Estimating developmental states of tumors and normal tissues using a linear time-ordered model

Tumor cells are considered to have an aberrant cell state, and some evidence indicates different development states appearing in the tumorigenesis. Embryonic development and stem cell differentiation are ordered processes in which the sequence of events over time is highly conserved. The "cancer attractor" concept integrates normal developmental processes and tumorigenesis into a high-dimensional "cell state space", and provides a reasonable explanation of the relationship between these two biological processes from theoretical viewpoint. However, it is hard to describe such relationship by using existed experimental data; moreover, the measurement of different development states is also difficult.

Here, by applying a novel time-ordered linear model based on a co-bisector which represents the joint direction of a series of vectors, we described the trajectories of development process by a line and showed different developmental states of tumor cells from developmental timescale perspective in a cell state space. This model was used to transform time-course developmental expression profiles of human ESCs, normal mouse liver, ovary and lung tissue into "cell developmental state lines". Then these cell state lines were applied to observe the developmental states of different tumors and their corresponding normal samples. Mouse liver and ovarian tumors showed different similarity to early development stage. Similarly, human glioma cells and ovarian tumors became developmentally "younger".

The time-ordered linear model captured linear projected development trajectories in a cell state space. Meanwhile it also reflected the change tendency of gene expression over time from the developmental timescale perspective, and our finding indicated different development states during tumorigenesis processes in different tissues.