Biological network inference

The general cycle to modeling biological networks is as follows:{{citation needed|date=May 2022}}

1. Prior knowledge
2. * Involves a thorough literature and database search or seeking an expert's opinion.
3. Model selection
4. * A formalism to model your system, usually an ordinary differential equation, boolean network, or Linear regression models, e.g. Least-angle regression, by Bayesian network or based on Information theory approaches.{{cite journal | vauthors = van Someren EP, Wessels LF, Backer E, Reinders MJ | title = Genetic network modeling | journal = Pharmacogenomics | volume = 3 | issue = 4 | pages = 507–525 | date = July 2002 | pmid = 12164774 | doi = 10.1517/14622416.3.4.507 }}{{cite journal | vauthors = Banf M, Rhee SY | title = Computational inference of gene regulatory networks: Approaches, limitations and opportunities | journal = Biochimica et Biophysica Acta (BBA) - Gene Regulatory Mechanisms | volume = 1860 | issue = 1 | pages = 41–52 | date = January 2017 | pmid = 27641093 | doi = 10.1016/j.bbagrm.2016.09.003 | doi-access = free }} it can also be done by the application of a correlation-based inference algorithm, as will be discussed below, an approach which is having increased success as the size of the available microarray sets keeps increasing {{cite journal | vauthors = Faith JJ, Hayete B, Thaden JT, Mogno I, Wierzbowski J, Cottarel G, Kasif S, Collins JJ, Gardner TS | display-authors = 6 | title = Large-scale mapping and validation of Escherichia coli transcriptional regulation from a compendium of expression profiles | journal = PLOS Biology | volume = 5 | issue = 1 | pages = e8 | date = January 2007 | pmid = 17214507 | pmc = 1764438 | doi = 10.1371/journal.pbio.0050008 | doi-access = free }}{{cite journal | vauthors = Raimondo S, De Domenico M | title = Measuring topological descriptors of complex networks under uncertainty | journal = Physical Review E | volume = 103 | issue = 2–1 | pages = 022311 | date = February 2021 | pmid = 33735966 | doi = 10.1103/PhysRevE.103.022311 | arxiv = 2009.06326 | bibcode = 2021PhRvE.103b2311R | s2cid = 221655165 }}
5. Hypothesis/assumptions
6. Experimental design
7. Data acquisition
8. * Ensure that high quality data is collected with all the required variables being measured
9. Network inference
10. * This process is mathematical rigorous and computationally costly.
11. Model refinement
12. * Cross-check how well the results meet the expectations. The process is terminated upon obtaining a good model fit to data, otherwise, there is need for model re-adjustment.

A network is a set of nodes and a set of directed or undirected edges between the nodes. Many types of biological networks exist, including transcriptional, signalling and metabolic. Few such networks are known in anything approaching their complete structure, even in the simplest bacteria. Still less is known on the parameters governing the behavior of such networks over time, how the networks at different levels in a cell interact, and how to predict the complete state description of a eukaryotic cell or bacterial organism at a given point in the future. Systems biology, in this sense, is still in its infancy {{citation needed|date=March 2024}}.

There is great interest in network medicine for the modelling biological systems. This article focuses on inference of biological network structure using the growing sets of high-throughput expression data for genes, proteins, and metabolites.{{cite journal | vauthors = Tieri P, Farina L, Petti M, Astolfi L, Paci P, Castiglione F | title = Network Inference and Reconstruction in Bioinformatics | journal = Encyclopedia of Bioinformatics and Computational Biology | volume = 2 | pages = 805–813 | date = 2018 | doi = 10.1016/B978-0-12-809633-8.20290-2| isbn = 9780128114322 | s2cid = 65155962 }} Briefly, methods using high-throughput data for inference of regulatory networks rely on searching for patterns of partial correlation or conditional probabilities that indicate causal influence.{{cite journal | vauthors = Marbach D, Costello JC, Küffner R, Vega NM, Prill RJ, Camacho DM, Allison KR, Kellis M, Collins JJ, Stolovitzky G | display-authors = 6 | title = Wisdom of crowds for robust gene network inference | journal = Nature Methods | volume = 9 | issue = 8 | pages = 796–804 | date = July 2012 | pmid = 22796662 | pmc = 3512113 | doi = 10.1038/nmeth.2016 }}{{cite book | vauthors = Sprites P, Glamour C, Scheines R | year = 2000 | title = Causation, Prediction, and Search: Adaptive Computation and Machine Learning | edition = 2nd | publisher = MIT Press }} Such patterns of partial correlations found in the high-throughput data, possibly combined with other supplemental data on the genes or proteins in the proposed networks, or combined with other information on the organism, form the basis upon which such algorithms work. Such algorithms can be of use in inferring the topology of any network where the change in state of one node can affect the state of other nodes.

Genes are the nodes and the edges are directed. A gene serves as the source of a direct regulatory edge to a target gene by producing an RNA or protein molecule that functions as a transcriptional activator or inhibitor of the target gene. If the gene is an activator, then it is the source of a positive regulatory connection; if an inhibitor, then it is the source of a negative regulatory connection. Computational algorithms take as primary input data measurements of mRNA expression levels of the genes under consideration for inclusion in the network, returning an estimate of the network topology. Such algorithms are typically based on linearity, independence or normality assumptions, which must be verified on a case-by-case basis.{{cite journal | vauthors = Oates CJ, Mukherjee S | title = Network Inference and Biological Dynamics | journal = The Annals of Applied Statistics | volume = 6 | issue = 3 | pages = 1209–1235 | date = September 2012 | pmid = 23284600 | pmc = 3533376 | doi = 10.1214/11-AOAS532 | arxiv = 1112.1047 }} Clustering or some form of statistical classification is typically employed to perform an initial organization of the high-throughput mRNA expression values derived from microarray experiments, in particular to select sets of genes as candidates for network nodes.{{cite journal | vauthors = Guthke R, Möller U, Hoffmann M, Thies F, Töpfer S | title = Dynamic network reconstruction from gene expression data applied to immune response during bacterial infection | journal = Bioinformatics | volume = 21 | issue = 8 | pages = 1626–1634 | date = April 2005 | pmid = 15613398 | doi = 10.1093/bioinformatics/bti226 | doi-access = free }} The question then arises: how can the clustering or classification results be connected to the underlying biology? Such results can be useful for pattern classification – for example, to classify subtypes of cancer, or to predict differential responses to a drug (pharmacogenomics). But to understand the relationships between the genes, that is, to more precisely define the influence of each gene on the others, the scientist typically attempts to reconstruct the transcriptional regulatory network.

{{Main|Gene co-expression network|l1=Gene Co-Expression Network}}

A gene co-expression network is an undirected graph, where each node corresponds to a gene, and a pair of nodes is connected with an edge if there is a significant co-expression relationship between them.

{{Main|Signal transduction}}

Signal transduction networks use proteins for the nodes and directed edges to represent interaction in which the biochemical conformation of the child is modified by the action of the parent (e.g. mediated by phosphorylation, ubiquitylation, methylation, etc.). Primary input into the inference algorithm would be data from a set of experiments measuring protein activation / inactivation (e.g., phosphorylation / dephosphorylation) across a set of proteins. Inference for such signalling networks is complicated by the fact that total concentrations of signalling proteins will fluctuate over time due to transcriptional and translational regulation. Such variation can lead to statistical confounding. Accordingly, more sophisticated statistical techniques must be applied to analyse such datasets.

{{cite journal | vauthors = Oates CJ, Mukherjee S | year = 2012 | title = Structural inference using nonlinear dynamics | journal = CRiSM Working Paper | volume = 12 | issue = 7 }}(very important in the biology of cancer)

{{Main|Metabolic network|l1=Metabolic Network}}

Metabolite networks use nodes to represent chemical reactions and directed edges for the metabolic pathways and regulatory interactions that guide these reactions. Primary input into an algorithm would be data from a set of experiments measuring metabolite levels.

{{Main|Interactome}}

One of the most intensely studied networks in biology, Protein-protein interaction networks (PINs) visualize the physical relationships between proteins inside a cell. in a PIN, proteins are the nodes and their interactions are the undirected edges. PINs can be discovered with a variety of methods including; Two-hybrid Screening, in vitro: co-immunoprecipitation,{{cite book | vauthors = Isono E, Schwechheimer C | title = Plant Developmental Biology | chapter = Co-immunoprecipitation and Protein Blots | volume = 655 | pages = 377–387 | date = 2010 | pmid = 20734274 | doi = 10.1007/978-1-60761-765-5_25 | publisher = Humana Press | isbn = 978-1-60761-765-5 | series = Methods in Molecular Biology | veditors = Hennig L, Köhler C | place = Totowa, NJ }} blue native gel electrophoresis,{{cite journal | vauthors = Wittig I, Braun HP, Schägger H | title = Blue native PAGE | journal = Nature Protocols | volume = 1 | issue = 1 | pages = 418–428 | date = June 2006 | pmid = 17406264 | doi = 10.1038/nprot.2006.62 | s2cid = 19715017 }} and more.{{cite journal | vauthors = Miernyk JA, Thelen JJ | title = Biochemical approaches for discovering protein-protein interactions | journal = The Plant Journal | volume = 53 | issue = 4 | pages = 597–609 | date = February 2008 | pmid = 18269571 | doi = 10.1111/j.1365-313X.2007.03316.x | doi-access = free }}

{{Main|Neural network|l1=Neural Network}}

A neuronal network is composed to represent neurons with each node and synapses for the edges, which are typically weighted and directed. the weights of edges are usually adjusted by the activation of connected nodes. The network is usually organized into input layers, hidden layers, and output layers.

{{Main|Food web|l1=Food Web}}

A food web is an interconnected directional graph of what eats what in an ecosystem. The members of the ecosystem are the nodes and if a member eats another member then there is a directed edge between those 2 nodes.

These networks are defined by a set of pairwise interactions between and within a species that is used to understand the structure and function of larger ecological networks.{{cite journal | vauthors = Bascompte J | title = Disentangling the web of life | journal = Science | volume = 325 | issue = 5939 | pages = 416–419 | date = July 2009 | pmid = 19628856 | doi = 10.1126/science.1170749 | s2cid = 2249052 | bibcode = 2009Sci...325..416B }} By using network analysis we can discover and understand how these interactions link together within the system's network. It also allows us to quantify associations between individuals, which makes it possible to infer details about the network as a whole at the species and/or population level.{{cite journal | vauthors = Croft DP, Krause J, James R | title = Social networks in the guppy (Poecilia reticulata) | journal = Proceedings. Biological Sciences | volume = 271 | issue = Suppl 6 | pages = S516–S519 | date = December 2004 | pmid = 15801620 | pmc = 1810091 | doi = 10.1098/rsbl.2004.0206 }}

{{Main|Chromatin}}

DNA-DNA chromatin networks are used to clarify the activation or suppression of genes via the relative location of strands of chromatin. These interactions can be understood by analyzing commonalities amongst different loci, a fixed position on a chromosome where a particular gene or genetic marker is located. Network analysis can provide vital support in understanding relationships among different areas of the genome.

{{Main|Gene regulatory network}}

A gene regulatory network{{cite journal | vauthors = Emmert-Streib F, Dehmer M, Haibe-Kains B | title = Gene regulatory networks and their applications: understanding biological and medical problems in terms of networks | journal = Frontiers in Cell and Developmental Biology | volume = 2 | pages = 38 | year = 2014 | pmid = 25364745 | pmc = 4207011 | doi = 10.3389/fcell.2014.00038 | doi-access = free }} is a set of molecular regulators that interact with each other and with other substances in the cell. The regulator can be DNA, RNA, protein and complexes of these. Gene regulatory networks can be modeled in numerous ways including; Coupled ordinary differential equations, Boolean networks, Continuous networks, and Stochastic gene networks.

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The initial data used to make the inference can have a huge impact on the accuracy of the final inference. Network data is inherently noisy and incomplete sometimes due to evidence from multiple sources that don't overlap or contradictory data. Data can be sourced in multiple ways to include manual curation of scientific literature put into databases, High-throughput datasets, computational predictions, and text mining of old scholarly articles from before the digital era.

A network's diameter is the maximum number of steps separating any two nodes and can be used to determine the How connected a graph is, in topology analysis, and clustering analysis.

The transitivity or clustering coefficient of a network is a measure of the tendency of the nodes to cluster together. High transitivity means that the network contains communities or groups of nodes that are densely connected internally. In biological networks, finding these communities is very important, because they can reflect functional modules and protein complexes{{cite journal | vauthors = Hsia CW, Ho MY, Shui HA, Tsai CB, Tseng MJ | title = Analysis of dermal papilla cell interactome using STRING database to profile the ex vivo hair growth inhibition effect of a vinca alkaloid drug, colchicine | journal = International Journal of Molecular Sciences | volume = 16 | issue = 2 | pages = 3579–3598 | date = February 2015 | pmid = 25664862 | pmc = 4346914 | doi = 10.3390/ijms16023579 | doi-access = free }}

The uncertainty about the connectivity may distort the results and should be taken into account when the transitivity and other topological descriptors are computed for inferred networks.

Network confidence is a way to measure how sure one can be that the network represents a real biological interaction. We can do this via contextual biological information, counting the number of times an interaction is reported in the literature, or group different strategies into a single score. the [https://www.ebi.ac.uk/training/online/courses/network-analysis-of-protein-interaction-data-an-introduction/building-and-analysing-ppins/assessing-reliability-and-measuring-confidence/ MIscore] method for assessing the reliability of protein-protein interaction data is based on the use of standards.{{cite journal | vauthors = Villaveces JM, Jiménez RC, Porras P, Del-Toro N, Duesbury M, Dumousseau M, Orchard S, Choi H, Ping P, Zong NC, Askenazi M, Habermann BH, Hermjakob H | display-authors = 6 | title = Merging and scoring molecular interactions utilising existing community standards: tools, use-cases and a case study | journal = Database | volume = 2015 | pages = bau131 | date = 2015-01-01 | pmid = 25652942 | pmc = 4316181 | doi = 10.1093/database/bau131 }} MIscore gives an estimation of confidence weighting on all available evidence for an interacting pair of proteins. The method allows weighting of evidence provided by different sources, provided the data is represented following the standards created by the IMEx consortium. The weights are number of publications, detection method, interaction evidence type.

{{Main|Closeness centrality|l1=Closeness}}

Closeness, a.k.a. closeness centrality, is a measure of centrality in a network and is calculated as the reciprocal of the sum of the length of the shortest paths between the node and all other nodes in the graph. This measure can be used to make inferences in all graph types and analysis methods.

{{Main|Betweenness centrality|l1=Betweenness}}

Betweeness, a.k.a. betweenness centrality, is a measure of centrality in a graph based on shortest paths. The betweenness for each node is the number of these shortest paths that pass through the node.

{{Main|Network theory|l1=Network Theory}}

For our purposes, network analysis is closely related to graph theory. By measuring the attributes in the previous section we can utilize many different techniques to create accurate inferences based on biological data.

Topology Analysis analyzes the topology of a network to identify relevant participates and substructures that may be of biological significance. The term encompasses an entire class of techniques such as network motif search, centrality analysis, topological clustering, and shortest paths. These are but a few examples, each of these techniques use the general idea of focusing on the topology of a network to make inferences.

A motif is defined as a frequent and unique sub-graph. By counting all the possible instances, listing all patterns, and testing isomorphisms we can derive crucial information about a network. They're suggested to be the basic building blocks complex biological networks. The computational research has focused on improving existing motif detection tools to assist the biological investigations and allow larger networks to be analyzed. Several different algorithms have been provided so far, which are elaborated in the next section.

Centrality gives an estimation on how important a node or edge is for the connectivity or the information flow of the network. It is a useful parameter in signalling networks and it is often used when trying to find drug targets.{{Cite web |last=EMBL-EBI |title=Centrality analysis {{!}} Network analysis of protein interaction data |url=https://www.ebi.ac.uk/training/online/courses/network-analysis-of-protein-interaction-data-an-introduction/building-and-analysing-ppins/topological-ppin-analysis/centrality-analysis/ |access-date=2022-05-05 |language=en}} It is most commonly used in PINs to determine important proteins and their functions. Centrality can be measured in different ways depending on the graph and the question that needs answering, they include the degree of nodes or the number of connected edges to a node, global centrality measures, or via random walks which is used by the Google PageRank algorithm to assign weight to each webpage.{{Cite journal | vauthors = Brin S, Page L |date=1998-04-01 |title=The anatomy of a large-scale hypertextual Web search engine |journal=Computer Networks and ISDN Systems |series=Proceedings of the Seventh International World Wide Web Conference |language=en |volume=30 |issue=1 |pages=107–117 |doi=10.1016/S0169-7552(98)00110-X |s2cid=7587743 |issn=0169-7552}}

The centrality measures may be affected by errors due to noise on measurement and other causes.{{cite journal | vauthors = Cantwell GT, Liu Y, Maier BF, Schwarze AC, Serván CA, Snyder J, St-Onge G | title = Thresholding normally distributed data creates complex networks | journal = Physical Review E | volume = 101 | issue = 6–1 | pages = 062302 | date = June 2020 | pmid = 32688475 | doi = 10.1103/PhysRevE.101.062302 | arxiv = 1902.08278 | bibcode = 2020PhRvE.101f2302C | s2cid = 67856476 }} Therefore, the topological descriptors should be defined as random variable with the associated probability distribution encoding the uncertainty on their value.

Topological Clustering or Topological Data Analysis (TDA) provides a general framework to analyze high dimensional, incomplete, and noisy data in a way that reduces dimensional and gives a robustness to noise. The idea that is that the shape of data sets contains relevant information. When this information is a homology group there is a mathematical interpretation that assumes that features that persist for a wide range of parameters are "true" features and features persisting for only a narrow range of parameters are noise, although the theoretical justification for this is unclear.{{Cite journal | vauthors = Carlsson G |date=2009 |title=Topology and data |url=https://www.ams.org/bull/2009-46-02/S0273-0979-09-01249-X/ |journal=Bulletin of the American Mathematical Society |language=en |volume=46 |issue=2 |pages=255–308 |doi=10.1090/S0273-0979-09-01249-X |issn=0273-0979|doi-access=free }} This technique has been used for progression analysis of disease,{{cite book | vauthors = Schmidt S, Post TM, Boroujerdi MA, van Kesteren C, Ploeger BA, Pasqua OE, Danhof M | chapter = Disease Progression Analysis: Towards Mechanism-Based Models |date=2011 | veditors = Kimko HH, Peck CC | title = Clinical Trial Simulations: Applications and Trends | series = AAPS Advances in the Pharmaceutical Sciences Series | volume = 1 |pages=433–455 |place=New York, NY |publisher=Springer |language=en |doi=10.1007/978-1-4419-7415-0_19 |isbn=978-1-4419-7415-0 }}{{cite journal | vauthors = Nicolau M, Levine AJ, Carlsson G | title = Topology based data analysis identifies a subgroup of breast cancers with a unique mutational profile and excellent survival | journal = Proceedings of the National Academy of Sciences of the United States of America | volume = 108 | issue = 17 | pages = 7265–7270 | date = April 2011 | pmid = 21482760 | pmc = 3084136 | doi = 10.1073/pnas.1102826108 | doi-access = free | bibcode = 2011PNAS..108.7265N }} viral evolution,{{cite journal | vauthors = Chan JM, Carlsson G, Rabadan R | title = Topology of viral evolution | journal = Proceedings of the National Academy of Sciences of the United States of America | volume = 110 | issue = 46 | pages = 18566–18571 | date = November 2013 | pmid = 24170857 | pmc = 3831954 | doi = 10.1073/pnas.1313480110 | doi-access = free | bibcode = 2013PNAS..11018566C }} propagation of contagions on networks,{{cite journal | vauthors = Taylor D, Klimm F, Harrington HA, Kramár M, Mischaikow K, Porter MA, Mucha PJ | title = Topological data analysis of contagion maps for examining spreading processes on networks | journal = Nature Communications | volume = 6 | issue = 1 | pages = 7723 | date = July 2015 | pmid = 26194875 | pmc = 4566922 | doi = 10.1038/ncomms8723 | arxiv = 1408.1168 | bibcode = 2015NatCo...6.7723T }} bacteria classification using molecular spectroscopy,{{cite journal | vauthors = Offroy M, Duponchel L | title = Topological data analysis: A promising big data exploration tool in biology, analytical chemistry and physical chemistry | journal = Analytica Chimica Acta | volume = 910 | pages = 1–11 | date = March 2016 | pmid = 26873463 | doi = 10.1016/j.aca.2015.12.037 | bibcode = 2016AcAC..910....1O }} and much more in and outside of biology.

The shortest path problem is a common problem in graph theory that tries to find the path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized. This method can be used to determine the network diameter or redundancy in a network. there are many algorithms for this including Dijkstra's algorithm, Bellman–Ford algorithm, and the Floyd–Warshall algorithm just to name a few.

Cluster analysis groups objects (nodes) such that objects in the same cluster are more similar to each other than to those in other clusters. This can be used to perform pattern recognition, image analysis, information retrieval, statistical data analysis, and so much more. It has applications in Plant and animal ecology, Sequence analysis, antimicrobial activity analysis, and many other fields. Cluster analysis algorithms come in many forms as well such as Hierarchical clustering, k-means clustering, Distribution-based clustering, Density-based clustering, and Grid-based clustering.

Gene annotation databases are commonly used to evaluate the functional properties of experimentally derived gene sets. Annotation Enrichment Analysis (AEA) is used to overcome biases from overlap statistical methods used to assess these associations.{{cite journal | vauthors = Glass K, Girvan M | title = Annotation enrichment analysis: an alternative method for evaluating the functional properties of gene sets | journal = Scientific Reports | volume = 4 | issue = 1 | pages = 4191 | date = February 2014 | pmid = 24569707 | pmc = 3935204 | doi = 10.1038/srep04191 | bibcode = 2014NatSR...4E4191G }} It does this by using gene/protein annotations to infer which annotations are over-represented in a list of genes/proteins taken from a network.

• Cytoscape tool
• Bayesian probability
• Network medicine

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{{DEFAULTSORT:Biological Network Inference}}

Category:Bioinformatics

Category:Systems biology

Category:Inference