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\begin{document}

\title{A framework for considering prior information in network-based
approaches to --omics data analysis}



\author[1]{Julia Somers}%
\author[1]{Madeleine R. Fenner}%
\author[1]{Dharani Thirumalaisamy}%
\author[1]{Garth Kong}%
\author[1]{William Yashar}%
\author[2]{Meric Kinali}%
\author[2]{Kisan Thapa}%
\author[1]{Olga Nikolova}%
\author[2]{Özgün Babur}%
\author[1]{Emek Demir}%
\affil[1]{Oregon Health \& Science University}%
\affil[2]{University of Massachusetts Boston}%


\vspace{-1em}



  
  \date{May 22, 2024}


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\selectlanguage{english}
\begin{abstract}
For decades, molecular biologists have been uncovering the mechanics of
biological systems. Efforts to bring their findings together have led to
the development of multiple databases and information systems that
capture and present pathway information in a computable network format.
Concurrently, the advent of modern omics technologies has empowered
researchers to systematically profile cellular processes across
different modalities. Numerous algorithms, methodologies, and tools have
been developed to use prior knowledge networks in the analysis of omics
datasets. Interestingly, it has been repeatedly demonstrated that the
source of prior knowledge can greatly impact the results of a given
analysis. For these methods to be successful it is paramount that their
selection of prior knowledge networks is amenable to the data type and
the computational task they aim to accomplish. Here we present a
five-level framework that broadly describes network models in terms of
their scope, level of detail, and ability to inform causal predictions.
To contextualize this framework, we review a handful of network-based
omics analysis methods at each level, while also describing the
computational tasks they aim to accomplish.%
\end{abstract}%



\sloppy


\textbf{Introduction}

Francois Jacob concluded his Nobel lecture in 1965 (awarded for modeling
Lac Operon with Monod and Lwoff) with a vision: ``We do not know how
molecules find each other, recognize each other, and combine to
constitute the regulatory network \ldots{} What is clear, however, is
that the problems to be solved by cellular biology and genetics in the
years to come tend increasingly to merge with those in which
biochemistry and physical chemistry are involved.''. The idea of a
network model, where genes and gene products are linked by molecular
processes, was present from the very first days of molecular biology.
Due to the sheer complexity of biological systems, biologists have
traditionally employed reductionist approaches where different fragments
of cellular processes are isolated and identified. An implicit goal of
this approach has been to assemble a network model in a piecemeal
fashion from these reductionist findings, which will eventually be able
to explain and predict the behavior of the biological system at large.

More than half a century later, tens of millions such reductionist
findings have accumulated in the literature. Multiple databases and
information systems have been developed to capture the pathway
information accumulated in scientific literature and present it in
computable format\textsuperscript{1}. Millions of interactions,
molecular processes and relationships are curated as networks, including
metabolic pathways, signaling pathways, gene regulatory networks,
molecular interaction networks, and genetic-interaction networks.

In parallel, our ability to systematically profile cellular processes
has grown with the development of modern omics technologies. We now have
a range of genomic, transcriptomic, metabolomic, and proteomic
techniques at our disposal. We can deeply profile a cellular system in a
given context, with an increasing ability to do so spatially and at the
level of single cells. These technologies allow us to generate
system-scale profiles without necessarily starting with a specific
hypothesis or isolating a specific component---challenging the
traditional piecemeal method. In most cases, the data-driven approaches
no longer seek explicit biological grounding of their
findings---clusters, subtypes and signatures replace mechanisms and
pathways. The perceived incompatibility between ``hypothesis driven,
reductionist'' and ``data-driven, system-scale'' camps led to one of the
most polarizing epistemological debates in modern molecular
biology\textsuperscript{2--4}.

Is this truly a fundamental divide---maybe we can have our cake and eat
it too? To bridge this gap, we need to computationally combine these
prior information fragments with -omics profiles to generate and test
mechanistic, falsifiable conjectures at scale. Over the last two
decades, thousands of algorithms and methods have been created in the
field of network biology to address various sub-problems of this grand
challenge, using diverse types of -omic data and prior knowledge. Given
multiple data modalities, prior information sources, and tasks, it is
often difficult to assess which algorithms are good for which biological
questions and how they are related to each other. Here we present a
framework to organize these methodologies into broad categories based on
their use of prior information and the computational task they target.
We also review a few examples from each category. Our goal in this
review is to give readers a foundational understanding of the different
types of networks, and a mental map to help match their needs with the
available tools and algorithms.

\textbf{Networks are models of biological systems}

A biological model is an idealistic construct, \emph{in simulacra} ,
that allows us to understand, explain and predict biological phenomena.
A network, in the current context, is a graph model of a biological
system which depicts molecular entities and the interactions between
them. Mathematically, a network is a graph G(V,E), where a set of
vertices or alternatively nodes (V) map to biological entities,
connected by a set of ordered pairs or edges E, which represent the
relationships between nodes. Network models vary greatly in their
coverage of established biological knowledge, level of detail and
interoperability with other networks. A network model can be as simple
as the interaction ''MDM2 binds to TP53'' or can cover a system-level
map that encompasses all known cellular processes. In some models, a
single node may represent one entity, whereas others may have multiple
nodes corresponding to the same entity but representing different
states. Similarly, edges may have directionality that indicates the flow
of cause and effect from reactant to product in an interaction or be
undirected. They may also be signed, meaning they describe the nature of
the reaction (ex. activation/inhibition), or unsigned. Some highly
complex network models even account for stochiometric ratios and
reaction dynamics equations in their construction.

Several domains of biology are modeled by networks, including: (i)
M\emph{etabolic pathways} (Figure 1A) are usually characterized by the
abstraction of enzymes, substrates, and products. Typically, these
reactions involve small molecules, and an enzyme, often a protein,
catalyzes the reaction. Inhibitors and activators can also modulate the
catalysis event. (ii) \emph{Signaling pathways} (Figure 1B), on the
other hand, encompass a range of biochemical reactions, including
binding, transportation, and catalysis events involving molecules and
complexes. These pathways may describe molecular states such as cellular
location, covalent and non-covalent modifications, and sequence
fragments. (iii) \emph{Gene regulatory networks} (Figure 1C) involve
transcription and translation events, along with their control
mechanisms. (iv) \emph{Molecular interactions} (Figure 1D) are typically
represented as undirected graphs and cover non-covalent binding events.
(v) \emph{Genetic interactions} (Figure 1E) capture relationships
between two genes when the observed phenotypic consequence of perturbing
both genes is different from what is expected given the phenotypes of
each single gene perturbation, such as in the case of epistasis.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

\textbf{Figure 1. Domains of biological systems described by networks}A.
Metabolic pathways are typically described as a series of sequential
reactions involving small molecules and catalytic enzymes. B. Signaling
pathways describe the passage of signaling events, often triggered by a
ligand/receptor combination. C. Gene regulatory networks are directed
graphs that describe the circuitry of regulatory effects exerted from
one gene to another. D. Molecular interaction networks are typically
unsigned diagrams that represent uncharacterized interactions between a
suite of molecules, often proteins. E. Genetic interactions describe the
relationships between genes. Edges here describe the nature of the
relationship, as opposed to the mechanisms that are involved in the
relationship.

\textbf{Creating Networks}

Network representations of biological systems have been around for
decades. Reconstruction of metabolic maps from early biochemical
experiments started in the 1950s with Boehringer Mannheim charts. Modern
reconstruction efforts like Reactome \textsuperscript{5} ,
SIGNOR\textsuperscript{6}, KEGG\textsuperscript{7}, RECON
\textsuperscript{8}, and Disease Maps \textsuperscript{9} encompass
hundreds of thousands of reactions, curated from scientific
publications. Despite this herculean effort, these manually curated
databases cannot keep up with the rate of scientific production given
the available resources. To support manual curation efforts, multiple
natural language processing (NLP) and crowd sourcing approaches to
extract computable models from scientific literature have been
developed\textsuperscript{10}, and recent language learning models
(LLMs) offer great promise in expanding these
efforts\textsuperscript{11}. Additionally, in the case where there is
very little existing literature about a system, networks can be inferred
de novo or by expanding existing models\textsuperscript{12}. This
approach was particularly popular in the early phases of COVID-19
pandemic, wherein many researchers used network-based approaches
grounded in SARS-CoV and MERS-CoV networks to extrapolate the molecular
processes governing SARS-CoV-2 biology\textsuperscript{13}. When PKNs
are incomplete or nonexistent, interactions captured in the data can be
used to infer a network structure. For example, in the case of high
throughput PPI assays the identified interactions are commonly
quantified based on confidence, then filtered using a cut-off score to
lessen any noise introduced by the mode of collection. The filter
chosen, which may be empirically or statistically informed, can have a
significant impact on the rate of false positives and negatives in the
resulting network\textsuperscript{14}. Finally, some high-throughput
modalities such as protein co-IP experiments can be readily expressed as
networks without referring to curated sources of prior knowledge.
Additional layers such as drug-target relationships can then be mapped
to these interaction networks, as was done during COVID-19 to nominate
targets for drug repurposing\textsuperscript{15}.

\textbf{Networks and Context}

The fragments which make up a network often come from different
biological contexts---here context is an umbrella term that implies
different models, diseases, conditions, observation modalities and
perturbations. For example, a group of researchers elucidates the
phosphorylation event that drives a signaling cascade using an array of
molecular techniques. Another research group identifies an inhibitor of
this phosphorylation event. Another identifies a handful of
transcription factors which assemble to produce this inhibitor, and so
on until a pathway model starts to take shape. An important
consideration in the implementation of this pathway is the context from
which each of its components arose. If each of these groups were working
with cell lines derived from different tissues, treated with different
perturbing agents, or grown under different environmental conditions -
could their results be stitched together into a common network? How to
assemble these fragments properly, and when and which type of context
restrictions should be used for a particular problem, are complicated
questions with no clearcut answer. It is often necessary to join
elements from different contexts to create networks that appropriately
match the scope of the high throughput data. For datasets with a narrow
scope within well-studied processes, such as a targeted metabolomics
assay quantifying components of glucose metabolism, it may be possible
to find a manually assembled quantitative model which combines fragments
from a consistent context. However, for most -omics applications, which
often involve untargeted high-throughput datasets, we often need to use
the context-insensitive network and derive the context from the data.

\textbf{Utility of Networks}

Omics profiles offer a molecular snapshot of a biological system under a
set of conditions\textsuperscript{16}. Molecular structures commonly
profiled by omics techniques include the genome (genomics), RNA
(transcriptomics), proteins and their post translational modifications
(proteomics), metabolites (metabolomics), and the epigenome
(epigenomics)\textsuperscript{17}. Some modalities can even be profiled
at the level of a single cell, giving much deeper resolution. These
technologies and the interpretation of their results with network-based
methods are a driving force in the field of systems biology. Using
networks, we can generate conjectures about the patterns in these highly
complex datasets and understand which observed relationships can be
explained by existing knowledge, and which relationships point to novel
findings.

This \emph{``explainability''} is key for the iterative process of
scientific discovery. If an algorithm can make somewhat accurate
predictions about the behavior of a system but cannot point to the
components that are likely to drive the observed behavior, then the
predictions can only be tested phenomenologically and not
mechanistically. This is a limiting and inefficient way of analyzing a
complex combinatorial system. There is no better example for this claim
than commercial drug discovery, which relies on very large
phenomenological screens for clinical trials. Despite substantial
efficiency gains, between 1950 and 2010 the costs of research and
development per approved drug approximately doubled every nine
years\textsuperscript{18} as we try to tackle increasingly complex
diseases.

A related benefit of a grounded, mechanistic inference is the ability to
``reason'' about the system's response to a previously unknown
perturbation such as a new drug combination or a mutation. This is an
extension of a biologist's intuition - e.g., inhibiting the inhibitor of
a target protein will activate it - but can be done at-scale.
Additionally, it enables us to identify the reasons behind the failure
of our predictions.

A perhaps less appreciated aspect of network-based approaches is the use
of networks as prior information to restrict the search space of
statistical algorithms. When evaluating potential network models in the
context of their ability to explain or fit a certain data \emph{de novo}
, the number of possible network models grows
exponentially,\(O(2^{n^{2}})\), as a function of the number of
nodes\textsuperscript{19}. This leads to substantial problems with model
overfitting, multiple hypothesis testing correction and model
degeneracy. Multiple hybrid methods were developed that use prior
information probabilistically along with \emph{de novo} inference to
center the inferred/evaluated models around known biology that can
restrict the search space substantially\textsuperscript{12}.

The combined effect of these advantages is an incremental, iterative
discovery process that can be done at-scale\emph{.} This is crucial,
given the rapid evolution of omics technologies and the ever-increasing
volume of omics data.

\textbf{Section 2: A framework for categorizing and classifying network
biology approaches.}

When conducting network-based omics analysis, the choice of prior
knowledge network can impact the results of the
analysis\textsuperscript{20}. Given the multitude of network databases
available, it is useful to have a framework that can guide researchers
to make informed decisions. Herein we define three `tasks' which
describe the overarching goal(s) of network-based approaches to omics
data analysis. These tasks include network inference, explanation
extraction, and phenotype prediction. Additionally, we define a
framework for classifying network models into five levels of increasing
level of detail: Gene Sets, Interaction Networks, Activity Flow, Process
Description, and Quantitative Models (Figure 2). Finally, we review a
sampling of network-based approaches at each of these five levels to
contextualize the framework. Our classification of networks and the
approaches that use them is intentionally broad to provide a high-level
organization allowing for nuances in this rapidly evolving area of
research.

\textbf{Computational Tasks}

Networks can be combined with -omics data to achieve a wide range of
computational tasks. Below we define some broad categories that describe
these computational tasks. These categories are not mutually exclusive,
as many computational methods have the capacity to perform multiple
tasks or hybrids of them. For example, methods which ``upscale
networks'', meaning they output a higher-level network from a
lower-level PKN, typically do both network inference and explanation
extraction, as they select a small subset of the input PKN that can
explain the correlations in the data and then will modify it to infer a
new, higher-level network. It is also common to use explanation
extraction or network inference task as a precursor to phenotype
prediction, especially in clinical applications.

\emph{Explanation extraction} aims to interpret patterns found within an
omics profile and contextualize them using prior information about the
system. It addresses hypotheses around system changes, such as
differential expression or altered interaction strengths, to elucidate
the mechanisms involved\textsuperscript{21}. Common examples of
explanation extraction tasks include enrichment-analysis and algorithms
that produce a relevant subgraph of a larger network. Explanation
extraction can also be thought of as emulating the literature search of
a molecular biologist to explain the data at hand. As a molecular
biologist reads the literature they ask ``Is this information fragment
compatible with my data? Does it explain it or contradict it? Is this
applicable to my experiment's context?''. The same questions are
interrogated by explanation extraction methods, but in a quantitative
manner that scales to high throughput data. Explanation extraction tools
generate valuable conjectures that can, for example, guide the selection
of subsequent perturbing agents, or recognize parallel mechanisms that
unify multiple datasets in a novel way\textsuperscript{12,19}.

\emph{Network inference} tasks produce a network model based on the
input -omics data. This can be achieved by integrating prior networks or
can be done \emph{de novo} . Due to the combinatorial complexity of the
model space and the inherent stochasticity of biological systems,
inference is always an underdetermined problem and coherence of inferred
networks and actual biological reality may be low, independent of the
performance of the model. Constraining inference to at least partially
conform with known biology can help by ``anchoring'' inferred networks.
Another option is to use a large number of biological models in an
ensemble learning strategy to reduce bias.

Some network inference approaches construct an entirely new model while
others expand on established networks, in either case, the goal is to
generate new mechanistic hypotheses. Upscaling algorithms are a common
example of network inference. These approaches infer a higher-level
representation (e.g. Activity Flow) from a lower-level prior network
(e.g. protein-protein interactions) using -omics profiles. Upscaling can
also be used to assign weights, direction, sign and rate constants to
edges on a graph.

\emph{Phenotype prediction} aims to predict how an organism or system
responds to disease states and perturbations. These methods may be
applied at a cellular level to project signaling events and
transformations as well as broad phenomena like cell proliferation and
survival, but they can also be extended to a network medicine approach,
where predictions are made at a patient level to inform diagnosis,
prognosis, or treatment response\textsuperscript{22,23}.

Effective phenotype prediction is arguably more difficult than the prior
two tasks. Phenotype is a function of the whole system that often
contains feedback loops and other non-linear response circuitry. It is
also inherently multimodal as at minimum, it requires one omic
measurement and one phenotype measurement modality --e.g. IC50, GR50 or
disease free survival. Each of these factors can be confounding to
phenotype prediction tools.

\textbf{Levels of Prior Knowledge Networks}

There are many different ways of representing molecular processes in a
graph model. The choice of representation is often dictated by the
volume of experimental data informing different parts of the model. As
models increase in their level of mechanistic detail, they also decrease
in the scope of the biology that they are able to cover. For example, a
level 2 PPI network with hundreds of proteins may be constructed from a
single co-precipitation assay, while just one relationship in a level 4
or 5 model may synthesize the results of many separate experiments. The
5 levels are expressed visually in Figure 2 and are explained in further
detail below.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

\textbf{Figure 2.} The 5 levels of network models. Scope refers
generally to the size of networks and the volume of interactions
recorded at that level. Mechanistic detail refers to whether the
stepwise processes of a reaction are explicitly given in the network
model. Causality refers to whether the network model can be used to make
causal inferences that can be statistically interrogated.

\emph{Gene Sets} , as the name implies, are curated lists of genes
grouped by association with a particular phenotypic outcome, molecular
pathway, or cellular event. Gene sets, although not networks per se, are
often derived from network representations, such as boundaries of KEGG
pathways. Pathway boundaries are
\emph{fiat}boundaries\textsuperscript{24}, induced primarily through
human demarcation. For example, despite covering the same biological
processes, KEGG pathways contain 4 times more entities on average
compared to BioCyc\textsuperscript{25} pathways, primarily due to
differences in curation guidelines. They also provide substantially
different results when these fiat boundaries are used as input for gene
set enrichment tasks \textsuperscript{26}. Although they encompass well
described biological mechanisms, gene sets do not contain mechanistic
detail in the form of directed and/or signed edges. Approaches at this
level typically perform explanation/extraction. Typically, this involves
testing for statistical enrichment of gene sets or their components to
propose explanations for observed cellular behavior, e.g. highlighting
the most dramatically enriched pathway in a cancer biopsy to determine
possible therapeutic targets. This can also be extended to a phenotype
prediction task if the gene set describes a particular phenotype, e.g. a
gene set composed of markers for epithelial to mesenchymal transition in
breast cancer cells.

\emph{Interaction Networks} represent interactions between biological
entities by unsigned, undirected edges. These edges don't contain any
cause/effect semantics and therefore can't be used to make causal
predictions. These simple interactions can be detected in large
quantities by through high-throughput methods, hence there are millions
of interactions present in existing data sources, an order of magnitude
more than subsequent levels. Additionally, interaction networks are
simple to align and integrate with one another, as each entity is
typically represented by only one node in the graph. They are commonly
used as a starting point in untargeted high throughput assays where
quantitative measurements are recorded for many entities and the
researcher wants to look broadly at their data without necessarily
seeking causal explanations.

\emph{Activity Flow} networks, like interaction networks, typically
contain one node for a given entity, allowing for easy integration of
multiple networks so long as naming conventions for entities are
consistent. In contrast, activity flow networks add a layer of
cause/effect semantics in the form of directed and, sometimes, signed
edges. For this reason, activity flow networks can be used for making
causal predictions, and while these networks are considerably smaller
than level 2, they are expansive enough that they can still be used for
interrogating untargeted high-throughput datasets.

\emph{Process Description} networks illustrate the mechanistic detail of
how a reaction occurs. Because these models describe the stepwise events
in a reaction, it is not uncommon that one edge could be informed by
multiple sources, making them very well grounded in the literature. They
are considerably smaller given that most, if not all, of their curation
must be done by hand. Unlike prior levels, these diagrams represent the
same entity with multiple nodes, corresponding to each of that entity's
states through a sequence of events, including covalent modifications,
cellular/subcellular locations, and/or complex memberships. This makes
the integration of multiple process description networks a considerably
more intensive exercise relative to levels 2 and 3.

\emph{Quantitative Models} were originally derived from canonical
chemical equations. These models are like process description networks
in that these representations explicitly model the stepwise process of a
reaction, but they are expanded to include quantitative factors like
concentrations, stoichiometry, and rate constants. An example of a
quantitative model would be a metabolic pathway represented as a
bipartite graph of substrates, products, catalysts, and reactants. They
are often used to describe systems which are very intensively studied
and are typically very small compared to the preceding levels, due to
the volume of research required to inform their curation.

Some networks and models fall into two consecutive categories. For
example, the networks used in PhosphositePlus\textsuperscript{27} and
CausalPath\textsuperscript{28} are represented as activity flow
networks, however both describe posttranslational modifications, which
lends to the mechanistic detail in a process description network.
Molecular Interaction Maps (MIMs)\textsuperscript{29} are equivalent in
semantic detail to process description but retain an activity flow-like
visualization. Finally, some large process description databases curate
quantitative values such as enzymatic constants to allow for
construction of quantitative models\textsuperscript{30}.

\textbf{Classifying Methods within the Framework}

To contextualize the above framework, we conducted a limited survey of
algorithms and software tools which use networks as prior information in
the analysis of omics data and categorized these methods based on the
level of network they employ and the computational task(s) they
accomplish. Given that hundreds of new algorithms and approaches are
published every year, an exhaustive survey is not feasible for the
present review. Methods are extremely diverse in their input,
operations, and output, but in any case, the overarching goal of these
approaches is to produce something that can be perceived and/or
interpreted by a human user. We do not include cross-method comparison
of features and performance. For each method we give a brief synopsis,
discuss key aspects of the method, and finally summarize any real-world
applications or validation in a biological system that the authors
describe in their manuscript.

\textbf{Level 1: Gene Sets}

\textbf{ReactomeGSA} \textsuperscript{31}

ReactomeGSA is an explanation extraction tool for comparative
pathway-based gene set analysis. ReactomeGSA defines its gene sets from
the pathways curated in the Reactome\textsuperscript{5} database, then
conducts a comparative gene set analysis at a pathway level to explain
and biologically ground the differences between omics datasets, making
it a quintessential explanation extraction tool with some phenotype
prediction applications.

ReactomeGSA performs a differential expression analysis on a pathway
scale for five quantitative omics data types, including microarray
intensities, transcriptomics counts (raw or normalized), proteomics
(spectral counts or intensity based quantitative data). ReactomeGSA is
also capable of analyzing single-cell RNAseq (scRNAseq) datasets by
calculating the mean expression for genes in a cluster and using this as
`pseudo-bulk' RNAseq to describe the cluster. For the analysis the user
selects an appropriate methodology depending on their datatype and
computational capacity. ReactomeGSA currently accommodates three gene
set analysis methodologies, PADOG\textsuperscript{32},
Camera\textsuperscript{33}, and ssGSEA via GSVA\textsuperscript{34}. The
results of the analysis are mapped to the complete pathway browser
database, where the user can view the pathway-level enrichment scores in
the hierarchical `tree-view' which also descending into individual
pathways to view the differential gene expression values mapped to the
corresponding genes in each pathway.

To demonstrate the clinical applications of ReactomeGSA the authors
conducted a comparative pathway analysis of tumor induced
plasmablast-like B-cell (TIPB) signaling across five TCGA cancer
cohorts. These included melanoma, breast cancer, ovarian cancer, lung
adenocarcinoma, and lung squamous cell carcinoma. The authors compared
TIPB-high vs -low in each cohort, in addition to some cross cohort
comparisons. They found that pathway-based gene sets describing B-cell
receptor signaling and apoptosis were enriched for TIPB-high melanoma
and ovarian cancer samples, which they later correlated with improved
survival in these groups. When compared to melanoma, lung adenocarcinoma
samples with high TIPB retained a unique signaling phenotype. These
samples exhibited downregulation of the pathway-based gene sets
describing B-cell receptor signaling, NF-kB signaling, p53 associated
DNA damage repair, cell cycle, and apoptosis.

\textbf{Level 2: Interaction Networks}

\textbf{SWAN} \textsuperscript{35}

SWAN incorporates prior knowledge network into the cutoff selection
process for correlation networks. This is a hybrid inference/extraction
algorithm that redefines the inference task as defining a cutoff
threshold such that the agreement with prior information is maximized.

SWAN works by first constructing a correlation network from the data.
The network is then filtered to remove edges that are not statistically
significant. The remaining edges are then ranked according to their
strength. Prior interaction networks can be easily integrated with
inferred correlation networks. SWAN then selects a cutoff for the
network based on prior knowledge. To calculate the correlation, SWAN
uses shrinkage partial correlation based on the GeneNet algorithm --
although this approach can be generalized to any correlation metric. The
overlap is measured using Fisher's exact test p-value, which indicates
the agreement between the calculated correlation network and prior
knowledge. The optimal cutoff is defined as the point where the overlap
is maximal.

SWAN was tested on pan-cancer data of 26 cancer types extracted from The
Cancer Genome Atlas (TCGA). The network was able to identify enriched
genes (OG) in the elevated pathways and suppressed genes (TSG) within
suppressed pathways with a p-value \textless{} 0.05. This result was
compared with the Gene Set Enrichment Analysis (GSEA) and revealed that
SWAN outperformed GSEA. To check if SWAN can study race-specific CNA
patterns, ovarian cancer samples from an African American population
were collected, and non-Hispanic white patients were used as control.
SWAN identified that the cytokine pathway was elevated in the former
population which can be mapped to the overall poor prognosis in these
patients. Furthermore, SWAN was also able to figure out the effect of
the knockdown of metallothionein 2A which led to an increase in
formation of u\selectlanguage{english}H2AX foci.

\textbf{GLRP} \textsuperscript{36}

Graph Layer-wise Relevance Propagation (GLRP) is a novel method that
extends the Layer-wise Relevance Propagation (LRP) technique to Graph
Convolutional Neural Networks (Graph-CNN). LRP is an existing technique
that explains the decisions made by deep learning models. The primary
goal of GLRP is to explain the classification results of various omics
data and molecular networks which could facilitate the decision-making
processes in personalized medicine.

This is a unimodal, hybrid phenotype prediction and
explanation/extraction algorithm that aims to ground predicted graphs to
known protein-protein interaction networks. GLRP interprets the
classification output by leveraging the molecular network and also
produces patient-specific subnetworks that can be used to explain
clinical outcomes and therapeutic vulnerabilities.

GLRP was trained on gene expression datasets of breast cancer and human
umbilical vein endothelial cells (HUVECs). Their predictive performance
was evaluated using the 10-fold cross-validation method. In the breast
cancer study, GLRP was used to classify patients into metastatic and
non-metastatic groups. The results were compared with the classification
performance of random forest and glmgraph models as well as weighted
gene co-expression network analysis. GLRP outperformed the other models,
and the developed patient-specific subnetworks identified meaningful
features in breast cancer samples.

\textbf{Level 3: Activity Flow}

\textbf{CausalPath} \textsuperscript{28}

CausalPath is an explanation extraction algorithm which uses causal
relationships from Pathway Commons\textsuperscript{37} as priors to
extract a mechanistic explanation for the patterns in proteomics,
phospho-proteomics, and transcriptomics datasets. CausalPath produces
causal hypotheses about the differences between comparable datasets, for
example, biopsies from different conditions or timepoints, or the
covariance across a cohort. These explanations are presented as an
activity flow sub-network, which can also be expanded as a more detailed
process description network. The method mimics a biologist's traditional
approach of explaining changes in data using prior knowledge, but does
this at the scale of hundreds of thousands of reactions.

CausalPath employs 12 pre-defined patterns that describe causal
relationships between biological entities in the network, for example, a
kinase phosphorylating another protein implies an expected correlation
between the kinase's abundance or activating phosphorylation with the
phosphorylation of the target protein). Using these pre-defined
patterns, CausalPath assembles an activity flow network showing the
causal relationships supported by the proteomic, phosphoproteomic and
transcriptomic data.

CausalPath was applied to several publicly available datasets covering a
wide range of scenarios and biological questions. In a set of
time-resolved epidermal growth factor (EGF) stimulation experiments,
CausalPath detected EGFR activation via downstream signaling of MAPKs,
including feedback inhibition on EGFR. From ligand-induced and
drug-inhibited cell-line experiments, CausalPath estimated the precision
of its predictions. From CPTAC (Clinical Proteomic Tumor Analysis
Consortium) protein mass spectrometry datasets for ovarian and breast
cancer, CausalPath elucidated general and subtype-specific signaling, as
well as regulators of well-known cancer proteins. In RPPA (Reverse Phase
Protein Array) experimental datasets of 32 TCGA (Cancer Genome Atlas)
cancer studies, CausalPath found a core signaling network that is
recurrently identified across many cancer types.

\textbf{CoPPNet} \textsuperscript{38}CoPPNet is a phenotype prediction
tool which uses level 3 networks to accomplish unsupervised subtyping of
cancer. CoPPNet first constructs a functional network of phosphorylation
sites based on their co-phosphorylation patterns, and then identifies
relevant subnetworks that correlate to subtypes.

The method first constructs a PhosphoSite Functional Association (PSFA)
Network that models potential functional relationships between
phosphosite pairs. Edges are inferred using information from existing
databases: PTMCode is used for functional, structural and evolutionary
associations, PhosphositePLUS for kinase-substrate associations and
inferring shared-kinase pairs, and BIOGRID PPI for protein-protein
interactions. Data from MS-based phospho-proteomics assays is then
incorporated using bi-weight mi-correlation to assess co-phosphorylation
(Co-P) of phosphosite pairs connected in the PSFA network, resulting in
a weighted PSFA network. Finally, subnetworks enriched in highly
co-phosphorylated phosphosite pairs are extracted. To achieve this, the
weighted PSFA network is searched for subnetworks using a greedy
algorithm to maximize Co-P score, resulting in a list of ranked
subnetworks referred to as Co-P modules. Modules are then assessed for
statistical significance, subtype specificity, predictive ability, and
reproducibility.

CoPPNet was applied to two independent breast cancer phospho-proteomic
datasets. The phosphorylation patterns of identified Co-P modules were
found to strongly correlated with known subtypes (Luminal vs. Basal),
and Co-P modules were shown to be reproducible across datasets from
different studies.

\textbf{IntOMICS} \textsuperscript{39}

IntOMICS is a Bayesian framework that reconstructs gene regulatory
networks from integrated multi-omic data including; gene expression, DNA
methylation, and copy number variation data as well as prior knowledge
from KEGG (regulatory relationships) and target gene-transcription
factor associations from ENCODE. This is a network inference algorithm
for level 3 representation.

The IntOMICS framework is based on the Werhli and Husmeier (W\&H)
algorithm\textsuperscript{40}, which encodes each omics data source into
separate energy functions. IntOMICS integrates the omics data by
encoding the energy functions into a Gibbs distribution. Effects of
multiple upstream controllers are additive. The inverse temperature
hyperparameters for each source are tuned by sampling from the posterior
distribution with Markov chain Monte Carlo (MCMC). Unlike the original
W\&H algorithm, IntOMICS uses an adaptive MCMC simulation and Markov
blanked resampling to improve the MCMC convergence speed.

For validation and comparison, the authors used IntOMICS to understand
the mechanism of chemoresistance using primary colon cancer samples from
a randomized Phase III clinical trial. Their goal was to identify
downstream mediators of \emph{ABCG2} , which has been shown to
contribute to chemoresistance. They compared the network generated from
IntOMICS to those from an unaltered implementation of the W\&H algorithm
as well as two other multi-omic integration frameworks, RACER and
KiMONo. IntOMICS nominated more downstream mediators of \emph{ABCG2} ,
which may be important for chemoresistance in colon cancer and survival.

\textbf{Level 4: Process Description}

\textbf{ScFEA/FLUXestimator} \textsuperscript{41}

Single cell flux estimation analysis (scFEA) is a prediction tool that
infers metabolic flux from scRNAseq data using hand-curated metabolic
pathways from KEGG as well as some hand curated mechanisms as prior
knowledge. In the web-application of scFEA, FLUXestimator, metabolic
pathways from Recon3d are also available.

scFEA constructs a reduced network based on the prior network topology,
genes with significant non-zero expression, and any preferred
sub-network specifications from the user. This reduced network, termed a
factor graph, is composed of metabolic modules (variables), representing
groups of connected reactions, linked by intermediate metabolites
(factors). For estimation, scFEA combines traditional flux-balance
analysis with an optimization goal of minimizing influx/outflux
imbalances while also incorporating enzyme transcript levels as a proxy
for enzyme activity to further constrain the model search space.

scFEA was validated experimentally using matched scRNAseq and targeted
metabolomics data collected from cells exposed to hypoxia and/or APEX1
knockdown. The authors observed that the predicted flux changes were
consistent with the observed changes in the metabolomics data.

\textbf{Fast-SL} \textsuperscript{42}

Fast-SL uses iterative search space reduction for rapid identification
of synthetic-lethal gene sets up to an order of four. The overarching
goal of this algorithm is to improve the computational efficiency and
speed of synthetic lethality prediction from large metabolic networks.
Because of its improved computational efficiency, Fast-SL is able to
predict higher order synthetic lethal gene sets.

For the deletion of a gene/reaction to be considered lethal, the maximum
growth calculated by flux balance analysis (FBA) must be smaller than
the specified cutoff (v\textsubscript{co}), typically 1\% of the
wild-type growth rate. The algorithm calculates the lethality cutoff
v\textsubscript{co} as 1\% of the `minimum norm', which corresponds to
the maximum wild-type growth rate. Beginning with single lethal (first
order) reactions, the search space is constrained to all reactions in
the system with a nonzero flux in the distribution from the prior step.
These reactions are denoted J\textsubscript{nz}. Reactions in
J\textsubscript{nz} are then exhaustively tested for single-lethality by
setting the flux of each individual reaction to zero, calculating the
biomass flux, and comparing it to the cutoff, v\textsubscript{co}. If
the biomass flux is less than the cutoff, the reaction is considered
lethal and added to the set of single lethal reactions
(J\textsubscript{sl}). Reactions in J\textsubscript{sl} are then pruned
from the search space for double lethal (second order) reactions
(J\textsubscript{db}). When calculating third order lethal reactions,
the search space would be further reduced as reactions in
J\textsubscript{db} are removed from J\textsubscript{nz}. The result is
an iteratively pruned search space which becomes smaller with increasing
order of lethal gene sets.

Using Fast-SL, the authors successfully identified lethal gene sets up
to an order of four in \emph{E. coli, S.Typhimurium, and M.
tuberculosis} . They validated these results with an exhaustive search
for first, second, and third order lethal gene sets. The authors
reported an ``exact match'' between the number of lethal sets identified
in the exhaustive search and those identified by Fast-SL. The authors
also compared Fast-SL to another algorithm, SL Finder, which is also
intended to reduce the computational intensity of identifying synthetic
lethal gene sets. Fast-SL identified 127 novel triplets in \emph{E.
coli} which were not found by SL Finder. These novel triplets were
predominantly involved in central carbon metabolism and amino acid
synthesis.

\textbf{Level 5: Quantitative Models}

\textbf{INTEGRATE} \textsuperscript{43}

INTEGRATE is a computational pipeline that integrates metabolomics and
transcriptomics data to characterize multi-level metabolic regulation.
The pipeline first computes differential reaction expression from
transcriptomic data and uses constraint-based modeling to predict if the
differential expression of metabolic enzymes directly originates
differences in metabolic fluxes. In parallel, the pipeline uses
metabolomics to predict how differences in substrate availability
translate into differences in metabolic fluxes. It is an
upscaling/inference algorithm.

This algorithm uses level 4 stoichiometries as constraints for flux
balance analysis, RNA levels as enzyme abundance proxies to predict
metabolomic fluxes then compare it with the observed data. The prior
information is a further curated subset of RECON3D metabolomic
construction called ERGO2. Once the metabolomic and transcriptomic data
is mapped to the network intermediary scores are calculated for Feasible
Flux Distributions (based on static analysis), Reaction Activity Scores
(based on RNA levels) and Reaction Propensity Score (based on substrate
levels). Agreement between these metrics, calculated by Variation
Concordance Analysis is the final output and can be used for both
explanation/extraction and upscaling.

The pipeline was applied to a set of immortalized normal and cancer
breast cell lines. The results showed that the pipeline was able to
identify metabolic reactions that are regulated at both the metabolic
and gene expression levels. The pipeline was also able to identify
metabolic reactions that are differentially regulated in cancer cells
compared to normal cells.

\textbf{SUMMER} \textsuperscript{44}

SUMMER (Shiny Utility for Metabolomics and Multiomics Exploratory
Research) uses reaction rate potentials to perform pathway enrichment
analysis on metabolomic data. SUMMER uses level 4 metabolomic networks
from the KEGG database\textsuperscript{7}. This is a network upscaling
method from level 4 to level 5 as a first step of quantitative modeling.

SUMMER uses reaction rate potentials to model the feedback effects
between an enzyme, its substrate(s), and its product(s). It also infers
the catalytic activity of each enzyme using integrated transcriptomics
or proteomics data. The method then uses this integrated model to
understand the change in reaction rate potentials between a perturbed
condition and a reference condition. The resulting ratio of the
resulting reaction rate potentials between a perturbed condition and a
reference condition is then bootstrapped to calculate a ranking score
between each reaction. Using the rank scores, SUMMER identifies the
``hotspot'' reactions in the network.

The authors applied SUMMER to re-analyze a metabolomic and
transcriptomic dataset generated from a mouse model of accelerated aging
and dementia. They wanted to understand the pathways that were altered
by a neuroprotective compound. They found that treatment with this
compound was associated with an increase in acetyl-CoA activity and an
enrichment of TCA cycle activity.

\textbf{Discussion}

Pathway or network analysis is often viewed as a one-size-fits-all
approach that can be applied universally to any dataset. However, as our
review demonstrates, network analysis encompasses a broad range of
approaches with unique data requirements and diverse PKN sources. Any
new project or program incorporating network analysis should carefully
define the task at hand, explore the available prior information
sources, and consider the integration and scalability challenges
associated with each resource.

Networks and network-based methods are invaluable tools for the analysis
of omics data. It is widely recognized that the selection of prior
knowledge network (PKN) can influence the outcome of analysis, therefore
selection of an appropriate PKN is key to producing reliable results.
With such an enormous suite of network resources available it can become
overwhelming to select an appropriate model. To address this challenge,
we present a framework for classifying PKNs and network-based methods.
This framework characterizes PKNs in terms of their scope, mechanistic
detail, and ability to inform causal predictions. We also outline some
common computational tasks to describe the aim of network-based
analyses. To contextualize the framework, we sampled a handful of
published network-based methods and discussed their PKN selection, the
tasks they aim to accomplish, their approach to analysis and their
real-world applications. While this sampling is not exhaustive, it
offers readers a practical glimpse into the application of the
framework.

Looking ahead, we anticipate network analysis to gain even greater
prominence, shifting towards more detailed approaches for two reasons.
First, the rapid advancements in multi-modal, spatial, and single-cell
modalities have enabled the measurement of subcellular protein
localization changes, post-translational modifications (PTMs), and
molecular complexes at a single-cell scale using imaging
modalities\textsuperscript{45}.This wealth of information primarily
resides in level 4 networks and, to a lesser extent, in level 3
networks. Effectively harnessing these rich datasets will necessitate
the utilization of more detailed PKNs. Second, recent breakthroughs in
large language models\textsuperscript{46} have significantly enhanced
our ability to extract knowledge from the literature. Combining this
capability with crowd-sourcing\textsuperscript{47} and human-in-the-loop
systems\textsuperscript{48} holds the potential to reduce curation costs
by two orders of magnitude\textsuperscript{47} enabling near-complete
curation of the entire biomedical literature on biological molecular
processes. The increased completeness of PKNs, along with improved and
larger datasets, will unlock extensive application areas for
increasingly sophisticated network models.

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