

HAP2_TF

SNC2

QCR6

organelle ATP synthesis coupled electron transport

COX7

AVT7 INH1

COX8

ATP3

ATX2

NBP2

YOR052C

YGR001C

ATP16

oxidative phosphorylation

MIR1

ATP2

CCW12

ERV46

IDP2

NDI1

CDC48

PTR2

YNL194C

PCK1

ICL1

PIN3

SIP4_TF

YGL088W

UBC8

ILV1

HAP4_TF

QCR7

QCR8COX13

THO1

QCR9

LPD1NDE2

AAT2

acetyl-CoA metabolic process

KNS1

FAS1

SDS23

SDH2 YET3

KGD1

PRB1

HXT5

AZF1_TF

IRA2

SKO1_TF

OM14 XBP1

FAA1

HSP78

YDJ1

SIS1

HSP104

HSF1_TF

protein folding

BIO2

STI1

MSN2_TF

aerobic respiration

HSP30

MSN4_TF

HSP42

YDR266C

Figure 4: GO processes and TF targets for subgraphs from the NIPD-inferred networks using thequiescent population. The text below each subgraph indicates the process. The diamonds representthe TFs. A TF is connected to the subgraph which is enriched in the targets of the TF. The circularnodes represent the genes in the network and color represents the extent of differential expression,red: up-regulated, green: down-regulated.

17

ion transport

CCW12

CDC48

BSD2

KGD2

oxidative phosphorylation

ATP2

HAP4_TF

SDH2

MIR1

PMT1

ATP16

RIP1

SIS1

PGM2

HSP78

SSA2

MSN2_TF

HSP30

protein folding

HSP104

HSP42

MSN4_TF

ACS1

YJR096W

HSP26

TDH1

SSE2

STI1

SOD1

HSF1_TF

HSP12

URA6

PTR2

PIN3

SIP4_TF

PCK1

IDP2

ATP1

ICL1

AYR1

PEX11

MDH3

PUS5PST2

ADH2

CYB2

ADY2

YER121W

FOX2

RPS14A

ammonium transport

PXA1

ATO3

nitrogen utilization

RPL25LSC2

FMP37

energy derivation by oxidation of organic compounds fatty acid metabolic process

ETR1YKL187C

URA2

CRC1

GSC2

YAT2

YIR035C

YAT1

PYC2

carnitine metabolic process

QCR8

COX13

ILV1

TPS2

ARO3

QCR6

QCR9

COX7

aerobic respiration

mitochondrial electron transport, ubiquinol to cytochrome c

APJ1

YDR154CEMP46

ALD3

SOL4

beta-alanine biosynthetic process

AVT6 ALD2

polyamine catabolic process

GDH3

UTR1 YGR201C

YMR114C

Figure 5: GO processes and TF targets for subgraphs from the NIPD-inferred networks using thenon-quiescent population. Legend is similar to Fig 4

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21

Appendix

1 Generation and analysis of simulated data

We first obtained a sub-network of n = 68 nodes, G1, from the E. coli regulatory network [23]. We

then generated two networks, G2 and G3, by flipping 20% and 60% of G1’s edges, respectively.

{G1,G2} comprised networks in HIGHSIM and {G1,G3} comprised networks in LOWSIM. For

each pair of networks, we generated initial datasets using a differential equation-based gene regu-

latory network simulator [19]. We then split the data into two parts, learned two INDEP models

for each partition, and generated data from these models. We repeated this procedure four times

producing eight sets of simulated data with different parameters but the same network topology.

It was possible to generate all eight sets from the regulatory network simulator by perturbing the

kinetic constants, but our current data generation procedure was faster.

We compared the structure of the networks inferred by INDEP and NIPD using a per-variable

neighborhood comparison. Assume we are comparing the INDEP-inferred networks against the true

networks in HIGHSIM. We compare each of the true networks, {G1,G2} one at a time. Let GINDEP1

and GINDEP2 be the two inferred networks inferred by INDEP using datasets from HIGHSIM. For

each variable, Xi, we compare Xi’s neighborhood in G1 to its inferred neighborhoods in both

GINDEP1 and GINDEP

2 to obtain match score F INDEPi1 and F INDEP

i2 , respectively. INDEP’s match of

Xi’s neighborhood in G1 is the max of F INDEPi1 and F INDEP

i2 . We obtain a match score for different

folds of the data. Similarly we obtain a match score for NIPD for all variables from different folds

of the data. We then obtain the number of variables on which NIPD has a significantly higher

match score compared to INDEP as a function of training data size. We repeat this procedure

for all eight datasets for HIGHSIM to obtain the average number of variables NIPD is better than

INDEP. We repeat this procedure for G2 and then for the NIPD.

22

2 Semantic similarity based-validation

We use the definition of semantic similarity from Lord et al. using [16]. Semantic similarity between

two annotation terms is defined as a function of the maximal amount of information present in a

common ancestor of the terms. For GO terms the information is inversely proportional to the

number of genes that are annotated with a term, that is a very specific term with few genes has

more information than a broader term that has many more genes annotated with it. The functional

similarity between two genes is given by the average semantic similarity of sets of GO process terms

associated with the genes. Let gi and gj be two genes connected by an edge in our inferred network.

Let Ti and Tj be the set of GO process terms associated with gi and gj , respectively. The average

semantic similarity, sim(gi, gj) for all pairs of terms is

sim(gi, gj) =1

|Tp| ∗ |Tq|∑

tp∈Ti,tq∈Tj

semsim(tp, tq)

Semantic similarity, semsim(tp, tq) = −log(mina∈Ppqpa), where Ppq is the set of common ancestors

of the terms tp and tq in the GO process “is-a” hierarchy. −log(pa) is the amount of information

associated with a term a, and pa is probability of the term defined as the ratio of the number of

genes annotated with the term a to the total number of genes with a GO process assignment.

We used semantic similarity for global validation of the inferred edges and also for assessing

the strength of association between combinations of single gene knock-outs and a target gene.

In both cases, we generated random networks with the same degree distributions as the inferred

networks and estimated a background semantic similarity distribution. For assessing the strength

of association between a gene, gi and the set of knock-out genes that are connected to it, Ki, we

had to compare the similarity of a gene with a set of genes. We assumed GO process terms for

the set Ki to be the union of all terms associated with the genes, gj ∈ Ki. We then computed the

semantic similarity between the term set associated with gene gi and the union of terms associated

with Ki.

23

3 Structure learning algorithm of NIPD in detail

Our score for structure learning is based on the pseudo-likelihood of the data given model and

requires us to compute the conditional probability distribution of each variable in a condition c.

We require that the parameters of this conditional distribution be dependent such that we can pool

the data from the different conditions to estimate the parameters. The conditional distribution,

P (Xi|Mci) in condition c is defined as a product:

P (Xi = xid|Mci = mcid) ∝∏

E∈powerset(C) : c∈E

P (Xi = xdi|M∗Ei = m∗Ei), (4)

where d is the data point index and M∗E is the Markov blanket (MB) of Xi exclusively in condition

set E. The proportionality term can be eliminated using the normalization term 1Zcid

. In our

conditional Gaussian case, 1Z1id

= N (µ1id|µ3id, σ21i + σ2

3i), where σ23i is the standard deviation from

the condition set {1, 2}, µ1id = wT1im

∗1id, is the mean of the conditional Gaussian using the dth data

point in condition 1. Thus, 1Z1id

is the probability of µ1id from a Gaussian distribution with mean

estimated from the pooled data. To make the product in Eq 4 a valid conditional distribution, we

need to subtract out the normalization term. However, working with the unnormalized form gives

us three benefits. First, and most important, it enables our score to be a decomposable sum on

taking logarithms. Second the normalization term behaves as a smoothing term for a condition-

specific mean, µ1id, preferring network structures with means µ1id closer to the shared mean µ3id.

Third, avoiding the computation of the Zid for each data point, gives us some runtime benefits.

Our structure learning algorithm begins with k empty graphs and proposes edge additions for all

variables, for all subsets of the condition set C. The while loop iteratively makes edge modifications

until the score no longer improves. The outermost for loop (Steps 4-17 ) iterates over variables

Xi to identify new candidate MB variables Xj in a condition set E. We iterate over all candidate

MBs Xj (Steps 5-15) and condition sets E (Steps 6-14) and compute the score improvement for

each pair {Xj ,E} (Step 16). In Steps 7-9 we add a check that if a variable Xj is already present

in any subset or super set D of E, we do not include it as a candidate. If the current condition

set under consideration has more than one conditions, data from these conditions is pooled and

24

parameters for the new distribution P (Xi|M∗Ei) is estimated using the pooled dataset (Steps 10-

12). A candidate move for a variable Xi is composed of a pair {X ′j ,E′} with the maximal score

improvement over all variables and conditions (Step 16). After all candidate moves have been

identified, we attempt all the moves in the order of decreasing score improvement (Step 18). Each

move adds the edge {Xi, X′j} in condition set E′. However, if either Xi or X ′j was already updated

in a previous move, we ignore the move. Because not all candidate moves are made, by sorting the

move order in decreasing score improvement, we enable moves with the highest score improvements

to be attempted first. The algorithm converges when no edge addition improves the score of the k

graphs.

Algorithm 1 NIPD1: Input:

Random variable set, X = {X1, · · · , X|X|}Set of conditions CDatasets of RV joint assignments, {D1, · · · ,D|C|}maximum neighborhood size, kmax

2: Output:Inferred graphs G1, · · · ,G|C|

3: while Score(G1, · · · ,G|C|) does not stabilize do4: for Xi ∈ X do {/*Propose moves*/ }5: for Xj ∈ (X \ {Xi}) do6: for E ∈ powerset(C) do7: if Xj ∈M∗

iD, s.t either D ⊂ E or E ⊂ D then8: Skip Xj .9: end if

10: if |E| > 1 then11: Estimate parameters for new conditional P (Xi|M∗

Ei ∪ {Xj}) using pooled dataset DE obtainedfrom merging all De s.t. e ∈ E.

12: end if13: compute ∆Score{XiXj}E.14: end for15: end for16: Store {Xi, X

′j ,E

′} as candidate move for Xi, where {X ′j ,E′} = arg maxj,E

∆Score{XiXj}E

17: end for18: Make candidate moves {Xi, X

′j ,E

′} in order of decreasing score improvement /*Attempt moves to modify graphstructures*/

19: end while

25

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Figure 1: Shared edges in the HIGHSIM and LOWSIM networks

METHOD POPULATION EDGE-CNT SHARED EDGE-CNT

NIPDQUIESCENT 378

271NON-QUIESCENT 402

INDEPQUIESCENT 171

25NON-QUIESCENT 200

Table 1: Structure of the inferred networks using INDEP and NIPD.

26

ATP3

HAP4_TFHAP1_TF

COX8INH1

COX7

QCR6

COX13

oxidative phosphorylation

UBC8QCR9

QCR7

aerobic respiration

QCR8

YGL088W

THO1

carnitine metabolic process

YAT1DOA4

UBP10PUF4URA2

YAT2

carboxylic acid biosynthetic process

protein deubiquitination

HEM3

YAP7_TF

AVT7TDH1

RTN2

tricarboxylic acid cycle intermediate metabolic process

AAT2

NDE2

KGD1

SDH2

YET3

ADH2

nitrogen utilization

ammonium transport

ADY2

ATO3

fatty acid beta-oxidation

MSS18

PEX11

AYR1

YIR016W

FOX2POT1

ETR1

YIL161W

JEN1

YIL039W

Figure 2: GO processes and TF targets for subgraphs from the INDEP-inferred networks using thequiescent population. The text below each subgraph indicates the process. The diamonds representthe TFs. A TF is connected to the subgraph which is enriched in the targets of the TF. The circularnodes represent the genes in the network and color represents the extent of differential expression,red: up-regulated, green: down-regulated.

HSF1_TF

mitochondrial electron transport, ubiquinol to cytochrome c

COX4

HAP4_TF

QCR8

MTH1

COX13

SML1

QCR9SED1

SDH2

aerobic respiration

SDH3

ATP16

SDS23

GSP1

mitochondrial electron transport, succinate to ubiquinone

SIP4_TF

CLB5

ATP synthesis coupled proton transport

STF2OM45

ATP1

NDE2

SSE2

polyamine catabolic process

ALD2

beta-alanine biosynthetic process

TDH1

ALD3

HSP26

HSP12

YGR201C

RPL25

ALD4

CCW12

ADY2RPS26B

ATO3

nitrogen utilization

ammonium transport

GDH2

PCK1

ICL1

RIP1

REG1ATP2

IDP2

generation of precursor metabolites and energy

KGD2

SIS1

SSA2

MSN2_TF

HSP104

MSN4_TF

protein folding

YGL010W

OM14

AFT2_TF

PRB1

CTT1

LEU4

CTA1

PRE8

response to reactive oxygen species

Figure 3: GO processes and TF targets for subgraphs from the INDEP-inferred networks using thenon-quiescent population. Legend is similar to Fig 2

27

Deletion combinations Downstream effect ProcessQUIESCENT

COX7∗, QCR8 COX13, QCR6, QCR9 ATP synthesis coupled electron transportADY2∗, CTA1∗ ATO3 ion transportETR1∗, ACS1 AYR1 carboxylic acid metabolic process

NON-QUIESCENTATP12, SDH2∗ ATP16 oxidative phosphorylationYMR31, QCR8 TPS2 trehalose bio-synthesis, mitochondrial functionADY2∗, YAL054C ATO3 ion transportNQM1, QCR8 COX13 aerobic respirationCOX7∗, QCR8 QCR9 electron transportSIP18, YGR236C AZR1 response to stimulusETR1∗, ADH2 LSC2 energy derivation by oxidation

Table 2: Knock-out combinations identified by NIPD in the quiescent and non-quiescent popula-tions. Genes with ∗ have been shown to have a phenotype in stationary phase or in quiescent andnon-quiescent cells in [2, 18].

METHOD POPULATION INFERRED-NW RAND-MEAN RAND-STD Z-PVALNIPD QUIESCENT 47 25.51 4.1839 2.80E-07

NON-QUIESCENT 76 28.91 4.8076 1.18E-22INDEP QUIESCENT 7 5.71 2.1569 0.5498

NON-QUIESCENT 10 7.7 2.2042 0.2967

Table 3: Statistical significance of the number of deletion gene combinations in the networks inferredby NIPD and INDEP. The second column is the number of combinations in the inferred networks,and the subsequent columns specify the mean and standard deviation and z-test p-value fromrandom networks.

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Deletion combination Downstream targetYCR010C,YHR138C YBR050CYKL217W,YMR136W YBR090CYDL218W,YGR088W YBR117CYCR021C,YOR374W YBR149WYGL121C,YLR312C YDL137WYIL136W,YOR374W YDL215CYAL054C,YDR504C YDR059CYDL223C,YDR262W YDR077WYCR021C,YLL026W YDR171WYDL222C,YDR262W YDR204WYDL222C,YDR262W YDR216WYDL223C,YDR262W YDR293CYCR010C,YDR256C YDR384CYBR230C,YIL101C YEL060CYHR138C,YMR096W YER020WYJL166W,YMR256C YFR033CYDR504C,YPL230W YGL036WYDR070C,YMR107W YGL054CYBR212W,YHR139C YGL156WYJL166W,YMR256C YGL191WYBR230C,YLR377C YGR079WYDR256C,YMR303C YGR180CYJL166W,YMR256C YGR183CYGR236C,YHR138C YGR235CYBR072W,YMR250W YGR248WYDL204W,YDL218W,YFL014W YGR256WYAL054C,YBR026C YIL124WYDL204W,YMR169C YJL016WYBL078C,YMR170C YJR049CYFL030W,YJR121W YJR077CYGR088W,YLR377C YKL141WYKR097W,YLL041C YKL182WYCR010C,YDR256C YKR009CYDR504C,YLL041C YLL019CYBR230C,YLR312C YLR311CYMR303C,YOR374W YML042WYDL218W,YHR139C YMR118CYDL204W,YMR175W YMR174CYBR212W,YHR139C YNL115CYIL136W,YKL217W YNL116WYDR262W,YLR312C YNL190WYDL222C,YKR097W YNL194CYDL223C,YHR139C YNL195CYHR096C,YOR317W YOL081WYBR026C,YCR021C YOL147CYDL168W,YDR070C,YLR327C YOR031WYCR010C,YHR138C YPL147W

Table 4: The deletion combinations identified by NIPD on the quiescent population.

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Deletion combination Downstream targetYAL054C,YBR067C YAL041WYHR139C,YMR170C YAL062WYDR070C,YGR236C YBL001CYBL049W,YIL136W YBL064CYIL136W,YKR097W YBL099WYBR230C,YHR138C YBR050CYKL217W,YMR107W YBR090CYDR256C,YOR374W YBR149WYBR214W,YNL055C YBR286WYJR121W,YLL041C YDL004WYBR056W,YBR067C YDL046WYCR005C,YLR327C YDL110CYFL014W,YMR096W YDL124WYJR121W,YNL055C YDL126CYGL121C,YHR138C YDL137WYBR212W,YOR374W YDL215CYHR097C,YMR191W YDL234CYDR504C,YKL217W YDR059CYFR049W,YJL166W YDR074WYDR262W,YLL041C YDR077WYBR212W,YLR377C YDR111CYFL030W,YJR121W YDR148CYCR021C,YLL026W YDR171WYDL222C,YDR262W YDR204WYDR256C,YLR312C YDR264CYDL223C,YDR262W YDR293CYAL054C,YCR010C YDR384CYKL109W,YPL134C YDR497CYHR096C,YLR312C YDR505CYDR070C,YGL121C YDR513WYIL136W,YNL015W,YOR374W YEL034WYBR230C,YMR096W YEL060CYBR230C,YCR010C YER121WYLR312C,YMR096W YGL010WYAL054C,YBR026C YGL080WYBR056W,YJL066C YGL173CYGR043C,YJL166W YGL191WYGR043C,YLR327C YGR008C

Deletion combination Downstream targetYAR035W,YMR191W YGR032WYJL166W,YMR256C YGR183CYIR038C,YMR170C,YMR175W YGR201CYGR236C,YMR175W YGR224WYDR070C,YHR138C YGR235CYBR026C,YMR303C YGR244CYDL204W,YMR169C,YMR250W YGR248WYDL218W,YFL014W YGR256WYCR005C,YDL204W YHR009CYCR005C,YHR139C YHR162WYGR236C,YHR096C,YMR107W YIL057CYIL101C,YIL160C YIR016WYDL168W,YDL204W YJL016WYFL030W,YJR121W YJR077CYBR230C,YNL055C YKL148CYGR043C,YGR088W YKL150WYAL054C,YMR303C YKL187CYCR010C,YDR256C,YMR303C YKR009CYAL054C,YKL217W YKR046CYHR096C,YLL041C YLL019CYCR021C,YER150W YLR216CYBR214W,YGL121C YLR356WYIL160C,YMR303C YML042WYBR056W,YBR067C YMR031CYDR070C,YLR327C,YPL230W YMR110CYBL078C,YMR170C YMR114CYDL218W,YMR175W YMR118CYDR504C,YMR191W YMR201CYBR230C,YKL217W YNL104CYIL136W,YKL217W YNL116WYDL168W,YPL230W YNL144CYDR262W,YLR312C YNL190WYDL222C,YJL066C YNL194CYBL048W,YIL101C YOL084WYBR026C,YCR021C YOL147CYDL168W,YGR236C,YLR327C YOR031WYDR504C,YLR395C YOR052CYDL223C,YMR136W YPL265W

Table 5: Deletion combinations identified by NIPD on the non-quiescent population.

Deletion combination Downstream targetYBR067C,YMR250W YAL061WYCR010C,YMR303C YDR384CYGR236C,YJL166W YER063WYHR139C,YKR097W YKL182WYIL160C,YKL217W YKR009CYBR067C,YDL223C YNL195CYBR026C,YMR303C YOL147C

Table 6: Deletion combinations identified by INDEP on the quiescent population.

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Deletion combination Downstream targetYCR010C,YOR374W YDR384CYMR169C,YMR170C YGR201CYIL101C,YIL160C YIR016WYAL054C,YDR256C,YMR303C YKR009CYHR096C,YLR377C YLL019CYDR256C,YGR088W YML092CYHR139C,YMR175W YMR118CYAR035W,YBR230C YNL104CYGL121C,YOR317W YOL081WYBL078C,YDL168W YOR031W

Table 7: Deletion combinations identified by INDEP on the non-quiescent population.

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