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Data-driven modelling of signal-transduction networks

Key Points

  • New experimental techniques are allowing the generation of complex data sets that characterize signal-transduction networks. It is no longer possible to inspect these data by intuition to extract the maximal amount of information that is embedded within them.

  • 'Data-driven models' are mathematical approaches that provide simplified representations of complex data sets. They are based solely on analysing the data itself, without having to make any assumptions about the underlying mechanisms.

  • This User's guide introduces three data-driven modelling approaches: clustering, principal components analysis (PCA), and partial least squares (PLS). Clustering provides a means for data organization, whereas PCA is a method for data condensation and PLS is a technique for data prediction.

  • Clustering groups observations together that have similar projections in the high-dimensional space defined by the signalling variables. Similarity can be defined by several difference distance metrics, such as Euclidean distance (for absolute distances) and Pearson distance (for correlations).

  • PCA and PLS factorize a data set into the product of two vectors (a scores vector and a loadings vector) that capture the leading eigenvalues of the covariance of the data. PCA calculates scores and loadings vectors to maximize the variance that is captured in the starting data matrix. By contrast, PLS calculates scores and loadings vectors to maximize the relationship between a matrix of independent variables and a matrix of dependent variables.

  • Data-driven models are poised to become standard tools in analysing signalling networks as complex protein data sets become easier to acquire and more difficult to interpret.

Abstract

New technologies are permitting large-scale quantitative studies of signal-transduction networks. Such data are hard to understand completely by inspection and intuition. 'Data-driven models' help users to analyse large data sets by simplifying the measurements themselves. Data-driven modelling approaches such as clustering, principal components analysis and partial least squares can derive biological insights from large-scale experiments. These models are emerging as standard tools for systems-level research in signalling networks.

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Figure 1: Alternative representations of a systems biology data set.
Figure 2: Clustering of row and column vectors by different distance metrics.
Figure 3: Principal components identified by PCA and PLS.

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Acknowledgements

The work cited in this review was supported by grants from the National Institutes of Health to M.B.Y. and an American Cancer Society postdoctoral fellowship to K.A.J.

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Correspondence to Michael B. Yaffe.

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Glossary

Matrix

A table of numbers. Alternatively, a matrix can be viewed as an arrangement of row or column vectors.

Vector

A mathematical quantity that has both magnitude (or length) and direction. The entries of a vector specify the magnitude of its projection in different directions.

Linear algebra

A branch of mathematics that involves linear manipulations of vectors and matrices.

Transformation

A mathematical function that can be applied to vectors and matrices.

Row vector

A vector that is composed of one entire row of a matrix with dimensions that are specified by the matrix columns.

Euclidean distance

A mathematical quantity that calculates the measurable geometric distance between two vectors pointing from a common origin.

Column vector

A vector that is composed of one entire column of a matrix with dimensions that are specified by the matrix rows.

Pearson distance

A mathematical quantity that calculates the difference in direction between two vectors pointing from a common origin.

k-means clustering

A clustering technique in which observations are grouped into a fixed number of pre-specified clusters called centroids.

Eigenvalue

A mathematical quantity that provides the scaling factor for an eigenvector of a given transformation. For PCA, eigenvalues quantify the contribution of different portions of the data set to the overall measured variation.

Scores vector

The principal component vector that describes how strongly each observation projects along the principal component.

Loadings vector

The principal component vector that describes how strongly each measured signal contributes to the principal component.

Unsupervised analysis

A type of computational learning approach in which the expected output is not specified. Hierarchical clustering and PCA are unsupervised analyses.

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Janes, K., Yaffe, M. Data-driven modelling of signal-transduction networks. Nat Rev Mol Cell Biol 7, 820–828 (2006). https://doi.org/10.1038/nrm2041

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