On minimising tumoural growth under treatment resistance.

Drug resistance is a major challenge for curative cancer treatment, representing the main reason of death in patients. Evolutionary biology suggests pauses between treatment rounds as a way to delay or even avoid resistance emergence. Indeed, this approach has already shown promising preclinical and early clinical results, and stimulated the development of mathematical models for finding optimal treatment protocols. Due to their complexity, however, these models do not lend themself to a rigorous mathematical analysis, hence so far clinical recommendations generally relied on numerical simulations and ad-hoc heuristics. Here, we derive two mathematical models describing tumour growth under genetic and epigenetic treatment resistance, respectively, which are simple enough for a complete analytical investigation. First, we find key differences in response to treatment protocols between the two modes of resistance. Second, we identify the optimal treatment protocol which leads to the largest possible tumour shrinkage rate. Third, we fit the "epigenetic model" to previously published xenograft experiment data, finding excellent agreement, underscoring the biological validity of our approach. Finally, we use the fitted model to calculate the optimal treatment protocol for this specific experiment, which we demonstrate to cause curative treatment, making it superior to previous approaches which generally aimed at stabilising tumour burden. Overall, our approach underscores the usefulness of simple mathematical models and their analytical examination, and we anticipate our findings to guide future preclinical and, ultimately, clinical research in optimising treatment regimes.

Oncogenic signaling is coupled to colorectal cancer cell differentiation state.

Colorectal cancer progression is intrinsically linked to stepwise deregulation of the intestinal differentiation trajectory. In this process, sequential mutations of APC, KRAS, TP53, and SMAD4 enable oncogenic signaling and establish the hallmarks of cancer. Here, we use mass cytometry of isogenic human colon organoids and patient-derived cancer organoids to capture oncogenic signaling, cell phenotypes, and differentiation states in a high-dimensional single-cell map. We define a differentiation axis in all tumor progression states from normal to cancer. Our data show that colorectal cancer driver mutations shape the distribution of cells along the differentiation axis. In this regard, subsequent mutations can have stem cell promoting or restricting effects. Individual nodes of the cancer cell signaling network remain coupled to the differentiation state, regardless of the presence of driver mutations. We use single-cell RNA sequencing to link the (phospho-)protein signaling network to transcriptomic states with biological and clinical relevance. Our work highlights how oncogenes gradually shape signaling and transcriptomes during tumor progression.

On tumoural growth and treatment under cellular dedifferentiation.

Differentiated cancer cells may regain stem cell characteristics; however, the effects of such a cellular dedifferentiation on tumoural growth and treatment are currently understudied. Thus, we here extend a mathematical model of cancer stem cell (CSC) driven tumour growth to also include dedifferentiation. We show that dedifferentiation increases the likelihood of tumorigenesis and the speed of tumoural growth, both modulated by the proliferative potential of the non-stem cancer cells (NSCCs). We demonstrate that dedifferentiation also may lead to treatment evasion, especially when a treatment solely targets CSCs. Conversely, targeting both CSCs and NSCCs in parallel is shown to be more robust to dedifferentiation. Despite dedifferentiation, perturbing CSC-related parameters continues to exert the largest relative effect on tumoural growth; however, we show the existence of synergies between specific CSC- and NSCC-directed treatments which cause superadditive reductions of tumoural growth. Overall, our study demonstrates various effects of dedifferentiation on growth and treatment of tumoural lesions, and we anticipate our results to be helpful in guiding future molecular and clinical research on limiting tumoural growth in vivo.

Mathematical modelling identifies conditions for maintaining and escaping feedback control in the intestinal epithelium.

The intestinal epithelium is one of the fastest renewing tissues in mammals. It shows a hierarchical organisation, where intestinal stem cells at the base of crypts give rise to rapidly dividing transit amplifying cells that in turn renew the pool of short-lived differentiated cells. Upon injury and stem-cell loss, cells can also de-differentiate. Tissue homeostasis requires a tightly regulated balance of differentiation and stem cell proliferation, and failure can lead to tissue extinction or to unbounded growth and cancerous lesions. Here, we present a two-compartment mathematical model of intestinal epithelium population dynamics that includes a known feedback inhibition of stem cell differentiation by differentiated cells. The model shows that feedback regulation stabilises the number of differentiated cells as these become invariant to changes in their apoptosis rate. Stability of the system is largely independent of feedback strength and shape, but specific thresholds exist which if bypassed cause unbounded growth. When dedifferentiation is added to the model, we find that the system can recover faster after certain external perturbations. However, dedifferentiation makes the system more prone to losing homeostasis. Taken together, our mathematical model shows how a feedback-controlled hierarchical tissue can maintain homeostasis and can be robust to many external perturbations.

A mechanistic model of metabolic symbioses in microbes recapitulates experimental data and identifies a continuum of symbiotic interactions.

Microbial symbioses based on nutrient exchange and interdependence are ubiquitous in nature and biotechnologically promising; however, an in-depth mathematical description of their exact underlying dynamics from first principles is still missing. Hence, in this paper a novel mechanistic mathematical model of such a relationship in a continuous chemostat culture is derived. In contrast to preceding works on the topic, only parameters which can be directly measured and understood from biological first principles are used, allowing for a higher degree of mechanistic understanding of the underlying processes compared to previous approaches. The predictive power of the model is validated by demonstrating that it accurately recapitulates both the temporal dynamics as well as the final state of a previously published cross-feeding experiment. The model is then used to examine the influence of the biological traits of the involved organisms on the position and stability of the equilibrium states of the system using bifurcation analyses. It is additionally demonstrated how manipulating the external metabolite concentrations of the system can shift the species interaction on a continuous spectrum ranging from mutualism over commensalism to parasitism. This further reinforces the idea of a continuous spectrum of symbiotic interactions as opposed to static and discrete categories. Finally, the practical implications of the results for the biotechnological application of such microbial consortia are discussed.