Systematic analysis of network-driven adaptive resistance to CDK4/6 and oestrogen receptor inhibition using meta-dynamic network modelling

Drug resistance is a widespread phenomenon across all cancer types and is a major obstacle to the development of curative therapeutic strategies (Vasan et al., 2019; Wang et al., 2019; Pich et al., 2022). Cellular heterogeneity is a known driver of drug resistance, wherein the treatment of a heterogenous population of cancer cells with cytostatic or cytotoxic drugs creates a selective pressure that results in the survival and expansion of any cells that are capable of overcoming the effects of said drugs (Knudsen et al., 2022; Jubran et al., 2022; Dagogo-Jack and Shaw, 2018). While this general phenomenon is well established (Turke et al., 2010; Patel et al., 2022; Cassidy, 2019), it is usually less clear exactly how and why some cells are able to overcome a drug treatment and others are not. Heterogeneity is a catch-all term used to describe any and all differences between cells; however, it could be argued that the majority of the differences between cells ultimately converge on differences in how their constituent proteins behave, that is their protein dynamics. To deepen our understanding of how tumour heterogeneity drives drug resistance, we must explore the relationship between cellular heterogeneity, protein dynamics, and drug resistance.

The efficacy of a targeted therapy largely comes down to how well and how long the targeted protein is suppressed, and how frequently and reliably this suppression results in either cytostasis or apoptosis. A cell can therefore be considered resistant if the target protein is insufficiently suppressed or is initially suppressed but later recovers, or if the suppression of the protein is insufficient to stimulate cytostasis or apoptosis (Herrera-Abreu et al., 2016; Ahmed et al., 2019). Proteins are embedded in complex networks, and protein dynamics are dictated by the properties of the networks in which they reside. While resistance is often due to direct effects, such as reduced drug-target binding affinity (Blombery et al., 2019; Yun et al., 2008) or excessive drug efflux from tumour cells (Xue and Liang, 2012; Smyth et al., 1998), it can also occur due to changes in the state of the biochemical networks of a cell that counteract the effects of the drug; a phenomenon referred to as adaptive resistance (Jin et al., 2020; Li et al., 2022; Cremers and Nguyen, 2019). PI3K, EGFR, and CDK4/6 are just few prime examples of proteins that have been targeted in the treatment of cancer that display acute and robust adaptive resistance (Wright et al., 2021; Herrera-Abreu et al., 2016; Ma et al., 2016). These studies also support the notion that it is rarely the behaviour of a single ‘gatekeeper’ protein that drives adaptive resistance, but an entire protein network that acts and is acted upon by the target protein (Park et al., 2020; Nguyen and Kholodenko, 2016). Frequently, however, we possess a limited knowledge and appreciation of the network-level mechanistic relationships that underpin adaptive resistance.

Understanding the relationship between cellular heterogeneity and adaptive drug resistance requires an ability to explore and characterise the heterogeneity that exists both within a tumour and between patients. This can be achieved in silico by investigating the behaviour of a network, that is the dynamics of its constituent proteins, over a broad range of network conditions, allowing us to observe the full spectrum of possible dynamics that can be displayed by a given network topology. A particularly useful technique for investigating protein signalling networks is ordinary differential equation (ODE) modelling (Bachmann et al., 2012). An ODE model is a mathematical representation of how the protein species within a network interact and evolve over time. ODE models have been extensively used to simulate and predict network-level responses to perturbations, such as growth-factor stimulation or drug treatment (Shankar et al., 2019; Clarke and Fisher, 2020; Altrock et al., 2015; Ghomlaghi et al., 2021). In an ODE model, the interactions between the network’s constituent proteins are converted into mathematical formulations using well-established biochemical rate laws (Tyson et al., 2019; Tandon et al., 2022; Deuflhard and Röblitz, 2015; Kearney et al., 2021; Shin et al., 2018). The end result is a set of ODEs – the model – that can be numerically solved using specialised ODE solvers, allowing one to simulate, and thus predict, how the concentrations of the protein species will change over time or in response to perturbations (Tyson et al., 2019; Tandon et al., 2022; Deuflhard and Röblitz, 2015; Kearney et al., 2021; Shin et al., 2018).

An ODE model is comprised of state variables, initial conditions (ICs), model parameters, and defined inputs and outputs (Tyson et al., 2019; Tandon et al., 2022; Deuflhard and Röblitz, 2015). Typically, the parameters, or reaction coefficients, represent the strength of protein interactions and state variables correspond to the concentrations of the protein species. ICs are the values of the state variables at the starting point of a simulation and represent the total abundance levels of the protein species within the model. Model input(s) are usually a perturbation to the modelled network, such as a growth factor stimulation or a drug inhibition. We can model network heterogeneity by producing a suite of ODE models, each with their own set of parameter values and/or ICs. In this manner, each model ‘instance’ represents a unique cellular context and produces a unique set of dynamic behaviours for its constituent proteins. By varying the parameters and ICs over wide ranges, we can delineate an extreme upper limit to the heterogeneity in dynamics facilitated by a network topology.

The process of creating models almost always involves a degree of abstraction, either explicitly, due to conscious decisions by the creator, or implicitly, due to imperfect knowledge of the system being modelled. This abstraction forces a model’s parameters to capture information beyond that which is being explicitly modelled and can potentially render the concept of a ‘true’ or ‘biologically accurate’ parameter value less meaningful. There is an array of factors that can influence reaction coefficients: post-translational modifications, catalysts/scaffolds, pH, etc., and they can all individually influence reaction coefficients over several orders of magnitude. In the context of cancer, this variability in reaction coefficients can become extreme, with mutations altering the properties of proteins and dramatically changing how strongly they interact with other proteins. By varying the parameters and ICs over wide ranges, we also potentially capture protein dynamics driven by factors we have not explicitly modelled.

Drug resistance is a problem almost as old as drug treatments, and many computational modelling frameworks have been developed to investigate the emergence of drug resistance during cancer treatment (Sun and Hu, 2018; Chisholm et al., 2016; Belkhir et al., 2021). A comprehensive review of the modelling frameworks developed to explore the relationship between cellular heterogeneity and drug resistance, in particular, was written by Chisholm et al., 2016. Most of the models covered within focused on population dynamics and were used to identify key processes that govern how resistance emerges within a heterogenous cell population. Notably, none of the models in this review attempted to link heterogenous intracellular processes with adaptive resistance mechanisms, or resistance in general. Perhaps most similar to the ensemble approach developed within this project, He et al. developed an ODE-based modelling technique termed RACIPE (random circuit perturbation; Huang et al., 2018). In contrast to our work, RACIPE was a quasi-Monte Carlo method developed to alleviate the necessity of identifying precise kinetic parameter values on which model predictions are supposedly dependent. While their technique does involve the exploration of a range of parameter values, it does so to make predictions about broadly robust outcomes in gene regulatory circuits, not to link parameter variation to heterogenous protein network dynamics. Thus, there is a need for a novel computational framework capable of systematically characterising network-dynamic heterogeneity and its relationship with adaptive resistance.

To address this need, we have developed a new modelling framework, coined Meta-Dynamic Network (MDN) modelling, which enables us to study the effects of network heterogeneity on protein signalling dynamics. In this paper we have applied MDN modelling to an early cell cycle (ECC) network model to systematically explore and illuminate adaptive resistance mechanisms that arise in response to targeted CDK4/6 and oestrogen receptor (ER) inhibition. The ECC network model developed herein incorporates the two major mitogenic signalling pathways that are largely responsible for cell cycle initiation, and the G1-S phase cell cycle regulatory network.

Using MDN modelling and the ECC network model, we have demonstrated that variation in both the strength of reaction coefficients (parameters) and the total abundance of proteins (IC values) can affect the qualitative shape and features of a network’s protein dynamics. Furthermore, we provide evidence that parameter variation induces a much greater variety in the qualitative shape and features of the network’s protein dynamics and is therefore much more likely to give rise to adaptive resistance dynamics. We also show that there is a surprisingly large number of contexts in which the network topology of the ECC network can facilitate resistance dynamics and that we can dissect these contexts to systematically characterise their underpinning kinetic drivers. Finally, we analysed existing publicly available biological data to qualitatively validate the existence of a spectrum of signalling dynamics in response to CDK4/6 inhibitors and propose a novel relationship between population signalling dynamics and population level drug sensitivity.

Heterogeneity is a defining feature of cancer and a major barrier to durable responses to targeted therapies. Clinical and experimental studies of CDK4/6 inhibitors in ER+ breast cancer consistently show wide inter- and intra-tumour variability in response and multiple, often co-existing resistance mechanisms (Zhou et al., 2023). Yet, despite this wealth of descriptive data, we still lack mechanistic frameworks that can systematically relate underlying molecular heterogeneity to the spectrum of signalling behaviours that enable adaptive drug resistance. In this work, we introduce MDN modelling as such a framework. By sampling broad ensembles of kinetic parameters and protein abundances on a fixed network topology, MDN modelling maps the full distribution of qualitative signalling dynamics (‘meta-dynamics’) accessible to a network architecture and identifies which of these trajectories are compatible with sustained target inhibition versus adaptive escape.

Our first key finding is that even within a single, fixed ECC network topology, variation in reaction kinetics and total protein abundances can generate a surprisingly rich repertoire of qualitative signalling behaviours. We use the term ‘meta-dynamics’ to denote the convergent distribution of these behaviours across a large ensemble of model instances, which represents a theoretical upper limit on what the network can manifest dynamically. Importantly, this repertoire includes trajectories in which continuous CDK4/6 inhibition fails to maintain target suppression and downstream cell-cycle arrest - canonical signatures of adaptive resistance. This provides a concrete mechanistic link between molecular heterogeneity and the well-described phenomenon of rapid signalling rewiring under targeted therapy, in which feedback and crosstalk restore pathway activity despite continued drug exposure (Cremers and Nguyen, 2019; Chandarlapaty, 2012).

We find that adaptive resistance can emerge from heterogeneity in both kinetic parameters and protein abundances, but not symmetrically. However, across the ECC network, we observe that perturbations to kinetic parameters (interaction strengths) are more potent and consistent drivers of adaptive resistance dynamics than changes in total protein abundance. This supports a hierarchical view of control: network topology and interaction strengths largely determine which qualitative behaviours are possible, while protein levels modulate how frequently particular regimes are accessed. That hierarchy is consistent with both systems-level perspectives on cellular heterogeneity (Movasat et al., 2025) and parameter-sensitivity analyses in whole-cell and signalling models, which have shown that many distinct parameter sets can collapse onto a limited set of functional outputs (Babtie and Stumpf, 2017).

Perhaps the most striking observation from our analysis is how rapidly the meta-dynamic distribution converges. Despite sweeping over 90 kinetic parameters and 50 total abundances across nine orders of magnitude, the distribution of qualitative response classes stabilises well before 100,000 accepted model instances. Doubling the ensemble size yields only negligible changes in the frequencies of each dynamic regime, see Figure 3—figure supplement 3. This reflects a strong filtering effect imposed by network topology rather than simply a statistical inevitability of sampling from fixed priors. When parameters or abundances are pushed to extremes, nodes tend to be driven into saturating states, either effectively ‘always off’ or ‘always on’, and become unresponsive to upstream perturbations. These saturated cases fall into the ‘no response’ category and do not generate new, more complex temporal patterns. Consequently, the ECC topology funnels the near-infinite combinatorial parameter space into a finite, recurring set of qualitative behaviours (e.g. monotonic decrease, rebound, biphasic). Such topology-constrained behavioural repertoires have also been noted in recent work that treats heterogeneity by assigning probability distributions to model parameters and analysing the resulting ensemble of single-cell behaviours (Yamada et al., 2018; Spencer et al., 2009). MDN modelling complements these approaches by emphasising qualitative dynamic classes and their frequencies rather than precise parameter posteriors.

At the level of individual nodes and subnetworks, our perturbation analyses reveal that adaptive resistance is a genuinely network-level property. Nearly every node in the ECC model can be implicated in at least one resistance subnetwork when viewed across the full heterogeneity ensemble, echoing the clinical and experimental literature where numerous, sometimes mutually exclusive mechanisms of CDK4/6 inhibitor resistance have been described - ranging from loss of RB1 to cyclin E/CDK2 activation, PI3K–AKT upregulation, FGFR signalling, and alterations in cell-cycle checkpoint control (Zhou et al., 2023). However, MDN modelling does not predict an unstructured ‘anything goes’ landscape. When we rank interactions by how frequently their perturbation participates in resistance-associated trajectories, a small set of hubs and co-regulated modules emerges. In other words, many routes to resistance exist, but they tend to be coordinated through a limited number of recurrent network motifs and subnetworks. This modular picture is consistent with reviews of adaptive resistance in breast cancer, which emphasise convergent rewiring of signalling hubs and feedback nodes despite diverse upstream lesions (Cremers and Nguyen, 2019).

As an additional, orthogonal validation of the resistance subnetworks identified by MDN modellilng, we compared our perturbation-derived resistance modules with gene-dependency patterns from the Cancer Dependency Map (DepMap; Ghandi et al., 2019). Although DepMap is not specific to CDK4/6 inhibition, hierarchical clustering of knockout dependencies for ECC-network genes revealed distinct vulnerability modules across >1000 cell lines (Figure 6—figure supplement 12). The existence of such modules supports the MDN modelling prediction that different cellular contexts rely on distinct but recurrent subnetworks to sustain proliferation, reinforcing the view that resistance is governed by coordinated network-level processes rather than isolated nodes.

Our findings also shed light on why CDK4/6 inhibition resistance is so pervasive yet difficult to capture with single biomarkers. Recent work integrating bulk, single-cell, and trial data has shown that tumours resistant to CDK4/6 inhibition are characterised by increased intra-tumoural heterogeneity and multiple, co-existing resistance signatures, including MYC-driven programmes and altered estrogen-response pathways (Migliaccio et al., 2025). Single-cell imaging and modelling studies have further demonstrated that cell-cycle dynamics and signalling trajectories at the single-cell level are critical determinants of CDK4/6 inhibitor sensitivity (Asghar et al., 2017). Our MDN modelling analysis provides a mechanistic underpinning for these observations: across a broad space of plausible network states, a surprisingly large fraction of configurations yield adaptive resistance-like signalling for key G1-S regulators, and simultaneous durable suppression of all relevant downstream effectors is rare. In such a landscape, static measurements of one or a few nodes are unlikely to robustly stratify patients, because resistance is inherently encoded in distributed, dynamic network behaviour rather than in single static markers.

Despite the theoretical nature of our study, qualitative comparison with single-cell signalling data supports the core results of MDN modelling. Experiments in isogenic breast epithelial cells have shown that CDK4/6 activity reporters display highly heterogeneous dynamics under inhibitor treatment, with some cells remaining durably suppressed, others partially rebounding, and others showing minimal inhibition (Yang et al., 2020; Asghar et al., 2017). Our meta-dynamic distributions reproduce this spectrum of behaviours despite being generated from a much broader parameter ensemble than any one cell line is likely to occupy. We emphasise that this comparison is intentionally qualitative: our goal is not to fit a specific cell line with a calibrated model, but to demonstrate that the ECC topology, when subjected to realistic heterogeneity, naturally gives rise to the types of signalling trajectories observed empirically. The close qualitative agreement between simulated and experimental distributions suggests that even nominally isogenic populations may explore a substantial portion of the network’s meta-dynamic landscape.

As with any model-based framework, MDN modelling has limitations that shape how its predictions should be interpreted. First, we use mass-action and first-order kinetics rather than more detailed Michaelis–Menten or cooperative rate laws. This was essential to keep the parameter space tractable for large-scale exploration, but it means that behaviours relying critically on enzyme saturation or higher-order cooperativity may be under-represented. Second, our parameter and abundance priors are deliberately broad and largely uniform in log-space, whereas biochemical parameters and expression levels in real cells are often better approximated by log-normal or other structured distributions (Bar-Even et al., 2015; Taniguchi et al., 2010; Bengtsson et al., 2005). In this sense, the present work should be viewed as defining what is possible for a given topology rather than estimating what is probable in a specific tumour context. Third, our model is deterministic and does not explicitly capture intrinsic biochemical noise. We argue that sampling across a broad ensemble of parameter and abundance sets can approximate the time-averaged consequences of genetic, epigenetic, and stochastic variation, but intrinsic noise at low copy numbers and rare event dynamics will require explicit stochastic formulations (Kwon et al., 2019). Finally, the ECC model abstracts some multi-protein modules into single nodes to maintain computational tractability. As a result, highly ranked ‘hub’ nodes in our analysis should be interpreted as implicating critical processes or modules, rather than single gene products, as the key levers of resistance.

These limitations point naturally to several avenues for future work. A priority is to constrain MDN modelling ensembles using experimentally inferred parameter and abundance distributions, for example by integrating Bayesian parameter-inference methods that represent cell-to-cell variability as probability distributions over model parameters. Another key direction is to couple MDN-derived resistance subnetworks with data-driven approaches that operate directly on patient-derived single-cell and spatial multi-omics data, which are increasingly used to dissect sample-level heterogeneity and its association with treatment response (Boyeau et al., 2025). Such integrated frameworks could bridge the gap between mechanistic prediction of resistance-enabling subnetworks and empirical identification of patient-specific vulnerabilities. On the dynamical side, embedding stochastic simulations or Langevin approximations within the MDNA framework would allow us to evaluate how intrinsic noise reshapes the meta-dynamic landscape and whether it introduces qualitatively new resistance regimes or primarily modulates the frequencies of existing ones. Finally, our perturbation analyses suggest that a finite set of recurrent resistance modules underpins a vast number of resistant states. This aligns with translational efforts that design rational combination therapies to pre-empt or overcome adaptive resistance by co-targeting signalling hubs and compensatory feedbacks (Yip et al., 2024) and MDN modelling could provide a principled way to enumerate and prioritise such combinations for experimental testing.

In summary, MDN modelling offers a systems-level framework that connects molecular heterogeneity to dynamic signalling behaviour and, ultimately, to adaptive drug resistance. By revealing how a fixed network topology can generate a finite but diverse set of resistance-associated trajectories and by identifying the hubs and modules that recurrently mediate these trajectories, our work complements empirical single-cell and clinical studies and suggests concrete strategies for network-level intervention. Although we have focused on the G1-S transition and CDK4/6 inhibition as a clinically important case study, the MDN modelling approach is broadly applicable to other signalling networks and therapeutic targets. As mechanistic models, single-cell datasets, and computational methods continue to mature, we envisage MDN-like frameworks playing an increasingly important role in predicting how tumours will escape targeted treatments and in guiding combination strategies to keep them one step ahead.

Code is available: https://github.com/IntegratedNetworkModellingLab/Meta_Dynamic_Analysis_eLife, copy archived at DrHartResearch, 2026.

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Author details

1. Anthony Hart

   1. Department of Biochemistry and Molecular Biology, Faculty of Medicine, Nursing and Health Sciences, Monash University, Clayton, Australia
   2. Biomedicine Discovery Institute, Monash University, Clayton, Australia
   3. Computational Systems Oncology Program, South Australian immunoGENomics Cancer Institute (SAiGENCI), The University of Adelaide, Adelaide, Australia
   4. Australian Research Council Centre of Excellence for the Mathematical Analysis of Cellular Systems (MACSYS), Parkville, Australia

   Contribution

   Conceptualization, Software, Formal analysis, Investigation, Visualization, Methodology, Writing – original draft, Project administration, Writing – review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0003-1557-6515

2. Sung-Young Shin

   1. Department of Biochemistry and Molecular Biology, Faculty of Medicine, Nursing and Health Sciences, Monash University, Clayton, Australia
   2. Biomedicine Discovery Institute, Monash University, Clayton, Australia
   3. Computational Systems Oncology Program, South Australian immunoGENomics Cancer Institute (SAiGENCI), The University of Adelaide, Adelaide, Australia

   Contribution

   Conceptualization, Supervision, Investigation, Methodology, Project administration, Writing – review and editing

   Competing interests

   No competing interests declared

3. Lan K Nguyen

   1. Department of Biochemistry and Molecular Biology, Faculty of Medicine, Nursing and Health Sciences, Monash University, Clayton, Australia
   2. Biomedicine Discovery Institute, Monash University, Clayton, Australia
   3. Computational Systems Oncology Program, South Australian immunoGENomics Cancer Institute (SAiGENCI), The University of Adelaide, Adelaide, Australia
   4. Australian Research Council Centre of Excellence for the Mathematical Analysis of Cellular Systems (MACSYS), Parkville, Australia

   Contribution

   Conceptualization, Supervision, Investigation, Methodology, Project administration, Writing – review and editing

   For correspondence

   lan.nguyen@adelaide.edu.au

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0003-4040-7705

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