Table 1.

Some specific changes in cellular and extra-cellular mechanical properties, observations from experiments and computational models.

Experimental observations	Model predictions
Extra-cellular mechanical properties
Matrix stiffening (effect of increased density, cross-linking) (Paszek et al., 2005; Levental et al., 2009)	Increased cell proliferation driven by heterogeneity in ECM mechanical properties, protrusions along high density gradients (Macklin and Lowengrub, 2007; Rubenstein and Kaufman, 2008; Anderson et al., 2009; Macklin et al., 2009)
Matrix re-organization (effect of degradation and realignment) (Wolf et al., 2007; Friedl and Wolf, 2008)	Cell Proliferation driven by matrix degradation through the expression of MMPs and along realigned matrix fibers (Franks et al., 2005; Painter, 2009; Giverso et al., 2010; D’Antonio et al., 2013)
Cellular mechanical properties
Increase in cell compliance or deformability (Cross et al., 2007; Fritsch et al., 2010; Jonas et al., 2011)	Tumorigenesis and increased malignancy, (Katira et al., 2012). Increased migration through porous ECM (Zaman, 2006; Zaman et al., 2007; Scianna and Preziosi, 2013)
Changes in cell adhesivity (Paredes et al., 2005; Ribeiro et al., 2010b)	Changes in tumor morphology, growth rates, and metastatic potential (Byrne and Chaplain, 1996; Armstrong et al., 2006; Ramis-Conde et al., 2008b; Frieboes et al., 2010; Rejniak et al., 2010; Katira et al., 2012)
Increase in cell contractility (Jonas et al., 2011; Kraning-Rush et al., 2012)	Increased migration rates and rigidity sensing (Moreo et al., 2008; Brodland and Veldhuis, 2012)