Mathematical models of cell phenotype regulation and reprogramming: Make cancer cells sensitive again!

Abstract

A cell’s phenotype is the observable actualization of complex interactions between its genome, epigenome, and local environment. While traditional views in cancer have held that cellular and tumor phenotypes are largely functions of genomic instability, increasing attention has recently been given to epigenetic and microenvironmental influences. Such non-genetic factors allow cancer cells to experience intrinsic diversity and plasticity, and at the tumor level can result in phenotypic heterogeneity and treatment evasion. In 2006, Takahashi and Yamanaka exploited the epigenome’s plasticity by “reprogramming” differentiated cells into a pluripotent state by inducing expression of a cocktail of four transcription factors. Recent advances in cancer biology have shown not only that cellular reprogramming is possible for malignant cells, but it may provide a foundation for future therapies. Nevertheless, cell reprogramming experiments are frequently plagued by low efficiency, activation of aberrant transcriptional programs, instability, and often rely on expertise gathered from systems which may not translate directly to cancer. Here, we review a theoretical framework tracing back to Waddington’s epigenetic landscape which may be used to derive quantitative and qualitative understanding of cellular reprogramming. Implications for tumor heterogeneity, evolution and adaptation are discussed in the context of designing new treatments to re-sensitize recalcitrant tumors.

1. Introduction

Cancer is traditionally viewed as a genetic disease caused by the random accumulation of mutations in critical genes or pathways that control proliferation and other “hallmark” traits [1]. Heterogeneity within a tumor would then arise through classic Darwinian evolutionary processes of mutation and clonal selection [2]. Expansion of heterogeneous phenotypes can then limit the effectiveness of treatment which is inevitably directed to the majority (average) clones, as insensitive phenotypic variants emerge.

However, it is becoming increasingly clear that the phenotype of a cancer cell is not just determined by its genotype. Epigenetic [3] and microenvironmental [4] factors provide additional significant contributions, such that two cancer cells with identical genotype may actually exhibit distinct phenotypes (Fig. 1).

Fig. 1.

Due to genetic instability, cancer cells in a tumor may have several distinct genomes (bottom). Each distinct genome underlies a unique epigenetic landscape (middle), which defines what cell phenotypes are possible (top). This allows both for cells with identical genomes to adopt distinct phenotypes, and also for cells with distinct genomes to identify identical phenotypes (left VS right). This opens up powerful possibilities for reprogramming cancer cells with diverse genetic backgrounds into more treatable or less malignant phenotypes.

This establishes provocative parallels with embryonic development in which a single genome can give rise to widely diverging differentiated phenotypes. This review discusses key advances toward a systems-level understanding of cell identity and reprogramming, first in the context of normal development, then connecting it to cancer heterogeneity and evolution. We review the foundational theory of cellular reprogramming, and discuss quantitative methods to predict or improve reprogramming efficiency and outcomes. In the last section, we position these exciting recent cell biological breakthroughs in the context of cancer heterogeneity and tumor evolution.

2. Cellular reprogramming

Within developmental biology, the traditional dogma of cellular differentiation has been that an organism begins as a zygote which gives rise to pluripotent stem cells [5]. Upon division, environmental cues [6] or stochastic effects [7] can give rise to a hierarchy of cells with increasingly differentiated states. Differentiation was considered an irreversible process, in which histone modifications and DNA methylation controlled the accessibility of key DNA regions [5] through opening or closing of the chromatin structure. However, differentiated cells still maintain all the DNA required for pluripotency. Indeed, it was shown that implanting the nucleus of a somatic cell into a denucleated oocyte could produce a stem cell [8], demonstrating the existence of unknown regulatory mechanisms in the oocyte cytoplasm which were able to re-activate the “locked” pluripotency state.

In 2006, Takahashi and Yamanaka found a set of 4 transcription factors (TFs): Oct3/4, Sox2, Klf4, and c-Myc (collectively “OSKM”), that could cause dedifferentiation of mouse embryonic fibroblasts to induced pluripotent stem cells (iPSCs) [9]. On average, though, only about 0.05% of transduced cells underwent transformation, and upon relaxation of the TF cocktail, the cells fell back into their previous, differentiated state [10]. Other studies have extended the gamut of reprogrammable cell types [11], and while in many cases efficiency has been greatly improved [12,13], deciphering the regulatory programs controlling cell identity promises to enable many biomedical applications [14,15], and may have future impacts on cancer therapy.

The OSKM TFs have been classified as “pioneer transcription factors,” able to bind enhancers in a closed chromatin state [16]. These factors were also found to promiscuously activate multiple off-target genes, such that final establishment of the pluripotent state very likely requires a system-wide rebalancing of the gene regulatory network (GRN) [16].

Mathematical modeling is appropriate for understanding the GRN dynamics underlying this rebalancing, and could accelerate discovery of key TFs to reprogram cells to a target phenotype. This may be especially true in cancer cells, in which phenotypes are often not clearly classifiable, especially with respect to treatment sensitivity. In the next sections, we will discuss theoretical frameworks which aim to clarify the topology of “epigenetic landscapes” in mathematical terms, and could help resolve the nature of cancer cell phenotypes and their drivers.

3. The epigenetic landscape and theory of attractors

In 1957, CH Waddington proposed the concept of an epigenetic landscape [17] (Fig. 2a), in which cells roll downhill through bifurcating channels representing differentiation pathways. As cells progress down these metaphorical slopes, they become increasingly committed to a terminal phenotype at the bottom. Distinct pathways are separated by ridges, confining cells to their differentiated identity. While this framework was intended purely as a conceptual tool to obtain a “rough and ready picture” that “cannot be interpreted rigorously” [17], it was nonetheless developed within the mathematical context of dynamical systems theory.

Fig. 2.

(a) Waddington’s depiction of the epigenetic landscape (taken from Ref. [17]) of cells rolling downhill through bifurcating channels. (b) An artistic rendering of a bumpy epigenetic landscape characterized by a quasi-potential. It consists of basins of attraction, such that some cell states may be more or less stable, depending on the height of the energy barrier between them. Small perturbations will not push cells out of their “basin of attraction”, however large and properly directed perturbations can reprogram cells by moving them into a neighboring basin.

This was reasonable since, within this theory, stable states (named attractors) commonly arise from dissipative systems which must exchange energy and matter with their environment to sustain function [18], a seemingly realistic and necessary behavior for cells. Thus, biologically, an attractor describes a state in which a cell identity can stably persist.

Over the past 50 years, several researchers have taken on the task of formalizing this attractor framework in the context of biology, in order to understand how signaling pathways and GRNs may robustly coordinate cell behavior [19–32]. The next section highlights these efforts and their potential relevance to cell reprogramming.

4. Gene regulatory dynamics and attractors

Stuart Kauffman proposed the idea of Boolean network models, in which genes can either be ON or OFF [20], in order to simulate the dynamics of GRNs. His models revealed that networks with certain structural properties did indeed settle into a small number of stable attractors, providing the first evidence that cell types may correlate with GRN attractors [20,21]. A few decades later, Huang et al. [22] provided an experimental justification for this intriguing idea. In mathematics, attractors by definition have an associated region called the “basin of attraction” (Fig. 2b) corresponding to all states that will eventually approach the attractor [33]. Huang et al. exploited the fact that HL60 human promyelocytic leukemia cells can be induced to differentiate into neutrophils via treatment with either DMSO or ATRA. Tracking the trajectory of a 2773-gene expression panel, they showed that HL60 cells respond divergently to treatment with these agents. However, the trajectories eventually converged to an identical neutrophil state. They reasoned that the divergent trajectories must both have been within the basin of attraction of the neutrophil state, which must then be an attractor [22].

This basin of attraction is ultimately responsible for the stability of an attractor, as small deviations from the attractor will remain confined within the same basin (Fig. 2b) [33,34]. Within this framework, it has been suggested that reprogramming can be achieved by forcing a cell out of its basin of attraction either through an external push, or an internal rewiring which causes the landscape to shift, such that the cell will be ultimately drawn toward an alternative attractor (Fig. 2b) [28,34–41]. These efforts provided a motivation for developing quantitative models to connect the dynamics of GRNs to cellular phenotype and reprogramming, as described in the next section.

5. Quantifying, drawing, and analyzing the epigenetic landscape

For biological systems, GRNs are comprised of hundreds to thousands of interacting genes. Mathematically, each gene represents a single dimension, and it is possible to routinely compute with all these dimensions. However, most humans can only visualize a maximum of 3 dimensions at once (2 genes, plus the landscape height, Fig. 2b), so that it is in general impossible to visually represent the entire high-dimensional epigenetic landscape for real biological systems. Nevertheless, quantifying this landscape can provide information about the barriers between separate basins, and visualizing 2D slices can promote an intuitive understanding of cells’ behaviors.

A common method to quantify the dynamics of a GRN is based on Hill kinetics [30–32,35,36,42–44] (Fig. 2). When each regulator of a given TF (say, x_i) acts independently, the dynamics take the form

$$\frac{\text{d}{x}_i}{\text{d}t}=\sum _{j\in \mathit{\text{activators}}}\frac{a_{j.i}{x}_j^{n_{j,i}}}{K_{j,i}^{n_{j,i}}+x_j^{n_{j,i}}}+\sum _{j\in \mathit{\text{repressors}}}\frac{b_{j.i}{K}_{j,i}^{n_{j,i}}}{K_{j,i}^{n_{j,i}}+x_j^{n_{j,i}}}-k_i{x}_i$$ (1)

where a_j,i and b_j,i represent the maximum contribution or inhibition of the jth TF on expression of x_i (Fig. 3a), K_j,i reflects the threshold for the jth TF to influence x_i, n_j,i controls how switchlike or gradual the regulation is (Fig. 3b), and k_i represents the natural decay rate of x_i. More complicated forms are able to account for interactions between TFs [45].

Fig. 3.

Hill kinetics are commonly used to quantify the dynamics of GRNs. (a) A single activating interaction showing the characteristic sigmoidal shape of the Hill curve. Low regulator concentrations do little to induce expression of the target gene, however as the concentration approaches a threshold value (red dotted line) the regulatory strength increases rapidly. At the red dotted line, the regulator has half of its maximum possible influence on its target. Further increases in concentration gradually cause the influence to asymptotically approach the maximum regulation (blue dotted line). Here, a = b = 3, K = 0.3, and n = 3. (b) The Hill curve becomes more switchlike as n becomes larger. Here, a = b = 1, K = 0.5, and n ∈ {1, 2, 3, 5, 7, 10, 50} as the switch becomes more instantaneous.

The epigenetic landscape is often thought of as analogous to potential energy from physics, and is ideally computed as a function, $U(\overrightarrow{x})$, such that cells roll down the gradient of $U(\overrightarrow{x})$ under the dynamics of the GRN

$$\frac{\text{d}\overrightarrow{x}}{\text{d}t}=-\nabla U(\overrightarrow{x}).$$ (2)

In practice, however, even simple GRNs are not gradient systems [19,29,30,46], and cannot be fully described by Eq. (2). One proposed method to overcome this is to split Eq. (1) into a portion which is describable by a landscape and some remainder [29,30]

$$\frac{\text{d}\overrightarrow{x}}{\text{d}t}=-\nabla \tilde{U}(\overrightarrow{x})+{\overrightarrow{F}}_{\mathit{\text{remainder}}}(\overrightarrow{x})$$ (3)

where $\tilde{U}(\overrightarrow{x})$ is commonly referred to as a “quasi-potential” (Fig. 2b). (Eq. 3) essentially separates the dynamics of relaxing toward the attractor ($-\nabla \tilde{U}(\overrightarrow{x})$) from the dynamics along the attractor (${\overrightarrow{F}}_{\mathit{\text{remainder}}}(\overrightarrow{x})$) [30,31]. However, there are infinitely many ways to construct such a decomposition (Eq. (3)) and the precise method chosen will influence the resulting landscape and difficulty of computation [29]. Nevertheless, given a landscape it is possible to identify pathways of least resistance [24,29,32,35,40] for cells to transition between attractors, and it has been proposed [32,40] that such paths may provide a roadmap for efficient reprogramming strategies. Indeed, by varying parameters, from (Eq. 1) it is possible to quantify how much each individual interaction contributes to the barrier height between attractors. In a model of stem cell differentiation, Li found that previously established reprogramming factors had a large impact on the barrier height along the path of least resistance between attractors in a model of stem cell differentiation [32].

Alternative methods have been proposed to quantify the energy landscape, including network entropy [47] and a stitched-together landscape of potential energy changes [46], and although these methods are more phenomenological, they have been shown to qualitatively agree with intuitive expectations, and may be appropriate for very high-dimensional systems.

6. Boolean network models can identify reprogramming strategies

Eq. (1) models regulatory interactions as sigmoidal functions (Fig. 3), so that low concentrations have no regulatory impact, and high concentrations saturate toward a maximal impact. By letting the Hill coefficient n become large, the transition from zero to maximal impact becomes instantaneous (Fig. 3b) [48], mimicking the Boolean structure proposed by Kauffman [20]. Boolean models therefore represent a coarse-grained approach which is useful to derive qualitative results.

Using Boolean models to describe cellular reprogramming, Crespo et al. [49] developed network models of several biological systems. Simulations of activations and knockdowns which drove the systems between attractors revealed experimentally validated cocktails of reprogramming factors.

Alternatively, Lang et al. [50] built a Hopfield neural network (a type of Boolean model) to simulate dynamics leading toward 63 distinct cell states. This approach revealed multiple attractors between cell types, which they suggested may be responsible for the partial reprogramming observed experimentally. Furthermore, they computed the contribution of each TF to the stability of a state and were able to identify many known reprogramming TFs.

7. Simple models reveal topological properties of reprogramming

It has been proposed that GRNs maintain separated basins through clusters of TFs which mutually activate one another’s expression via positive feedback, and reciprocally inhibit expression of alternative clusters through negative feedback [41,51–53] giving rise to multi-stability [19,43,54,55] (Fig. 4). Intuitively, once one module becomes dominant, it simultaneously reinforces its own activity, while silencing its repressors. Depending on the parameters of such systems, which are potentially influenced by multiple external factors [19,55], stable states may become destabilized (Fig. 4). This is one way to force cells into the basin of an alternative attractor (Fig. 2b). Thus, positive and negative feedback loops are a key driver of multistability, and represent a promising motif for cellular reprogramming.

Fig. 4.

(a) A common regulatory motif which consists of two TFs which repress one-another’s expression, while activating their own. (b–d) Possible attractors and basins of attraction for different parameter sets from Eq. (1). While there is a stable “hybrid” state in (b), it can be destabilized as in (c) and (d) by reducing the strength of self-activation. Similarly, by adjusting the activating and repressing parameters, one phenotype may become more epigenetically favorable (d) than the other (c).

Inspired by this observation, Crespo and Del Sol [52] identified reprogramming factors by simply searching for positive feedback loops whose elements are differentially expressed between distinct cell states. Within these feedback loops, genes with maximum out-degree were predicted to be master regulators. This technique was able to identify known reprogramming recipes for the several cell types they tested [52].

Other researchers have studied structural properties of simple models in which entire clusters of TFs are simulated as single, auto-activating and cross-inhibiting nodes (Fig. 5) [41,43,56]. For instance, MacArthur et al. [41] built a simple model for stem cell differentiation by coupling 3 auto-activating lineage-specific modules and a pluripotency module with negative feedback loops. They found that increasing differentiation factors led to an irreversible progression through pluripotent, tripotent, bipotent, and finally terminally differentiated states. Noise added to the pluripotency module enabled differentiated cells to stochastically dedifferentiate, while noise in other modules had no effect.

Fig. 5.

(a) Example topology of a GRN extending the motif in Fig. 4a in which TFs specific to a certain cell type (given as colors) predominately promote one another’s expression through positive feedback loops, and inhibit TFs specific to alternative cell types. (b) This topology is often amenable to reducing to interactions between clusters of TFs. (c) Such topologies commonly give rise to multistable systems where each cluster of TFs are activated in particular phenotypes. (d) Reprogramming by activating TFs from a target phenotype may destabilize several of the phenotypic attractors, but may still maintain a rugged landscape with partially reprogrammed cells and off-target effects. Further activations or knockdowns can alleviate this and result in more complete and stable reprogramming.

This TF clustering approach was adopted by Cahan, Morris, and coworkers [57,58] who developed CellNet to score performance of reprogramming experiments between a predefined set of 21 cell types (though it has now expanded to include 36: 16 human cell types and 20 mouse cell types), and suggest TFs to push partially reprogrammed cells the rest of the way. To build CellNet, the authors identified network-based clusters of TFs with specific enrichment for a distinct cell type. TFs are prioritized as reprogramming targets based on their differential expression levels and centrality within these clusters. Applying their method to established protocols of cellular reprogramming, the authors consistently found evidence of partial reprogramming. In many cases, further manipulation of prioritized TFs improved target cell function and stability [58].

Others have considered GRNs arranged as a hierarchy of positive and negative feedback loops, which lead to hierarchies of differentiation [36,43]. Artyomov et al. studied topological reprogramming properties of such networks [56], and observed that successful reprogramming was only achievable by targeting TF modules of the immediate progenitor or the immediate neighbor of the current state [56].

Rackham et al. developed Mogrify [59] based on a similar principal by prioritizing TFs based on their proximity to differentially expressed genes. They integrated topological information from gene regulatory networks from the STRING database [60] and FANTOM consortium [61], and assign a score to TFs based on a combined score of their own differential expression between the two tissue types, and also by weighting the differential expression of downstream target genes based on their regulatory distance and specificity. They have applied this approach to prioritize TFs to reprogram between any of 173 cell types and 134 tissues in humans, identifying and validating several novel reprogramming experiments.

8. Reprogramming in cancer

While often thought of as a purely mutational disease, cancer is recognized as having a significant epigenetic component [3], supporting the idea that the methods of cellular reprogramming may find new applications in treatment.

Tumors are known to be heterogeneous cell populations including multiple types of cancer cells as well as various non-malignant supporting cells. The behaviors and interactions between all these cell types leads to the overall phenotype of the tumor. For instance, clonal evolution in cancer can lead to selection of resistant subpopulations of tumor cells during treatment [63]. The cancer stem cell hypothesis suggests that tumors have a small population of cells which persist through treatment, and which are able to give rise to and replenish the entire pool of tumor phenotypic diversity [64].

Different groups have shown that tumor cells can be reprogrammed to iPSCs using the same factors as in normal cells [65–67]. For instance, Miyoshi et al. [65] found that the Yamanaka OSKM factors were able to induce an embryonic stem cell-like phenotype in gastrointestinal cancer cell lines, and found that these transformed cells showed re-activation of tumor suppressor genes, increased chemosensitivity, and decreased invasiveness.

Likewise, Zhang et al. [66] showed that overexpression of Oct4, Nanog, Sox2, Lin28, Klf4, and c-Myc was able to reprogram human sarcomas into iPSCs. Furthermore, they showed that these tumorous iPSCs could be redifferentiated into connective tissue and red blood cells, and that this process resulted in a loss of tumorigenicity.

Glioblastomas (GBMs) contain rare populations of cells, tumor propagating cells with stem-like properties, which are known to drive tumor progression and therapeutic resistance. Suva et al. [67] showed that activation of Pou3f2, Sox2, Sall2, and Olig2 is able to transform GBM cells to behave like these tumor propagating cells.

Taking another direction, Vêncio et al. [68] showed that reprogramming the tumor microenvironment could also have a therapeutic effect. They found that CD90+ prostate cancer-associated stromal cells could be reprogrammed to iPSCs by overexpressing Pou5f1, Lin28, Nanog, and Sox2, causing the reprogrammed stromal cells to lose their tumor supporting phenotype.

These studies have relied on the vast amount of knowledge and expertise developed in the stem cell reprogramming field, and serve as proof-of-principals to establish reprogramming as a viable avenue for treatment. However, the extreme diversity of cancer heterogeneity provides challenges and opportunities for additional reprogramming strategies between different cancer-specific phenotypes, or even reverting the cancer phenotype to a non-malignant one. Prioritizing targets to drive conversions between these different phenotypes will benefit from the application of the computational and mathematical frameworks reviewed in this paper.

Indeed, it has been argued that the view of cell types as attractors of some epigenetic landscape is applicable not only to understand epigenetic regulation in normal tissue, but also cancer and cancer heterogeneity. For instance, several groups have advocated that the malignant state itself represents an attractor of some epigenetic landscape, and that healthy, non-malignant states may still be reachable via reprogramming [69–72].

Additionally, other groups including ourselves have found that distinct TF network attractors specify heterogeneous cancer phenotypes. For instance, we [62] found that neuroendocrine-epithelial and mesenchymal-like heterogeneity in small-cell lung cancer could be explained as attractors of a TF network derived following a mixed bioinformatics, modeling, and experimental workflow in Fig. 6. Significantly, we found that treatment with chemotherapeutics caused shifts toward a hybrid phenotype, suggesting that epigenetically modulated cancer heterogeneity contributes to treatment resistance. Reprogramming cells out of resistant states and into sensitive ones is likely to improve treatment effectiveness in such cases.

Fig. 6.

A workflow we used in our recent work [62] in which we identify and model a TF network controlling phenotypic heterogeneity in small-cell lung cancer. It consists of three phases. First, analyzing gene expression data to identify distinct cellular phenotypes and co-expressed clusters of genes which distinguish those phenotypes (as in Fig. 5). Second, identifying TFs which regulate those co-expressed gene clusters and assembling them into a TF network. Finally, simulating the dynamics of the TF network to identify stable attractors. We used a Boolean modeling approach to find SCLC phenotype attractors.

Many of these results have also been demonstrated by other groups using microRNA perturbations to reprogram cancer cells, instead of TFs. This builds off of reports that microRNAs can efficiently reprogram cells [73,74]. Tsuno et al. [75] showed that lentiviral induction of miR-520d was able to reprogram hepatoma cells to a stem-like state which, when injected into mice, showed no malignancy. Importantly, Ogawa et al. [76] administered miR-302 and miR-369 in vivo to reprogram colon tumors to less malignant states, showing that the reprogrammed tumor cells had higher activation of apoptosis. Other groups have also shown the potential of miR-302 to reprogram cancer cells toward a stem-like state [77,78], and may improve drug sensitivity [78].

9. Moving to the clinic: opportunities and challenges

One of the primary challenges facing cancer researchers and clinicians today is that while treatment may be initially efficacious, the tumor eventually relapses, and has become refractory to further treatment [79]. It would therefore be powerful to find ways to reprogram tumor cells back to a sensitive phenotype, or adjuvant treatments which prevent the emergence of resistant phenotypes altogether.

Early efforts to develop such treatments will benefit by focusing on cancer types with well-established signatures of heterogeneity, such as small-cell lung cancer [62], glioblastoma [80], non-small-cell lung cancer [81] or breast cancer [82,83], and phenotype-specific drug sensitivity patterns. Based on these gene signatures, a workflow like that shown in Fig. 6 can be used to identify a GRN underlying that cancer’s epigenetic landscape, and transitions between sensitive and resistant attractors.

Clinically, transcriptomic profiling of multiregion biopsies [84] or of circulating tumor cells (liquid biopsies) [85] could be used to determine the specific phenotypic composition of a patient’s primary tumor and/or metastases. Optimal combinations of TF activations or knockdowns for this specific patient can then be identified to stabilize the sensitive cells, and destabilize the resistant ones.

Historically it has been difficult to develop chemical therapeutics targeting transcription factor function, but recent advances have shown that this is a promising area of future research [86]. Nevertheless, there are several, alternate approaches which may result in indirect perturbations of a patient’s TF network, including combinations of drugs, signaling pathways, microRNAs, and epigenetic agents.

Bioinformatically, the Connectivity Map [87] and LINCS L1000 [88] databases provide information about gene expression changes resulting from pharmacological or genetic perturbations. Interrogating these online resources with appropriate datasets from clinical tumors may help identify existing approved compounds which are statistically linked to activation or inhibition of target TFs. Nevertheless, the mechanism of these changes is generally not well understood, and off-target effects may limit the effectiveness of this approach.

Mechanistically, signal transduction pathways carry information through a cell and often end in the activation, deactivation, and/or degradation of one or many TFs. Importantly, the phosphorylation events that carry information through signaling pathways are well suited to pharmacological inhibition or activation.

Another promising approach is through clinical overexpression or inhibition of microRNAs. Currently no microRNA therapeutics are FDA approved, however there are several under preclinical investigation, and a few in clinical trials. Significantly, as discussed above, in some cases microRNAs have been shown to be effective reprogramming agents, including in cancer, and they may therefore become important components of reprogramming therapies.

Gene expression is intrinsically limited by the accessability of a region of DNA, and chromatin structure can help lock in a cell’s identity. Chemical agents which act as histone deacetylase inhibitors or DNA methyltransferases can cause extensive changes in gene expression and plasticity, and have been shown as effective reprogramming agents. Furthermore, there are several FDA approved epigenetic therapeutics which may be used in combination with other strategies to improve reprogramming efficacy.

Biologically, the actions of signaling networks, microRNAs, chromatin structure, and TF regulation occur over several timescales, from seconds or minutes (within a single cell’s lifetime), to hours and days (spanning cell generations) [89]. We foresee that a key theoretical challenge will be to reconcile the dynamics of these different timescales, and across cell divisions.

10. Discussion

60 years after its introduction, Waddington’s epigenetic landscape remains a powerful metaphor to understand differentiation and reprogramming. Recent advances in cancer biology have painted a clearer picture of the importance of epigenetic regulation in maintaining malignancy and heterogeneity, and indeed several studies have already shown the feasibility of using TFs to reprogram cancer cells, particularly in the context of dedifferentiation.

Analysis of stability, perturbations, and topology have all been applied to identify possible reprogramming targets with great success in normal developmental biology, and provided insights into how cells maintain barriers between differentiated states through feedback loops.

However, it is not always clear how dysregulation in cancer GRNs may give rise to unique phenotypes. Nevertheless, recent results have suggested that these same tools may be useful to decode cancer epigenetic regulation.

As our understanding of epigenetic regulation improves, we should be able to create detailed models which provide a theoretical, high-resolution depiction of the control of cancer and cancer heterogeneity which will be indispensable in the search for therapeutic options. The outcome of such research could fundamentally reverse the standard approach to personalized therapy, in which new drugs are developed to match specific subtype of cancer. Instead, we may find ways to develop therapies which reprogram resistant cells into a sensitive state, matching cells to the drug.