Epithelial-to-mesenchymal transition (EMT) is a fundamental cellular process and plays an essential role in development, tissue regeneration, and cancer metastasis. Interestingly, EMT is not a binary process but instead proceeds with multiple partial intermediate states. However, the functions of these intermediate states are not fully understood. Here, we focus on a general question about how the number of partial EMT states affects cell transformation. First, by fitting a hidden Markov model of EMT with experimental data, we propose a statistical mechanism for EMT in which many unobservable microstates may exist within one of the observable macrostates. Furthermore, we find that increasing the number of intermediate states can accelerate the EMT process and that adding parallel paths or transition layers accelerates the process even further. Last, a stabilized intermediate state traps cells in one partial EMT state. This work advances our understanding of the dynamics and functions of EMT plasticity during cancer metastasis.
KeywordsCancer cell plasticity, partial EMT, microstate, macrostate, intermediate state, Markov 1 process, stabilized state. 2 Introduction 3 Epithelial-to-mesenchymal transition (EMT) is a fundamental cellular process in which 4 polarized epithelial cells lose various cell-cell junctions and adhesion and gain migratory 5 and invasive properties to become mesenchymal cells [1, 2]. EMT is very important in 6 embryonic development, tumorigenesis, metastasis, tumour stemness, and therapy 7 resistance [3, 4]. Remarkably, EMT is not a binary process but proceeds with multiple 8 partial intermediate states, collectively known as partial or hybrid EMT states [3, 5-11].9The partial EMT state retains some characteristics of epithelium but also shows 10 features of mesenchymal cells [12][13][14]. One partial EMT state was predicted through 11 mathematical modeling of the EMT core regulatory network and was verified with 12 quantitative experiments by our previous works [5, 6]. Thereafter, many different partial 13 EMT states were proposed [8, 9,[15][16][17]. More and more experimental data shows a 14 different number of partial EMT states in various cancer cell lines [18-23]. Recently, 15 r 1, 2019 1/26 several partial EMT phenotypes were found during cancer metastasis in vivo in a skin 16 cancer mouse model [24, 25] and prostate cancer [26]. While many partial EMT states 17 have been found, their functions are still not fully understood during cancer 18 metastasis [4, 27-29]. 19 Currently, the function of partial EMT states has being studied in the context of 20 coupling with other cellular processes. For example, acquisition of stem-like properties 21 dictates its coupling with cancer stemness [11, 30-34], circulating tumor cells 22 (CTCs) [35, 36], and drug resistance [37]. Thus, the partial EMT cells hold the highest 23 metastatic potential. As well, partial EMT, instead of full EMT, is found to be critical 24 for renal fibrosis [38-40]. There are many potential couplings of partial EMT and other...