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We explored the underlying mechanisms of differentiation, dedifferentiation, reprogramming and transdifferentiation cell type switchings from landscape and flux perspectives.
Lineage reprogramming is a new regenerative method to convert a matured cell into another cell including direct transdifferentiation without undergoing a pluripotent cell state and indirect transdifferentiation with an initial dedifferentiation-reversion reprogramming to a pluripotent cell state. Each cell type is quantified by a distinct valley on the potential landscape with higher probability.
We investigated three driving forces for cell fate decision making: stochastic fluctuations, gene regulation and induction, which can lead to cell type switchings.
We showed that under the driving forces the direct transdifferentiation process proceeds from a differentiated cell valley to another differentiated cell valley through either a distinct stable intermediate state or a certain series of unstable indeterminate states.
The dedifferentiation process proceeds through a pluripotent cell state. Barrier height and the corresponding escape time from the valley on the landscape can be used to quantify the stability and efficiency of cell type switchings.
We also uncovered the mechanisms of the underlying processes by quantifying the dominant biological paths of cell type switchings on the potential landscape. The dynamics of cell type switchings are determined by both landscape gradient and flux. The flux can lead to the deviations of the dominant biological paths for cell type switchings from the naively expected landscape gradient path. As a result, the corresponding dominant paths of cell type switchings are irreversible.
We also classified the mechanisms of cell fate development from our landscape theory: super-critical pitchfork bifurcation, sub-critical pitchfork bifurcation, sub-critical pitchfork with two saddle-node bifurcation, and saddle-node bifurcation. Our model showed good agreements with the experiments.
It provides a general framework to explore the mechanisms of differentiation, dedifferentiation, reprogramming and transdifferentiation. This is an open-access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability: The authors confirm that all data underlying the findings are fully available without restriction. Relevant data are included within the paper. NSFC website is: www. NSF website: www.
The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing interests: The authors have declared that no competing interests exist. A pluripotent undifferentiated cell can differentiate into types of differentiated cells. Each cell type has a specific regulated gene expression. Cellular differentiation is determined by the underlying gene regulatory network during the process of development, which leads the primary cell into its ultimate fate-a particular phenotype.
Induced pluripotent stem iPS cells provide the opportunity to obtain pluripotent stem cells which potentially have therapeutic uses  , . Recently many studies have been reported that one type of cells can be converted to another type of functional cells directly  — .
This is a big step forward in the cell biology since there is no need to create iPS cells first for cell type switching, skipping many intermediate steps.
This direct reprogramming technology is called the lineage reprogramming. Thus an adult cell can be reprogrammed directly to new cells as lineage switching. The lineage switching through direct transdifferentiation without going through the iPS state might be applied to regenerative medicine with less risk of cancer.
However, it is still challenging to quantify the mechanisms of the differentiation, dedifferentiation, reprogramming and transdifferentiation  — . Different valleys represent different cell phenotypes cell fates on the cell development potential landscape  — . Waddington visualized the undifferentiated state as the local maximum and differentiated states as the local minimum on the landscape .
In our landscape picture, the undifferentiated state and differentiated state are both local minima in certain regions of the landscape. Undifferentiated state has relatively low expressions of differentiation mark genes while differentiated state has at least one high expressions of differentiation mark genes. In addition, Waddington believed the differentiation is a downhill process driven by the funneled landscape gradient. In our picture, the differentiation can occur with several different mechanisms, through funneled landscape, through stochastic fluctuations and the probability fluxes even when the landscape is not funneled towards the differentiated states, and through induction.
The process of the cell development can be viewed as the system moving from one valley primary or stem cell phenotype through bifurcation to another valley differentiated cell phenotype on the potential landscape. And the transdifferentiation process can be viewed as the system escaping from one stable differentiated valley to another differentiated valley through certain paths on the potential landscape shown in Figure 1 A.
The differentiated cells can switch to another lineage cell type through an explicit pluripotent stable state. Indirect transdifferentiation mechanism which requires an initial dedifferentiation step shown in Figure 1 A. It illustrates a differentiated cell reprogrammed back to a pluripotent state with less differentiated, and then can be re-differentiated to another type of differentiated cell  ,  , . This is a possible strategy of pluripotent lineage reprogramming while the enhancement of efficiency is required.
The underlying process is a transdifferentiation involving a stepwise dedifferentiation. In addition to indirect transdifferentiation, there is another lineage reprogramming approach: the direct transdifferentiation mechanism as shown in Figure 1 A.
Direct transdifferentiation is a mechanism of converting one type of differentiated cells to another type of differentiated cells without undergoing through a pluripotent state or progenitor cell type. The differentiated cells down regulate their own cell-specific genes and activate the target cell-specific genes , thus they can switch to another lineage cell type through an explicit intermediate stable state or a series of indeterminate states  —  ,  , .
In our study, the intermediate state is defined as an intermediate stable state with low or medium pluripotency and having very low expressions of the differentiation mark genes, while a series of indeterminate states are defined as a series of unstable states with low or medium pluripotency and very low expressions of differentiation mark genes in the course of lineage switching.
Sridharan et al  showed that partially reprogrammed cells as an intermediate stage of the reprogramming process can switch to the completely reprogrammed iPS state. Thus the states of partially reprogrammed cells may exist along the paths from a differentiated state or to iPS state.
The research by Mikkelsen  showed that partially reprogrammed cells can be trapped at a common intermediate state. Thus the states of partially reprogrammed cells may exist along the paths from a differentiated state to another differentiated state through an intermediate or indeterminate states.
These intermediate state and indeterminate states may have certain expressions of stem cell marker genes and thus can be viewed as partially reprogrammed cells.
This is supported by the observation that fibroblast cells specific genes are efficiently silenced and the embryonic reprogramming is not fully induced in partially reprogrammed cells . We believe that different experimental and environmental conditions can lead to quite different results and change the topological structure of the potential landscape  , .
The partially reprogrammed cells may be trapped in certain regions in the gene expression space. A: The scheme of dedifferentiation including reprogramming and differentiation and transdifferentiation.
B: A model for the gene circuit for cell development. C: The phase diagram for the gene circuit with. D: The cell fate landscape obtained from the Hamilton-Jacobi equation versus and , and the phase diagram was drawn on the intrinsic potential landscape with stable states represented by black solid lines and unstable states represented by black dash line.
The red dash lines represent the dedifferentiation reprogramming and redifferentiation process while the yellow solid lines represents the transdifferentiation process. In this study, we term direct transdifferentiation as transdifferentiation and indirect transdifferentiation requiring an initial dedifferentiation or reprogramming step as dedifferentiation. The goal of regenerative medicine can potentially be realized through the processes of differentiation, dedifferentiation, reprogramming and transdifferentiation .
Recent advances have shown that there are three possible driving forces for cell type switchings: 1 Stochastic Fluctuations. Cells choose their pathways of differentiation stochastically in the process of development without apparent regards to environment or history . Some studies in cell development reveal that intrinsic stochasticity is an important mechanism for development . The extrinsic fluctuations are also expected to play a role in cell development. Thus the fluctuations can be a driving force for the processes of cell type switchings.
Lineage specific cells can be reprogrammed to a pluripotent state through over-expressions of some defined transcription factors  , . Transfection of certain cell specific genes into the primary cells, and over-expressions of the target lineage specific genes as well as certain stem cell-associated genes can induce the processes of cell type switchings. Given the three driving forces for cell fate decision making, it is still challenging on how to quantify the processes of cell type switchings on the landscape, and how to connect them to experiments.
These processes of cell type switchings are controlled by their underlying gene regulatory network. The lineage-specific transcription factors play a critical role in the processes of cell type switchings.
In this study, we explored a simple cell differentiation network module with autoregulation and mutual antagonism between transcription factors lineage-specific genes  ,  , which exists in many cell differentiation processes, shown in Figure 1 B.
The lineage-specific genes can strongly instruct the cellular lineage choice. The circuit is composed of a pair of self activating autoregulation and mutual inhibiting cross-antagonism cell-specific genes and  , .
In iPSC or ESC embryonic stem cell , pluripotent genes are often highly expressed, and most lineage related genes are off. However, there are examples of gene regulatory circuits with the same architecture in our study which control binary decisions at branch points of cell differentiation in multi-potent cells. Such mutual antagonism gene circuit modules where the self activation can also be indirect in binary branch points of cell lineage commitment can often be found.
A lot of studies have explored the primed multipotent common myeloid progenitor CMP can differentiate to either myeloid cell or erythroid cell in blood cell formation by mutual antagonism interaction of transcription factor gene and shown in Figure 2 A  , . These three circuits all can be viewed as and in our network. A: The interaction of and in determining myeloid cell or erythroid cell, and in determining inner cell mass or trophectoderm, and in determining epiblast or primitive endoderm.
B: Scheme for the gene circuit of B cell to macrophage conversion. The dashed lines indicate uncertainty. C: Scheme for the gene circuit in determining mesendodermal and ectodermal. We will study this key network module to uncover the underlying functional mechanisms of cell type switchings. The phase diagram in Figure 1 C suggests that the system can have five different phase regions, each of which has different underlying landscapes with different distribution of valleys.
Furthermore, we show how stochastic fluctuation, gene regulation and induction induce the cell type switchings. The potential landscape and flux both direct the processes of cell type switchings. Probability flux provide a curling force breaking the detailed balance and lead the biological paths of cell type switchings to be deviated from the paths obtained by steepest descent gradient of the landscape.
The forward and backward paths of cell type switchings are irreversible, without passing through the saddle point. Furthermore, the flux can become the main driving force for cell type switching when the landscape is not biased towards the specific processes  , .
Barrier height and dynamic transition speed are used to quantify the global stability of the landscape topography. The stability here represents the ability for a cell to stay at a certain cell type state against certain fluctuations.
In practice, the fluctuations in some cases maybe small but never zero. We uncover and classify four mechanisms of cell type switchings: super-critical pitchfork bifurcation, sub-critical pitchfork bifurcation, sub-critical pitchfork with two saddle-node bifurcation, and saddle-node bifurcation. We start with gene circuit module for typical differentiation. The gene regulatory circuit for cell fate decision has two mutual repression and self-activation lineage-specific transcription factors: and shown in Figure 1 B.
It is more complete to consider three or more gene system.
Dedifferentiation, transdifferentiation and reprogramming: three routes to regeneration
We explored the underlying mechanisms of differentiation, dedifferentiation, reprogramming and transdifferentiation cell type switchings from landscape and flux perspectives. Lineage reprogramming is a new regenerative method to convert a matured cell into another cell including direct transdifferentiation without undergoing a pluripotent cell state and indirect transdifferentiation with an initial dedifferentiation-reversion reprogramming to a pluripotent cell state. Each cell type is quantified by a distinct valley on the potential landscape with higher probability. We investigated three driving forces for cell fate decision making: stochastic fluctuations, gene regulation and induction, which can lead to cell type switchings.
Dedifferentiation, transdifferentiation and reprogramming: three routes to regeneration.
Dedifferentiation, Transdifferentiation and Reprogramming: Three Routes to Regeneration