  During tissue invasion individual tumor cells exhibit two interconvertible
migration modes, namely mesenchymal and amoeboid migration. The cellular
microenvironment triggers the switch between both modes, thereby allowing
adaptation to dynamic conditions. It is, however, unclear if this
amoeboid-mesenchymal migration plasticity contributes to a more effective tumor
invasion. We address this question with a mathematical model, where the
amoeboid-mesenchymal migration plasticity is regulated in response to local
extracellular matrix resistance. Our numerical analysis reveals that
extracellular matrix structure and presence of a chemotactic gradient are key
determinants of the model behavior. Only in complex microenvironments, if the
extracellular matrix is highly heterogeneous and a chemotactic gradient directs
migration, the amoeboid-mesenchymal migration plasticity allows a more
widespread invasion compared to the non-switching amoeboid and mesenchymal
modes. Importantly, these specific conditions are characteristic for in vivo
tumor invasion. Thus, our study suggests that \emph{in vitro} systems aiming at
unraveling the underlying molecular mechanisms of tumor invasion should take
into account the complexity of the microenvironment by considering the combined
effects of structural heterogeneities and chemical gradients on cell migration.
