Focus Issue: Adding Math to the Signaling Toolkit

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Science Signaling  17 Apr 2012:
Vol. 5, Issue 220, pp. eg5
DOI: 10.1126/scisignal.2003112


This issue of Science Signaling, which complements the 13 April issue of Science, showcases the application of computational approaches to signal transduction research. Research and commentary highlight how mathematical modeling combined with experimental data can yield new insights into how cells interpret, process, and respond to external and internal cues.

The relationship between mathematics and biology is relatively young and has sometimes been rocky; however, the power generated by the combination of experimental observation and mathematical modeling is becoming increasingly apparent. In particular, the predictive power of computational approaches and their experimental validation have provided important insights into signaling mechanisms in many systems. In this Focus Issue, which complements the Science Special Issue on Computational Biology, we present a range of research and commentary articles that highlight the application of mathematical models to signaling problems.

Cells rarely receive extracellular signals in isolation. In addition, for some signals, different responses are required for brief, sustained, or pulsatile periods of stimulations. Computational approaches can provide insight into how cells interpret and respond to the vast array of inputs. In a Research Article in the Archives, Hsueh et al. used both experimental and computational approaches to understand the responses of macrophages to combinations of, three, or four, or five stimuli. They found that the number of responses was limited despite the large number of possible combinations of ligands used to stimulate the macrophages. In a Research Article in this issue, Klinke et al. measured multiple parameters in the response of a T cell line to the proinflammatory cytokine interleukin-12 (IL-12), which determines T cell fate. Combining measurements of receptor abundance, activation of signaling intermediates, changes in cell numbers, and secretion of cytokines, the authors developed a mathematical model that suggested that the T cell response was determined both by the current exposure to IL-12 and the “memory” of previous exposure.

Many signals diffuse from their source of production or site of release, creating concentration gradients, which adds another layer of complexity to the interpretation of signals. In the process of chemotaxis, cells orient their movement according to gradients of external signals. A set of Articles in the Archives highlights the LEGI model, which postulates that cells detect an external gradient by balancing a fast local excitation and a slower global inhibition. In a Research Article, Wang et al. show that the signaling output of the LEGI signaling module is amplified and that different cells have different amplification thresholds. In another Research Article, Takeda et al. describe the configuration of the signaling network that enables cells to rapidly adapt to changes in chemoattractant concentration (see also the accompanying Perspective by Iglesias in the Archives). Cells undergoing chemotaxis extend cellular protrusions called pseudopods in the direction of movement, and another set of articles in the Archives describes a model that explains the formation of pseudopods and how they are used for navigation (see the Research Article by Otsuji et al. and the Perspective by Van Haastert).

Computational analysis can also be applied to how cells process information that passes through signal transduction cascades. A Research Article in the Archives shows how mathematical modeling, combined with biochemical analysis, can provide insight into the regulation of the mammalian (or mechanistic) target of rapamycin (mTOR) pathway. mTOR exists in two complexes, mTORC1 and mTORC2, which have different sensitivities to the inhibitor rapamycin. As Fingar and Inoki discuss in an accompanying Perspective, the analysis by Dalle Pezze et al. uncovered a previously unknown mechanism to regulate insulin-dependent regulation of mTORC2 signaling that was independent of the regulation of mTORC1. These findings may aid in the development of selective regulators of mTORC1 and mTORC2.

In addition to the analysis of specific pathways, computational analysis can reveal insights into networked pathways, as exemplified by a Research Article in the Archives. To understand epithelial-mesenchymal interactions, O’Connell et al. performed gene expression profiling of developing molar tissues and computational analyses to construct a gene regulatory network. This network contained a key feedback circuit mediated by diffusible signaling molecules of the Wnt and Bmp families that controlled the production of signaling molecules in other pathways and was self-sustaining and was validated in mice with mutations expected to disrupt the Wnt-Bmp signaling pathways. In a Review in this issue, Kholodenko et al. discuss the application of various mathematical and computational models to integrate the vast quantities of data generated by proteomic, genomic, and metabolomic techniques. These models generate signaling networks that show how cells respond to external and internal stimuli and how information flows through these networks to determine the cell’s behavior. In an Editorial Guide in the Archives, Gough and Foley discuss the complexity of signaling networks in terms of the dynamics of the components within networks and how the networks themselves can be affected by the information that flows through them (see also the Research Article in the Archives by Jiang et al.). In a Protocol by Yosef et al. in the Archives, the authors developed software to map the functional protein networks that can be built based on genomic screens of cells in response to various stimuli. In addition, the software can be used to identify protein subnetworks that are organized around anchor proteins. Results from additional experiments can be used to further refine the networks within the software.

An alternative approach that can be taken to understand signaling networks is to engineer synthetic systems and monitor their properties. In a Research Article in this issue, Matsuda et al. engineered genetic circuits within cells based on the receptor Notch and its ligand Delta. As Slusarczyk and Weiss discuss in their accompanying Perspective, Matsuda et al. established a system in which the signal was propagated throughout the cells in a cell contact–dependent manner. Use of this synthetic approach should lead to a better understanding of the minimal mechanism required for cellular phenotypes of interest.

Our understanding of the complex cellular responses to a signal can be enriched by computational approaches. In a Perspective in the Archives, Hlavacek and Faeder discuss the need to combine characterization of broad cellular responses (at the macroscopic level) and more focused interactions (at the microscopic level) to fully understand how diseases occur as a result of a breakdown in signaling networks. Such knowledge could then be used to develop targeted therapies. In a Review in Science, Mogilner et al. discuss the use of quantitative mathematical models to understand the mechanisms that underlie cell polarity. The authors characterize the biological scope of these models as being either focused (which are mathematically simple) or broad (which are mathematically complex) and discuss how these different types of models can be used to address different questions about the system being analyzed.

A frequently analyzed signaling output is protein phosphorylation, and in a Protocol in this issue, Li et al. developed software to analyze data from peptide arrays, which are used to analyze the properties of protein kinases. Previously, peptide array data have mostly been analyzed with methods adapted from those that are used to analyze DNA microarrays. In their software, Li et al. take account of technical and biological characteristics of peptide arrays that are distinct from those of microarrays to generate a method of analysis that identifies more peptides than are identified by other methods. In a Perspective in this issue by Das et al., the authors discuss how genome-wide analysis was used to identify functional motifs within conserved sequences that encode disordered regions in proteins (see the Research Resource by Nguyen Ba et al. in the Archives). This analysis also predicted previously uncharacterized motifs that may encode other functions within these disordered regions, which has implications for protein engineering.

Transcriptional responses are another set of signaling outputs that can be complex and thus can benefit from computational analyses, which can yield previously unappreciated connections between signaling proteins. In a Research Article in the Archives, Wexler et al. performed a genome-wide analysis of the response of cultured neural progenitor cells to Wnt1 and identified a reciprocal relationship between Wnt signaling and progranulin, deficiency of which is associated with frontotemporal dementia. Computational approaches can also help to explain unexpected observations, as shown by a Research Article in the Archives by Parker et al. (see also the Perspective by Whitington et al.). It might be expected that high-affinity binding sites for a transcription factor would confer broad expression domains for a gene. However, Parker et al. noted that the enhancer of a broadly expressed target gene of the morphogen Hedgehog (Hh) possessed low-affinity sites for the transcription factor Cubitus interruptus (Ci), whereas an Hh target with a more restricted expression domain had high-affinity binding sites for Ci. Computational modeling indicated that these expression patterns could be explained by cooperative binding of the repressor forms of Ci to enhancer sites, a model that was confirmed by in vivo experiments.

In a Review in Science, Morelli et al. discuss the importance of combining experimental measurements with computational modeling to investigate patterning in the developing embryo. The authors emphasize the importance of models that make predictions that can be experimentally verified, a point also raised by Yaffe in a 2011 Editorial Guide in the Archives. Researchers who combine computational approaches with model validation and experimentally tested predictions are encouraged to consider submitting their work to Science Signaling and should refer to the Information for Authors for more details (http://stke.sciencemag.org/about/ifora.dtl).

Featured in This Focus Issue

Research Articles

  • M. Matsuda, M. Koga, E. Nishida, M. Ebisuya, Synthetic signal propagation through direct cell-cell interaction. Sci. Signal. 5, ra31 (2012). [Abstract] [Full Text] [PDF]

  • D. J. Klinke II, N. Cheng, E. Chambers, Quantifying crosstalk among interferon-γ, interleukin-12, and tumor necrosis factor signaling pathways within a TH1 cell model. Sci. Signal. 5, ra32 (2012). [Abstract] [Full Text] [PDF]


  • R. K. Das, A. H. Mao, R. V. Pappu, Unmasking functional motifs within disordered regions of proteins. Sci. Signal. 5, pe17 (2012). [Abstract] [Full Text] [PDF]

  • A. L. Slusarczyk, R. Weiss, Understanding signaling dynamics through synthesis. Sci. Signal. 5, pe16 (2012). [Abstract] [Full Text] [PDF]


  • B. Kholodenko, M. B. Yaffe, W. Kolch, Computational approaches for analyzing information flow in biological networks. Sci. Signal. 5, re1 (2012). [Gloss] [Abstract] [Full Text] [PDF]


  • Y. Li, R. J. Arsenault, B. Trost, J. Slind, P. J. Griebel, S. Napper, A. Kusalik, A systematic approach for analysis of peptide array kinome data. Sci. Signal. 5, pl2 (2012). [Abstract] [Full Text] [PDF]

Related Resources

Editorial Guides

  • N. R. Gough, Focus Issue: Series on computational and systems biology. Sci. Signal. 4, eg8 (2011). [Abstract] [Full Text] [PDF]

  • N. R. Gough, J. F. Foley, Focus Issue: Unraveling signaling complexity. Sci. Signal. 2, eg10 (2009). [Abstract] [Full Text] [PDF]

  • N. R. Gough, M. B. Yaffe, Focus Issue: Conquering the data mountain. Sci. Signal. 4, eg2 (2011). [Abstract] [Full Text] [PDF]

  • M. B. Yaffe, Seeing the signaling forest and the trees. Sci. Signal. 1, eg5 (2008). [Abstract] [Full Text] [PDF]

  • M. B. Yaffe, The complex art of telling it simply. Sci. Signal. 4, eg11 (2011). [Abstract] [Full Text] [PDF]

Research Articles

  • P. Dalle Pezze, A. G. Sonntag, A. Thien, M. T. Prentzell, M. Gödel, S. Fischer, E. Neumann-Haefelin,T. B. Huber, R. Baumeister, D. P. Shanley, K. Thedieck, A dynamic network model of mTOR signaling reveals TSC-independent mTORC2 regulation. Sci. Signal. 5, ra25 (2012). [Abstract] [Full Text] [PDF]

  • R. C. Hsueh, M. Natarajan, I. Fraser, B. Pond, J. Liu, S. Mumby, H. Han, L. I. Jiang, M. I. Simon, R. Taussig, P. C. Sternweis, Deciphering signaling outcomes from a system of complex networks. Sci. Signal. 2, ra22 (2009). [Abstract] [Full Text] [PDF]

  • P. Jiang, A. C. Ventura, E. D. Sontag, S. D. Merajver, A. J. Ninfa, D. Del Vecchio, Load-induced modulation of signal transduction networks. Sci. Signal. 4, ra67 (2011). [Abstract] [Full Text] [PDF]

  • D. J. O’Connell, J. W. K. Ho, T. Mammoto, A. Turbe-Doan, J. T. O’Connell, P. S. Haseley, S. Koo, N. Kamiya, D. E. Ingber, P. J. Park, R. L. Maas, A Wnt-Bmp feedback circuit controls intertissue signaling dynamics in tooth organogenesis. Sci. Signal. 5, ra4 (2012). [Abstract] [Full Text] [PDF]

  • M. Otsuji, Y. Terashima, S. Ishihara, S. Kuroda, K. Matsushima, A conceptual molecular network for chemotactic behaviors characterized by feedback of molecules cycling between the membrane and the cytosol. Sci. Signal. 3, ra89 (2010). [Abstract] [Full Text] [PDF]

  • D. S. Parker, M. A. White, A. I. Ramos, B. A. Cohen, S. Barolo, The cis-regulatory logic of Hedgehog gradient responses: Key roles for Gli binding affinity, competition, and cooperativity. Sci. Signal. 4, ra38 (2011). [Abstract] [Full Text] [PDF]

  • K. Takeda, D. Shao, M. Adler, P. G. Charest, W. F. Loomis, H. Levine, A. Groisman, W.-J. Rappel, R. A. Firtel, Incoherent feedforward control governs adaptation of activated Ras in a eukaryotic chemotaxis pathway. Sci. Signal. 5, ra2 (2012). [Abstract] [Full Text] [PDF]

  • C. J. Wang, A. Bergmann, B. Lin, K. Kim, A. Levchencko, Diverse sensitivity thresholds in dynamic signaling responses by social amoebae. Sci. Signal. 5, ra17 (2012). [Abstract] [Full Text] [PDF]

  • E. M. Wexler, E. Rosen, D. Lu, G. E. Osborn, E. Martin, H. Raybould, D. H. Geschwind, Genome-wide analysis of a Wnt1-regulated transcriptional network implicates neurodegenerative pathways. Sci. Signal. 4, ra65 (2011). [Abstract] [Full Text] [PDF]

Research Resource

  • A. N. Nguyen Ba, B. J. Yeh, D. van Dyk, A. R. Davidson, B. J. Andrews, E. L. Weiss, A. M. Moses, Proteome-wide discovery of evolutionary conserved sequences in disordered regions. Sci. Signal. 5, rs1 (2012). [Abstract] [Full Text] [PDF]


  • D. C. Fingar, K. Inoki, Deconvolution of mTORC2 “in silico”. Sci. Signal. 5, pe12 (2012). [Abstract] [Full Text] [PDF]

  • W. S. Hlavacek, J. R. Faeder, The complexity of cell signaling and the need for a new mechanics. Sci. Signal. 2, pe46 (2009). [Abstract] [Full Text] [PDF]

  • P. A. Iglesias, Chemoattractant signaling in Dictyostelium: Adaptation and amplification. Sci. Signal. 5, pe8 (2012). [Abstract] [Full Text] [PDF]

  • P. J. M. Van Haastert, How cells use pseudopods for persistent movement and navigation. Sci. Signal. 4, pe6 (2011). [Abstract] [Full Text] [PDF]

  • T. Whitington, A. Jolma, J. Taipale, Beyond the balance of activator and repressor. Sci. Signal. 4, pe29 (2011). [Abstract] [Full Text] [PDF]


  • N. Yosef, E. Zalckvar, A. D. Rubinstein, M. Homilius, N. Atias, L. Vardi, I. Berman, H. Zur, A. Kimchi, E. Ruppin, R. Sharan, ANAT: A tool for constructing and analyzing functional protein networks. Sci. Signal. 4, pl1 (2011). [Abstract] [Full Text] [PDF]

Virtual Journal

  • A. Mogilner, J. Allard, R. Wollman, Cell polarity: Quantitative modeling as a tool in cell biology. Science 336, 175–179 (2012). [Abstract] [Full Text]

  • L. G. Morelli, K. Uriu, S. Ares, A. C. Oates, Computational approaches to developmental patterning. Science 336, 187–191 (2012). [Abstract] [Full Text]

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