A systems approach to integrative biology: an overview of statistical methods to elucidate association and architecture

Abstract

An organism's ability to maintain a desired physiological response relies extensively on how cellular and molecular signaling networks interpret and react to environmental cues. The capacity to quantitatively predict how networks respond to a changing environment by modifying signaling regulation and phenotypic responses will help inform and predict the impact of a changing global enivronment on organisms and ecosystems. Many computational strategies have been developed to resolve cue-signal-response networks. However, selecting a strategy that answers a specific biological question requires knowledge both of the type of data being collected, and of the strengths and weaknesses of different computational regimes. We broadly explore several computational approaches, and we evaluate their accuracy in predicting a given response. Specifically, we describe how statistical algorithms can be used in the context of integrative and comparative biology to elucidate the genomic, proteomic, and/or cellular networks responsible for robust physiological response. As a case study, we apply this strategy to a dataset of quantitative levels of protein abundance from the mussel, Mytilus galloprovincialis, to uncover the temperature-dependent signaling network.

Fig. 1

Relating data type and dimension to modeling strategies. Association, architecture, and regulation are three broad paradigms for mathematical modeling of biological systems. When the number of observed variables is significantly greater than the number of experimental conditions, computational strategies that inform association and correlation are most applicable. As the number of experimental conditions increases, one can begin to infer network topology and architecture. Regulation is best understood in the context of time, when system dynamics are appropriately evaluated.

Fig. 2.

(A) Heatmap of protein abundances in M. galloprovincialis. Protein abundances are normalized by taking the z-score of each predictor variable across conditions. Columns represent protein abundances at the given temperature in °C relative to those at 13°C. This figure was produced from data in Tomanek and Zuzow (2010). Protein names are followed by the ID number to differentiate similar proteins. Ward hierarchical clustering reveals that proteins in similar functional groups exhibit similar protein expression data. Tight clustering of the tubulin family shows that the experimental design and clustering method capture most of the variance in the data. PCA of relative protein abundances in M. galloprovincialis at 13°C, 24°C, 28°C and 32°C. The scores (B) and loadings (C) from PC decomposition are shown with the inclusion of the first two PCs. The scores show that the data at 13°C and 24°C have the most similarity. The loadings are colored according to their putative functional group. Both α-tubulin and β-tubulin proteins are labeled and cluster tightly together.

Fig. 3.

(A) Undirected protein regulatory network in M. galloprovincialis. Pearson correlation coefficients are used to identify nodes, or proteins, that are similarly regulated and subsequently clustered. Temperature, highlighted in the shaded subnetwork, is shown to interact with P23 (gelsolin), which interacts with P13 (nucleoside diphosphate kinase), P18B (Cu-Zn superoxide dismutase), and P24A (actin). Positive correlations are shown with a solid line and negative correlations with a dashed line. The disconnected networks suggest that most proteins interact with a close neighborhood of proteins, rather than more globally across the network. (B) Directed protein regulatory network inferred using the GENIE3 algorithm. Directed networks illustrate information flow as described by the arrows among nodes. This network suggests that P21A (α-tubulin) and P6 (proteasome-α-type-1) are upstream regulators of P4B (α-crystalline-Hsp23).