Multiway modeling and analysis in stem cell systems biology

<p>Abstract</p> <p>Background</p> <p>Systems biology refers to multidisciplinary approaches designed to uncover emergent properties of biological systems. Stem cells are an attractive target for this analysis, due to their broad therapeutic potential. A central theme of systems biology is the use of computational modeling to reconstruct complex systems from a wealth of reductionist, molecular data (e.g., gene/protein expression, signal transduction activity, metabolic activity, etc.). A number of deterministic, probabilistic, and statistical learning models are used to understand sophisticated cellular behaviors such as protein expression during cellular differentiation and the activity of signaling networks. However, many of these models are bimodal i.e., they only consider row-column relationships. In contrast, multiway modeling techniques (also known as tensor models) can analyze multimodal data, which capture much more information about complex behaviors such as cell differentiation. In particular, tensors can be very powerful tools for modeling the dynamic activity of biological networks over time. Here, we review the application of systems biology to stem cells and illustrate application of tensor analysis to model collagen-induced osteogenic differentiation of human mesenchymal stem cells.</p> <p>Results</p> <p>We applied Tucker1, Tucker3, and Parallel Factor Analysis (PARAFAC) models to identify protein/gene expression patterns during extracellular matrix-induced osteogenic differentiation of human mesenchymal stem cells. In one case, we organized our data into a tensor of type protein/gene locus link × gene ontology category × osteogenic stimulant, and found that our cells expressed two distinct, stimulus-dependent sets of functionally related genes as they underwent osteogenic differentiation. In a second case, we organized DNA microarray data in a three-way tensor of gene IDs × osteogenic stimulus × replicates, and found that application of tensile strain to a collagen I substrate accelerated the osteogenic differentiation induced by a static collagen I substrate.</p> <p>Conclusion</p> <p>Our results suggest gene- and protein-level models whereby stem cells undergo transdifferentiation to osteoblasts, and lay the foundation for mechanistic, hypothesis-driven studies. Our analysis methods are applicable to a wide range of stem cell differentiation models.</p

Scatter plot of the category names projected on the 1'st vector of the category component matrix of Tucker3 analysis

<p><b>Copyright information:</b></p><p>Taken from "Multiway modeling and analysis in stem cell systems biology"</p><p>http://www.biomedcentral.com/1752-0509/2/63</p><p>BMC Systems Biology 2008;2():63-63.</p><p>Published online 14 Jul 2008</p><p>PMCID:PMC2527292.</p><p></p

Scatter plot of locus link onto the first vector of the locus link component matrix of Tucker3 analysis

<p><b>Copyright information:</b></p><p>Taken from "Multiway modeling and analysis in stem cell systems biology"</p><p>http://www.biomedcentral.com/1752-0509/2/63</p><p>BMC Systems Biology 2008;2():63-63.</p><p>Published online 14 Jul 2008</p><p>PMCID:PMC2527292.</p><p></p

Tensor to model time evolution of stem cell differentiation under different control

<p><b>Copyright information:</b></p><p>Taken from "Multiway modeling and analysis in stem cell systems biology"</p><p>http://www.biomedcentral.com/1752-0509/2/63</p><p>BMC Systems Biology 2008;2():63-63.</p><p>Published online 14 Jul 2008</p><p>PMCID:PMC2527292.</p><p></p

We projected the data over the first component vector (with explained variance of 85

64%) of the second mode (populations and time) obtained for Tucker3 analysis. At one end we have undifferentiated hMSC (Tissue Culture Plastic, or TCP) and at the other end we have the target state (fully differentiated hOST). In between we plot the data for each stimulus and time point (e.g., NSD2 = no stretch, day 2; SD5 = stretch, day 5). Because the "SD" points lie closer to the target (hOST) than their corresponding "NSD" conditions on days 2 and 5, we conclude that the stimulus "stretch" accelerates osteogenic differentiation when compared to the same stimulus without stretch.<p><b>Copyright information:</b></p><p>Taken from "Multiway modeling and analysis in stem cell systems biology"</p><p>http://www.biomedcentral.com/1752-0509/2/63</p><p>BMC Systems Biology 2008;2():63-63.</p><p>Published online 14 Jul 2008</p><p>PMCID:PMC2527292.</p><p></p

Scatter plot of he category names projected on to the first component of category mode in PARAFAC analysis

<p><b>Copyright information:</b></p><p>Taken from "Multiway modeling and analysis in stem cell systems biology"</p><p>http://www.biomedcentral.com/1752-0509/2/63</p><p>BMC Systems Biology 2008;2():63-63.</p><p>Published online 14 Jul 2008</p><p>PMCID:PMC2527292.</p><p></p