Roadmap on plasticity and epigenetics in cancer

Abstract

The role of plasticity and epigenetics in shaping cancer evolution and response to therapy has taken center stage with recent technological advances including single cell sequencing. This roadmap article is focused on state-of-the-art mathematical and experimental approaches to interrogate plasticity in cancer, and addresses the following themes and questions: is there a formal overarching framework that encompasses both non-genetic plasticity and mutation-driven somatic evolution? How do we measure and model the role of the microenvironment in influencing/controlling non-genetic plasticity? How can we experimentally study non-genetic plasticity? Which mathematical techniques are required or best suited? What are the clinical and practical applications and implications of these concepts?

Keywords: cancer; epigenetics; plasticity.

Figure 1.

CAFs are comprised of multiple subpopulations that can interconvert based on the cues from the TME. CAF subtypes differentially influence various aspects of cancer progression.

Figure 2.

Integration of novel technologies to better understand CAF heterogeneity. Biomimetic models, experimental tools, and functional readouts are used to generate experimental data that can be coupled with mathematical models to make predictions based on model perturbations.

Figure 3.

Utilizing reporter systems to track the CSC state in real time in various microenvironmental conditions, therapeutic contexts, organoid models, and in vivo could provide valuable insight into development, progression, heterogeneity and therapy resistance in tumors such as GBM.

Figure 4.

The epigenetic cancer state-space. (A) A phenotypic landscape derived from epigenetic states is shown for normal (left) and cancer (right). The cancer state-space is the normal landscape perturbed by oncogenic events resulting in a lower energy barrier and therefore a higher probability of undergoing a state-transition to the cancer state. In both cases, the evolution of the system is modelled as a particle undergoing Brownian motion in the state-space. (B) (Left) The evolution of the system represented as a trajectory in the state-space over time. The location in the state-space is shown for two samples; one (red samples) that undergoes state-transition to cancer, defined by the red line and one (blue samples) that does not. (Right) Once the state-space is constructed, new samples can be projected into the space to make individual predictions based on the evolution of the probability density function with Fokker-Planck equations corresponding to the equation of motion.

Figure 5.

Models of acquired therapy resistance. (A) Pre-existent fully resistant subpopulations expand due to therapy-induced competitive release. (B) Full resistance develops from tolerant cells or cells sheltered from therapy by proximity to protective stromal niches due to stochastic occurrence of resistance-conferring (epi)genetic mutation. (C) Resistance as the result of plasticity-mediated therapy induced phenotypic ‘reprogramming’. (D) Multifactorial, gradual acquisition of resistance resulting from integration of multiple contributing inputs.

Figure 6.

Understanding of acquired resistance requires consideration of epigenetic reprogramming, stochastic genetic and epigenetic changes, converging at the level of inclusive fitness ‘seen’ by selection. Such an integration requires development and use of mathematical modelling tools.

Figure 7.

Crosstalk among the chromosomal and non-chromosomal epigenetic arms can drive emergent phenomenon in cancer cells, enabling phenotypic plasticity in many interconnected dimensions/axes.

Figure 8.

The BaM³ method. A schematic representation of the data and method integration of the BaM³ method. Details can be found in [86].

Figure 9.

LEUP features. LEUP allows for predictions even when lacking exact mechanistic knowledge. Machine learning offer solutions in similar situations. However, LEUP models are still more interpretable and facilitate generalisation.

Figure 10.

Modeling impact in a pharmaceutical setting.

Figure 11.

Bet hedging without phenotypic memory. (A) CRN (approximate majority) that is a bistable switch between states of all s or all r molecules, using a facilitating molecule b. (B) Probability that the CRN produces phenotype S, for a given fraction of starting s molecules. (C) Simulation using 53s and 47r upon cellular division (dashed line in panel (B)) and treating with six pulses of therapy. (D) Simulation using 46s and 54r, with the same therapy as panel (C).

Figure 12.

Bet hedging with phenotypic memory. (A) Adding molecular memory and decay shifts the probability curve when the dividing cell still has molecules remaining. Green and red curves show the shifts for 10s and 10r remaining molecules at division, which are added to the 53s/47r baseline. This will bias the probability of producing daughter cells toward preserving the parental phenotype. (B) Simulation with 53s/47r, slow s-decay, and fast r-decay shows a persister population: there is no sustained relapse during remission, only survival, then rapid regrowth once treatment ends. (C) When decay rates are swapped (s-decay is fast and r-decay is slow), we see a population that maintains a high density, representative of a multicellular tissue. Unlike in figure 11(D), the off-treatment population has almost 50% sensitive cells. (D) With a different genotype (57s/43r) and slow decay for both molecules, the population can grow continuously under therapy. Compare with panel (B), where indefinite therapy would hold the population to low-level spikes rather than sustained growth. (E) For some parameters, the population can be driven extinct, suggesting that agents that affect the hedging and decay rates may be powerful combination therapies that could enhance the primary cytotoxic agent’s effect.