Mapping Phenotypic Plasticity upon the Cancer Cell State Landscape Using Manifold Learning

Any given tumor is made up of a unique collection of cancer cells that exist within a spectrum of diverse genotypic and phenotypic cell states. Understanding the scale and functional implications of such heterogeneity is a significant scientific challenge because this diversity is clinically associated with aggressive disease, resistance to conventional chemotherapies, and poor overall survival (1–6). Yet this implies that targeting specific cell populations within a tumor, or preventing the emergence of particularly aggressive subpopulations, could lead to enhanced therapies and improved survival outcomes for patients. To reach this goal, strategies to identify and therapeutically target key intratumoral cell populations are vital.

It is long established that genetic diversity is a critical mediator of intratumoral heterogeneity (5). Studies in glioma demonstrate that intratumoral heterogeneity may consist of anywhere between 0 and 8,000 coding mutations (7) that provide tumors with crucial survival advantages like permitting survival in evolving microenvironments or in response to therapeutic insults (5, 7–10). In some instances, genetic heterogeneity is already present within the primary tumor, such that chemotherapy favors the emergence of otherwise minor or dormant clones (11). In other cases, disease progression is driven by the therapy-induced emergence of clones with de novo mutations that are not present in the primary tumor (12). Given the spontaneous, random, and stochastic nature of such mutations, designing therapies and clinical trials to prevent their initial emergence or selection remains challenging (5).

Importantly, there is now substantial evidence that nongenetic mechanisms can also significantly increase intratumoral heterogeneity and disease progression (4, 13, 14). In this setting, distinct cancer cell states are created by a process termed “phenotypic plasticity,” in which epigenetic, transcriptional, and/or translational mechanisms—rather than mutations—drive phenotypic cell state switching in a manner akin to normal development, wound healing, and organ regeneration (4, 13, 15–17). In fact, phenotypic plasticity is now recognized as a hallmark of cancer (18).

In contrast to genetically driven heterogeneity, phenotypic plasticity is dynamic, reversible, and responsive to regulation (19–24). Implicit here is the notion that phenotypic plasticity reflects molecular program switching under the control of specific pathways that may be therapeutically targetable. Understanding the molecular mechanisms regulating phenotypic plasticity thus constitutes the first step toward establishing what we term “state-gating strategies” for cancer therapy—controlling entry into or exit from specific phenotypic cell states. Given the failure of cytotoxic therapies to treat advanced-stage disease, mastering phenotypic plasticity to prevent cells from entering into highly aggressive or resistant cell states is a promising strategy to curtail both metastasis and therapy escape. Such therapeutic advances may prove clinically transformative (25, 26) but demand a new systematic understanding of cancer cell states, their plastic dynamics, and molecular regulation.

In this review, we consider the biology of nongenetic heterogeneity from the perspective of a cancer cell state landscape, whereupon cancer cells occupy a continuous spectrum of phenotypic states connected by trajectories defining dynamic cell state transitions, herein termed “plasticity.” We illustrate how single-cell “omics” measurement technologies now synergize with manifold learning–based analytical methods to illuminate the topology of this cancer cell state landscape. This reflects the recent proliferation of single-cell technologies that are providing unprecedented capacity to systematically characterize molecular mechanisms governing phenotypic plasticity at the cellular scale (27–30). Leveraging this revolutionary data, manifold learning techniques are also emerging to effectively model cell state dynamics in a way that mimics our understanding of the cell state landscape, being both globally complex (nonlinear) and locally continuous. Building on this tripartite synthesis of (i) the cancer cell state landscape paradigm, (ii) single-cell omics measurement methods, and (iii) manifold learning analysis tools, we further consider how this systematic framework will inform biological advances leading to novel therapeutics. Indeed, we believe this synthesis will promote not only new individual therapies but ultimately a new class of therapies that strategically target cancer cell plasticity itself to restrict cancer cell heterogeneity and adaptability.

Although there is mounting evidence that phenotypic plasticity drives disease progression in multiple cancer types (refs. 14, 16, 20, 27–30; for a recent review on this topic, see ref. 4), it remains a complex process to dissect. The temporal dynamics governing cell state changes can encompass trajectories spanning months to years, in line with disease progression or therapeutic treatment and response. Yet plasticity may also result from rapid changes in transcription, protein expression, and even localization within days, hours, or minutes. Cancer cell plasticity is also modulated by spatially resolved cues spanning organ, tissue, cellular, and subcellular scales. Thus, resolving both temporal and spatial dimensions is critical to understanding cancer cell plasticity and its role in both tumor progression and therapy resistance.

Much of our understanding of the molecular programs governing cancer cell plasticity derives from early observations revealing the co-option of developmental cell plasticity programs by cancer cells, such as transitions between epithelial and mesenchymal cell states. This includes epithelial-to-mesenchymal transition (EMT; refs. 31, 32) and the reverse process, mesenchymal-to-epithelial transition (MET; refs. 33, 34). In this paradigm, cancer cells defined as epithelial-like are considered less tumorigenic and generally lacking in cancer stem cell characteristics. Upon undergoing EMT to acquire a full mesenchymal or even hybrid epithelial/mesenchymal state, they are thought to gain stem cell characteristics that permit promotion of metastasis and chemotherapy resistance (35–37). These early studies have also revealed important information about the significance of ongoing cell plasticity dynamics. For example, EMT at the primary tumor site increases metastatic potential; yet among metastatic cells, the ability to also undergo the reverse MET process, even if only partially, better enables secondary tissue colonization and metastasis growth (38–43). Thus, metastatic efficiency is greatest when cancer cells retain the plasticity to use epithelial or mesenchymal attributes best suited at distinct stages of the metastatic cascade.

The epigenetic landscape of a cancer cell is an important determinant of its intrinsic propensity to undergo EMT or MET. For example, a bivalent chromatin configuration at the promoter of the EMT transcription factor ZEB1 predisposed basal breast cancer cells lacking stemness features to spontaneous ZEB1 activation and subsequent entrance into a cancer stem cell state. In contrast, the equivalent cells isolated from luminal breast cancer maintain repressed chromatin at the ZEB1 promoter and do not readily change cell state (19). Bivalent chromatin configuration also underlies phenotypic plasticity within cancer stem cell populations themselves, providing cancer stem cells with additional adaptability (44). Epigenetic modulation plays an important role not only in a cell's predisposition to invoke phenotypic plasticity but in the execution of the process. The transcription factors that execute EMT—for example, SNAI1—bind to the promoter of the CDH1 gene encoding E-cadherin, a gatekeeper of the epithelial cell state. This binding recruits components of the polycomb repressor complex and histone deacetylases to modify chromatin and mediate the silencing of CDH1 expression (45, 46). Accordingly, chromatin remodelers, writers, and readers provide important regulatory control over phenotypic plasticity and are the subject of therapeutic investigation (47, 48).

Notably, there are now several examples of phenotypic plasticity programs that drive cancer progression outside of those associated with developmental differentiation. Metabolic plasticity enables cancer cells to alter their utilization of metabolic programs to sustain growth and survival. These changes may occur in response to hyperproliferative cell states, changes in microenvironmental nutrient availability, or the requirement for de novo rate-limiting macromolecule synthesis (49). The capacity to change metabolic dependencies not only favors survival but may also favor metastatic outgrowth in distinct organs—for example, elevated fatty acid synthesis (50) or de novo serine synthesis (51) is enhanced in breast cancer brain metastases compared with primary tumors, whereas the pyruvate carboxylase–dependent resupply of metabolites is enhanced in breast cancer lung metastasis compared with primary tumors (52, 53). Beyond the impact of those changes on the cell's metabolism, epigenome regulators are also highly sensitive to changes in intracellular metabolism. Indeed, a cancer cell's epigenetic and transcriptional landscape can be altered, for example, by iron endocytosis (54), proline metabolism (55), or the metabolite 2-hydroxyglutarate (56).

Entrance and exit from slow-cycling, quiescent, dormant, or even senescent cell states are phenotypic plasticity programs that are particularly consequential for tumor relapse or recurrence (57–59). Cells that escape these latent states may reenter the cell cycle via activation of proteins controlling cycling (e.g., cyclin-dependent kinases; ref. 59), through upregulation of stemness markers (60), or by changing extracellular matrix composition in the dormant niche (61). Returning to the importance of metabolic plasticity in cell state determination, reactivation of cell cycling among therapy-resistant persister cells has been linked to the upregulation of fatty acid metabolism (62). Interestingly, survival in a dormant cell state has been linked to the upregulation of immune genes that provide a “cloak” to cancer cells to avoid immune detection. Similarly, downregulation of that immune program enables dormant cells to reenter the cell cycle (63).

Immune evasion is not only a critical component of tumor dormancy, it is also fundamental to robust tumor growth. Indeed, this biology underpins the breakthrough success of immunotherapy (64). Like most cancer therapeutics, however, intrinsic or acquired resistance to immunotherapy ensues, with evidence that phenotypic plasticity plays a significant role (65). Alongside the ability of EMT to drive cancer cells into more aggressive cell states, it also promotes immune evasion by decreasing levels of MHC-I and promoting high levels of PD-L1 on cancer cells (66, 67). These changes are in line with the direct impact of EMT-inducing cytokines, for example, TGFb, that drive EMT in cancer cells while suppressing innate and adaptive immune responses in the tumor microenvironment (67, 68). In fact, clear differences in the immune landscape have been noted in epithelial versus mesenchymal tumors, including a change from CD8⁺ T cells and M1 antitumor macrophages to M2 protumor macrophages, increased CD8⁺ T-cell exhaustion, and increased regulatory T-cell recruitment (67). These studies suggest that therapies preventing EMT, or conversely, enhancing MET, may be effective in sensitizing tumors to immunotherapy.

Perhaps the most alarming manifestation of phenotypic plasticity is in facilitating therapy evasion and the emergence of therapy-resistant disease (69, 70). A prime example of this is evidence demonstrating that a partial EMT is associated with entrance into a chemotherapy-resistant state (71). Similarly, radiotherapy can promote phenotypic plasticity in the stroma of distant metastatic organs, establishing a positive feedback loop with metastatic cancer cells, which in turn undergo a phenotypic transition that enhances their capacity to grow and evade therapy (72). Moreover, multiple studies have now proven that chemotherapies themselves—spanning anthracyclines, topoisomerase inhibitors, platinum-based therapies, and taxanes—all induce components of the EMT program and thereby chemotherapy resistance (73). Similarly, the evidence of partial MET at metastatic sites also leads to chemotherapy-resistant cell states (74). These studies show that chemotherapies affect multiple cell states and stages of metastasis to actively induce therapy-resistant phenotypes, as opposed to only creating resistance through a gradual selection of preexisting resistant clones. This active induction of resistant cancer cell states through nongenetic plasticity programs suggests a targetable vulnerability, such that the elucidation and modulation of these chemotherapy-induced plasticity programs will permit novel therapeutic strategies (25).

Together, these studies highlight the complex interplay of plasticity programs spanning developmental, metabolic, immune evasion, epigenetic, and drug resistance systems that cooperate to optimize cancer cell growth and survival (75–77). Beyond these insights, we are only on the cusp of understanding how underlying genetic mutations contribute additional dimensions to the control of phenotypic plasticity (78–81).

Given the sensitivity of phenotypic plasticity programs to environmental cues, it is interesting to consider how short or transient exposure can lead to long-term, stable phenotypic changes. For example, if a cancer cell is exposed to an EMT-inducing signal at the primary tumor site, how is the phenotype maintained once the cell transits into the circulation or to a distant metastatic site? Recent insights into miRNA/EMT transcription factor regulatory loops, for example, the miR200–ZEB1 feedback, demonstrate how negative feedback loops create a sensitive yet noise-resistant bistable response to short-term cytokine exposure (82). In this example, a 5-minute exposure to the EMT-inducing cytokine TGFb reinforces ZEB1 signaling to stabilize an EMT that persists for days and is capable of increasing metastatic potential. The bistability revealed here is emblematic of a hysteretic process in which differences in the histories of individual cells dictate divergent responses to equivalent stimuli. Such hysteresis raises further questions as to whether particular state transitions are (i) bidirectional, in which cells in state A can transition to state B and cells in state B can transition to state A; (ii) reversible, in which a single cell in state A can transition to state B and then back to state A; and (iii) asymmetrical, in which cells transition from state A to state B via a different trajectory versus cells transitioning from state B to state A, as in the hysteresis example above and depicted in the epithelial-to-hybrid epithelial/mesenchymal state and hybrid epithelial/mesenchymal-to-epithelial example in Fig. 1A. Ultimately, understanding how these plasticity pathways are regulated, together with defining permissive epigenetic states, is vital for a systematic understanding of the temporal dynamics giving rise to cancer cell heterogeneity and to the adaptive capacity of individual cancer cells.

Of course, phenotypic plasticity does not arise purely through cell-autonomous decision-making or stochasticity. Rather, it emerges as part of the complex, spatially distributed milieu comprising each evolving tumor site (83). Just as the recent history of a given cell may be encoded in hysteretic signaling motifs of the kinds discussed above, or in gene expression or epigenetic patterns, each cell's history is also manifest in its local spatial context. This context incorporates factors such as cell–cell interactions (homotypic; with other cancer cells and/or heterotypic; with fibroblasts, immune cells, vasculature, etc.); cell–extracellular matrix (ECM) interactions; extracellular soluble factors (autocrine/paracrine signaling ligands or cytokines); and chemical properties such as pH and the levels of O₂, CO₂, or reactive oxygen species. Importantly, the reciprocal relationship between each cell and its spatial context not only reflects the cell's history but also shapes its future, guiding decisions between processes such as proliferation, programmed death, motility, or particular cell state transitions. As a consequence, a robust understanding of cancer cell state dynamics—and how these give rise to population heterogeneity—cannot be disentangled from a parallel understanding of intratumoral spatial organization, since in the evolution of tumors, temporal and spatial determinants are fundamentally interwoven (84). This basic concept underpins established yet more specific questions about the existence and nature of so-called cancer stem cell niches, the composition and properties of tumor invasive fronts, and the interfaces between tumors and macrostructures such as vasculature or organ fascia. The mapping of phenotypic cell states via single-cell spatial transcriptomics (85, 86) and proteomic analyses (87) has enormous potential to resolve these questions.

Given the potential complexity and interplay of phenotypic plasticity programs, how do we begin to unravel, resolve, and ultimately understand how those programs contribute to the creation and evolution of a heterogeneous tumor? We can begin by thinking of cancer cells as occupying a cancer cell state “landscape” (Fig. 1A–C). On this landscape, cancer cells reside within a phenotypic continuum. We hypothesize that there may be multiple stable states connected by transitional trajectories permitting traversal of the cell state continuum and that some states and transitions will be favored at different sites or stages of cancer progression. Accordingly, we expect a final understanding of cancer cell states to reveal a more complex and multifaceted landscape—much like the landscape underpinning cellular differentiation envisaged by Conrad Waddington, as revisited by Sui Huang and colleagues (88), and like that proposed as an explanation of nongenetic cancer driver dynamics (89).

In the paradigm of the cancer cell state landscape, high-stability cell states constitute “valleys,” or “attractor states,” into whose orbit adjacent cells tend to fall (Fig. 1B). Conversely, unstable or unfavorable cell states constitute “mountain ranges” that cells cannot easily traverse. These valleys and mountain ranges, thus, partition the cellular landscape into accessible and inaccessible state spaces that collectively give rise to cancer cell heterogeneity. Plastic phenotypic transitions occur between cell attractor states via “canalising” features, for example, channels linking valleys (Fig. 1C). Crucially, it is becoming clear that specific molecular mechanisms underpin the plastic state transitions that constitute these canalizing features, making them prime targets for therapeutic intervention to control tumor heterogeneity.

A significant but often overlooked aspect of cellular dynamics within this landscape paradigm is that the landscape topology “shapes probabilistic outcomes” but is not wholly deterministic. Specifically, although the dynamics of an individual cell are heavily influenced by the local landscape topology (e.g., uphill or downhill gradients), the stochastic nature of cellular information processing nonetheless permits some movements counter to these gradients, meaning that cells can occasionally climb “uphill.” This accounts for the ability of cells to traverse landscapes that have multiple local minima without becoming permanently trapped in these. This “stochastic jittering” provides a degree of flexibility that maintains cell heterogeneity, while nonetheless being guided by the evolved topology or “logic” of the cell state landscape. This mirrors the classic concept of the “explore versus exploit” trade-off considered in evolutionary and complexity theories, in which exploration corresponds to stochastic jittering and exploitation corresponds to a strict following of topological cues (90).

Intriguingly, the level of stochastic jittering—essentially, noise in cellular information processing—is evidently a meta-property that is subject to evolutionary tuning. At the genomic level, mechanisms exist to rapidly raise this noise level in response to stress—for example, stress-induced chromosomal instability increases mutation rates, thereby promoting greater heterogeneity and thus improved population survivability in the presence of stressors (91). Understanding how this meta-property of “noise levels” may be embodied and tuned in the context of nongenetic cellular plasticity could provide an alternative lens through which to interpret and potentially modulate cell state landscapes and the cancer cell dynamics emerging upon them. For example, distinct epigenetic states, or epigenetic priming, such as, a bivalent chromatin configuration at critical gene mediators of phenotypic plasticity, increase the likelihood of normal and cancer cells changing states (19, 92).

Overall, defining tumor-specific cancer cell state landscapes is critical to understanding the diversity of cell states that exist, the transitional trajectories that link significant states, and how these topologies contribute to disease progression and site-specific metastasis. Using such knowledge, we may define the molecular programs controlling plasticity, thereby informing the design of novel therapeutics to block deleterious trajectories or activate beneficial ones. By thus effectively remodeling cancer landscape topologies, we envision a new treatment strategy to prevent cancer progression and therapy resistance. Yet to enact this vision, sophisticated new combinations of experimental and computational tools must now elucidate the specific molecular programs driving plastic transitions that bridge the continuum of cancer cell states.

Recent advances in measurement technologies have facilitated the measurement of gene expression, DNA accessibility, protein content, or genomic mutations across tens of thousands of single cells and now even allow for the measurement of multiple modalities in the same cell. This is a revolutionary change from the previous half century of research where techniques such as flow cytometry recorded only one or two dozen features per cell and involved iterative gating of cells into high or low expression on a per-marker basis. The recent explosion in the number of features provided by cutting-edge single-cell techniques now requires a new framework for data analysis.

One emerging approach is manifold learning (Fig. 1D), which models the cellular landscape as a “manifold” to elucidate the states that cells can occupy. The manifold assumption holds that, despite the measurement space of cells being very high dimensional [∼20,000 gene dimensions in the case of single-cell RNA sequencing (scRNA-seq)], the data actually lie in an intrinsically lower dimensional space due to informational redundancy, that is, dependency between the genes. Thus, by discovering the real intrinsic (often nonlinear) axes of variation, we can understand the true shape of the data. This in turn can be used for denoising data (i.e., restoring data to its manifold-intrinsic dimensions), clustering data (discretizing the lower dimensional representations; Fig. 1E, left), and analyzing trajectories (by associating the intrinsic axes with gene expression, etc.).

The term “manifold” comes from Riemannian geometry and describes a space that is smooth, differentiable, and locally Euclidean (93). For example, measured features (e.g., gene counts in an scRNA-seq space) define a space with tens of thousands of dimensions in which relationships between genes, as well as between genes and phenotypes (94–96), may be nonlinear. We understand, however, that cells progress smoothly between states rather than jumping discretely as an electron might change orbitals, implying that the landscape of cellular states consists of locally smooth patches of cells. Each individual patch can be thought of as analogous to Waddington's landscape, in terms of gene configuration, wherein valleys represent the viable cell states. Intrinsic dimensionality in the gene space is further reduced by informational redundancy resulting from gene interactions and coregulation of gene modules. This suggests the cell phenotypic manifold has lower dimensionality than that implied by the combinatorial diversity of genes or proteins comprising each cell, a prediction validated, for instance, by the quantification of discernible phenotypic diversity produced by large-scale chemical compound screening (97, 98). These constraints on the gene space mean that the cellular landscape is in many cases suitable to be computed from scRNA-seq data using manifold learning techniques. Manifold learning may be limited in settings with very small or disconnected data. For example, bulk sequencing, though high dimensional, typically contains only limited samples (<20). In such cases, the cellular state space or landscape cannot be mapped, and more traditional statistical testing may be applied to understand differential expression signatures. Alternatively, if the data contain selectively sampled points from disparate clusters or curated markers designed to decide between only known cell types, then a supervised classification approach may be preferable.

A particularly elegant framework available within the manifold theory is data diffusion (ref. 99; Fig. 1D). The goal of diffusion geometry is to identify the major trajectories and density centers of a manifold. Diffusion geometry can be defined by the creation of a Markovian diffusion operator, which involves the computation of distances between data points, converted to affinities via a kernel function (such as a Gaussian function), with the subsequent normalization of the affinities. Eigenvectors of the diffusion operator, also called diffusion components (or diffusion maps), reveal major pathways or trajectories within the data. If the original kernel is anisotropic—that is, adapts to the effect of data density—the diffusion operator then shows diffusion, similar to Brownian motion in ambient space, and delineates the geometry of the cellular landscape. On the other hand, if the kernel is isotropic, the Markovian diffusion operator shows a combination of Brownian motion and drift toward density centers. Both modalities can be useful for mapping the cellular landscape in cancer. The diffusion operator applied to an initial distribution of cells can show the pathways that lead to favorable or “low energy” attractor states where many cells gather. Thus, energy changes in the landscape can be revealed to a large extent simply by looking at data density, as this approximates potential energy at that landscape location. Overall, diffusion-based manifold learning has been used successfully for many types of cellular analysis, including trajectory and clustering pseudotime analysis (refs. 100–106; Fig. 1E, center), data visualization (107), data denoising (108), differentiation potency analysis (109), and comparative analysis of single-cell data types (110), and joint embedding from multimodal data (111). Thus, diffusion operators are used to analyze both steady state and transitional behaviors in these systems.

Another promising approach for learning cellular manifolds is deep learning. Self-supervised deep learning methods such as autoencoders re-create their (high-dimensional) input as (high-dimensional) output following encoding to a low-dimensional “latent space” embedding. Methods such as SAUCIE (112), sCVI (113), VASC (114), and a recent two-stage variational autoencoder architecture (115) developed for single-cell phenotypic imaging data constrain (typically smoothing) the structure of the latent space to produce state space manifold representations suitable for biological inference.

Archetypal analysis (116) constitutes a third analytical approach (Fig. 1E, right) wherein a convex hull is fitted to the data such that corners of the convex hull represent extrema and other data points are convex mixtures of the extrema (116, 117). In contrast to clustering, which assumes cells occupy distinct and disconnected spaces, the archetypal analysis describes a spectrum of cell states. Recently, archetypal analysis has been advanced with neural networks AAnet and DeepAA (118), providing scalable and nonlinear extensions of the classic archetypal analysis framework. Taken together, the manifold model provides an expansive and growing framework for single-cell data analysis.

With methodologic advances in data acquisition and manifold learning in place to map the “static” topology of the cancer cell state landscape, including through the integration of data from several measurement modalities (Fig. 2A) (119), it is now vital to understand how cells dynamically traverse this landscape. At the molecular level, understanding the mechanisms that control, initiate, or inhibit phenotypic plasticity constitutes an opportunity to gain therapeutic control over those cancer cell dynamics and thereby curb disease progression.

Biomedical technologies usually negotiate a trade-off of the ability to measure many cellular components (genes, proteins, etc.), with the ability to allow the cell to continue to carry out its function. Thus, it is very difficult to devise technologies that can follow a cell unperturbed in time with a high-dimensional measurement. However, high-dimensional data can be collected as static snapshot measurements, and newly emerging computational techniques, particularly involving deep learning, can allow us to learn continuous dynamics and causal effects even using discrete time-series data (Fig. 2B).

Among these approaches, pseudotime trajectory (101, 102, 109) methods were first applied to learn biological dynamics, in which data from a single time point are used to infer a “pseudotime” dimension along which cells transition. Effectively, if the cellular data were collected under a transitional or differentiation condition, the largest axis of variation could be associated with the developmental process. Since the term “pseudotime” was coined in 2014, over 50 methods have been described for trajectory inference. Yet a major drawback of these techniques is that they learn a simple ordering of cells without modeling the dynamics that underlie the probability that a cell will follow one path or another. A newer data-augmented technique for learning cellular transitions is RNA velocity (120, 121). RNA velocity learns transcriptional dynamics based on the ratio between spliced and unspliced transcripts that are naturally found within scRNA-seq data, where the ratio of spliced to unspliced RNA is used to determine if the cell is increasing or decreasing the expression of each gene, that is, learning a velocity vector for each cell. However, this is a very localized snapshot of a global process.

To elucidate underlying dynamic processes across the cellular state space, some groups have leveraged advances in computational optimal transport. Optimal transport is a mathematical technique that quantifies the minimum cost mapping between two distributions. For example, Waddington optimal transport (122) is a method that has been used to describe cellular dynamics during induced pluripotent stem cell reprogramming. However, Waddington optimal transport restricts these dynamics to linear shifts in the ambient space.

To learn nonlinear dynamics on an underlying cellular manifold, we recently described TrajectoryNet, which combines RNA velocity (capturing local transitions) with the global transport ability of optimal transport (123). TrajectoryNet uses a newly devised class of neural network called a NeuralODE (ordinary differential equation). Neural­ODEs (Fig. 2B, center) learn a time-varying derivative of a complex dynamic system parameterized via a neural network by setting network weights using an ODE solver instead of standard back-propagation and gradient descent. The resulting network can predict the future state of a measured cell based on the underlying geometry of the data set and predicted intracellular dynamics based on RNA velocity. This framework can enforce directionality through time and along a manifold representation of the data.

We anticipate that emerging models of cellular dynamics will increasingly leverage stochasticity to more closely model cellular processes. Currently, optimal transport models used in TrajectoryNet and Waddington optimal transport are deterministic, meaning that two cells with identical transcriptional profiles will produce identical future state prediction. However, it is possible that these cells have different posttranscriptional regulatory regimes and will therefore diverge in their specific fates. Stochastic differential equation models (124) might be more suited to capture such divergent potentials among similar cells.

Although we do not yet fully understand the intricacies of the tumor ecosystem's dynamism, we posit that cancer progression, metastasis, and therapy resistance all depend heavily on the emergence of landscape topologies permitting adaptive phenotypic cell state dynamics (Fig. 3A). It is vital to understand that, even as individual cells move dynamically upon these landscapes, the landscape topologies are themselves mutable, being sensitive to microenvironmental changes, metastatic relocation, or therapeutic challenges (125). In the clinical context, the inherently adaptive nature of the tumor ecosystem, thus, actively enables therapeutic evasion.

Yet recognition of the mutability of cancer cell state landscapes illuminates a new therapeutic strategy: intentional remodeling of the landscape topology to “corral” cancer cells into states that are more therapeutically vulnerable. By designing therapies that erect barriers to undesirable cell states or shape new channels toward preferable states, we envisage a new class of state-gating therapeutics designed to control the cancer cell state equilibrium. Moreover, we foresee potential for powerful synergies when combining such state-gating therapies with existing anticancer therapies.

For example, as detailed above, it is becoming apparent that some chemotherapies fail because they actively promote plastic transitions to resistant cancer cell states by creating or enhancing transitional trajectories (i.e., channels; Fig. 3B). Given this, multiple approaches can be conceived to enhance and sustain the effectiveness of chemotherapies by activating transitions from the resistant to chemosusceptible states (Fig. 3C), inhibiting transition to the resistant state (Fig. 3D), or preventing self-renewal of the resistant state (Fig. 3E). To design such state-gating strategies, however, now demands that we understand the molecular programs enabling specific trajectories of cell plasticity.

Significantly, state-gating strategies differ fundamentally from traditional targeted therapies. They are designed to target topological “channels” to modulate state plasticity rather than targeting specific topological “wells” to attack particular cancer cell states. Considering this, we may conceive of a future scenario where state-gating approaches are used to shift cells toward, or corral cells within, cell-attractor states that are vulnerable to chemotherapy or other targeted treatments.

Developing clinical assays to define and quantify distinct tumor cell phenotypic states, and their evolution in response to specific treatments, remains a significant clinical challenge. With clinical pathology tests often limited to IHC stains of a small number of proteins (generally in the range of one to three), it is not yet generally possible to define phenotypic cell states in a clinically sufficient manner or to use that information to inform therapeutic strategy. Despite these limitations, several studies have demonstrated how the simultaneous analysis of even a limited set of markers can successfully define a range of phenotypic cell states in human carcinomas and their association with more aggressive disease, poorer clinical outcome, and resistance to therapy (73, 126). For example, b-catenin, E-cadherin, and Vimentin define the evolution of EMT cell states in untreated and treated human carcinomas (including breast, prostate, non–small cell lung, esophageal carcinomas). CD104 and CD44 can define differing tumorigenicities of cancer cell subpopulations in breast cancer models (35), whereas CD51, CD61, and CD106 define different tumorigenic and metastatic potential in models of squamous cell carcinoma (21). Although such data hint at the clinical potential of defining phenotypic cell state spaces, we are only beginning to understand the diversity of cell phenotypes that exist within tumors, the levels of plasticity coupling these states, and how therapies change the phenotypic landscape. As the field continues to develop technologies for systematic single-cell measurement of this complex biology, we envisage that manifold learning methods will also continue to develop in parallel to enable the full exploitation of these profoundly transformative data. These methods hold great promise to delineate both intrinsic and extrinsic factors underlying phenotypic plasticity, enabling the next generation of diagnostic and therapeutic capabilities.

The cancer cell state landscape paradigm, matched to the analytical framework of manifold learning, provides a coherent prism through which to explore the adaptive phenotypic plasticity of cancer cell populations. The complementarity detailed herein between single-cell measurement modalities and computational approaches for manifold learning is vital to advance our understanding of the integrated signaling, genetic, and epigenetic regulatory networks that control cancer cell state plasticity and thus the cancer cell state landscape. In turn, such understanding is critical for the design of novel state-gating therapeutics whose capacity to constrain specific trajectories of plasticity could be used to lock cancer cells into vulnerable states that are targetable with existing chemotherapies and targeted therapies. We believe this dual strategy of combining state-gating and state-targeting therapies will substantially undermine one of cancer's most problematic capabilities—its adaptability—thereby transfor­matively improving cancer patient outcomes.

D.B. Burkhardt reports personal fees from Cellarity during the conduct of the study, as well as personal fees from Cellarity outside the submitted work. B.P. San Juan reports grants from St Vincents Clinic Foundation and Tour de Cure outside the submitted work; a patent for methods of treating cancer (PCT/AU2020/051146) pending; and is about to commence a phase I/II clinical trial (4CAST) based on preclinical work (https://www.medrxiv.org/content/10.1101/2022.03.21.22269988v1) that is proof of principle of some of the ideas and therapeutic strategies defined in the manuscript. J.G. Lock reports grants from the National Health and Medical Research Council, the Australian Research Council, and the Ramaciotti Foundation during the conduct of the study. C.L. Chaffer reports grants from the National Health and Medical Research Council of Australia, the Cancer Institute of New South Wales, and the National Breast Cancer Foundation and other support from the Nelune Foundation during the conduct of the study; a patent for methods of treating cancer (PCT/AU2020/051146) pending; and is a managing director of and shareholder in Kembi Therapeutics Pty Ltd, which owns certain patents including WO/2012/064943 and WO/2019/113301. No disclosures were reported by the other author.

D.B. Burkhardt was supported, in part, by the Eunice Kennedy Shriver National Institute of Child Health and Human Development of the NIH (F31HD097958). J.G. Lock received funding from the National Health and Medical Research Council of Australia (GNT1184009, GNT1181230, and GNT2012848), the Australian Research Council (DP220104036), and the Ramaciotti Foundation Biomedical Research Award. C.L. Chaffer and B.P. San Juan were supported by the National Health and Medical Research Council of Australia (GNT1088122 and GNT1181230), National Breast Cancer Foundation research grant IIRS-19-092, and philanthropic support from the Nelune Foundation Rebecca Wilson Fellowship. C.L. Chaffer was supported by a Cancer Institute New South Wales Fellowship (CDF181243). S. Krishnaswamy is supported by Chan-Zuckerberg Initiative grants 182702 and CZF2019-002440, National Science Foundation career grant 2047856, Sloan Fellowship FG-2021-15883, and NIH grants R01GM135929 and R01GM130847.