A Dimension Reduction Approach for Energy Landscape: Identifying Intermediate States in Metabolism‐EMT Network

Dimension reduction is a challenging problem in complex dynamical systems. Here, a dimension reduction approach of landscape (DRL) for complex dynamical systems is proposed, by mapping a high‐dimensional system on a low‐dimensional energy landscape. The DRL approach is applied to three biological networks, which validates that new reduced dimensions preserve the major information of stability and transition of original high‐dimensional systems. The consistency of barrier heights calculated from the low‐dimensional landscape and transition actions calculated from the high‐dimensional system further shows that the landscape after dimension reduction can quantify the global stability of the system. The epithelial‐mesenchymal transition (EMT) and abnormal metabolism are two hallmarks of cancer. With the DRL approach, a quadrastable landscape for metabolism‐EMT network is identified, including epithelial (E), abnormal metabolic (A), hybrid E/M (H), and mesenchymal (M) cell states. The quantified energy landscape and kinetic transition paths suggest that for the EMT process, the cells at E state need to first change their metabolism, then enter the M state. The work proposes a general framework for the dimension reduction of a stochastic dynamical system, and advances the mechanistic understanding of the underlying relationship between EMT and cellular metabolism.