Collateral sensitivity networks reveal evolutionary instability and novel treatment strategies in ALK mutated non-small cell lung cancer.

 View ORCID ProfileAndrew Dhawan, Daniel Nichol, Fumi Kinose,  View ORCID ProfileMohamed E. Abazeed,  View ORCID ProfileAndriy Marusyk,  View ORCID ProfileEric B.Haura,  View ORCID ProfileJacob G. Scott

doi: http://dx.doi.org/10.1101/075846

This article is a preprint and has not been peer-reviewed [what does this mean?].

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Abstract

Drug resistance remains an elusive problem in cancer therapy, particularly with novel targeted therapy approaches. Much work is currently focused upon the development of an increasing arsenal of targeted therapies, towards oncogenic driver genes such as ALK-EML4, to overcome the inevitable resistance that develops as therapies are continued over time. The current clinical paradigm after failure of first line ALK TKI is to administer another drug in the same class. As to which drug however, the answer is uncertain, as clinical evidence is lacking. To address this shortcoming, we evolved resistance in an ALK rearranged non-small cell lung cancer line (H3122) to a panel of 4 ALK tyrosine kinase inhibitors used in clinic, and performed a collateral sensitivity analysis to each of the other drugs. We found that all of the ALK inhibitor resistant cell lines displayed a significant cross-resistance to all other ALK inhibitors. To test for the stability of the resistance phenotypes, we evaluated the ALK-inhibitor sensitivities after drug holidays of varying length (1, 3, 7, 14, and 21 days). We found the resistance patterns to be stochastic and dynamic, with few conserved patterns. This unpredictability led us to an expanded search for treatment options for resistant cells. In this expansion, we tested a panel of 6 more anti-cancer agents for collateral sensitivity among the resistant cells, uncovering a multitude of possibilities for further treatment, including cross-sensitivity to several standard cytotoxic therapies as well as the HSP-90 inhibitors. Taken together, these results imply that resistance to targeted therapy in non-small cell lung cancer is truly a moving target; but also one where there are many opportunities to re-establish sensitivities where there was once resistance.

http://biorxiv.org/content/early/2016/09/19/075846

Ordinary Differential Equations in Cancer Biology

Margaret P Chapman, Claire J. Tomlin

Abstract

Ordinary differential equations (ODEs) provide a classical framework to model the dynamics of biological systems, given temporal experimental data. Qualitative analysis of the ODE model can lead to further biological insight and deeper understanding compared to traditional experiments alone. Simulation of the model under various perturbations can generate novel hypotheses and motivate the design of new experiments. This short paper will provide an overview of the ODE modeling framework, and present examples of how ODEs can be used to address problems in cancer biology.

Link: dx.doi.org/10.1101/071134

Agent based models to investigate cooperation between cancer cells

Joao Xavier, William Chang

doi: http://dx.doi.org/10.1101/031070 

Abstract

We present a type of agent-based model that uses off-lattice spheres to represent individual cells in a solid tumor. The model calculates chemical gradients and determines the dynamics of the tumor as emergent properties of the interactions between the cells. As an example, we present an investigation of cooperation among cancer cells where cooperators secrete a growth factor that is costly to synthesize. Simulations reveal that cooperation is favored when cancer cells from the same lineage stay in close proximity. The result supports the hypothesis that kin selection, a theory that explains the evolution of cooperation in animals, also applies to cancers.

Population heterogeneity in the epithelial to mesenchymal transition is controlled by NFAT and phosphorylated Sp1

Population heterogeneity in the epithelial to mesenchymal transition is controlled by NFAT and phosphorylated Sp1

Russell Gould, Anirikh Chakrabarti, Jeffrey Varner, Jonathan Butcher

Link: http://biorxiv.org/content/early/2015/10/13/028993

Epithelial to mesenchymal transition (EMT) is an essential differentiation program during tissue morphogenesis and remodeling. EMT is induced by soluble transforming growth factor β (TGF-β) family members, and restricted by vascular endothelial growth factor family members. While many downstream molecular regulators of EMT have been identified, these have been largely evaluated individually without considering potential crosstalk. In this study, we created an ensemble of dynamic mathematical models describing TGF-β induced EMT to better understand the operational hierarchy of this complex molecular program. These models incorporate mass action kinetics within an ordinary differential equation (ODE) framework to describe the transcriptional and post-translational regulatory events driving EMT. Model parameters were estimated from multiple data sets using multiobjective optimization, in combination with cross-validation. TGF-β exposure drove the model population toward a mesenchymal phenotype, while an epithelial phenotype was maintained following vascular endothelial growth factor A (VEGF-A) exposure. Simulations predicted that the transcription factors phosphorylated SP1 and NFAT were master regulators promoting or inhibiting EMT, respectively. Surprisingly, simulations also predicted that a cellular population could exhibit phenotypic heterogeneity (characterized by a significant fraction of the population with both high epithelial and mesenchymal marker expression) if treated simultaneously with TGF-β and VEGF-A. We tested this prediction experimentally in both MCF10A and DLD1 cells and found that upwards of 45% of the cellular population acquired this hybrid state in the presence of both TGF-β and VEGF-A. We experimentally validated the predicted NFAT/Sp1 signaling axis for each phenotype response. Lastly, we found that cells in the hybrid state had significantly different functional behavior when compared to VEGF-A or TGF-β treatment alone. Together, these results establish a predictive mechanistic model of EMT susceptibility, and potentially reveal a novel signaling axis which regulates carcinoma progression through an EMT versus tubulogenesis response.

DOI: http://dx.doi.org/10.1101/028993

Cell-cell interactions and evolution using evolutionary game theory

David Basanta

Cancers arise from genetic aberrations but also consistently display high levels of intra-tumor heterogeneity and evolve according to Darwinian dynamics. This makes evolutionary game theory an ideal tool in which to mathematically capture these cell-cell interactions and in which to investigate how they impact evolutionary dynamics. In this chapter we present some examples of how evolutionary game theory can elucidate cancer evolution.

Link: http://dx.doi.org/10.1101/028746

 

Cancer evolution simulation identifies possible principles underlying intratumor heterogeneity

Atsushi Niida, Satoshi Ito, Georg Tremmel, Seiya Imoto, Ryutaro Uchi, Yusuke Takahashi, Yusuke Takahashi, Koshi Mimori, Satoru Miyano

Cancer arises from accumulation of somatic mutations and accompanying evolutionary selection for growth advantage. During the evolutionary process, an ancestor clone branches into multiple clones, yielding intratumor heterogeneity. However, principles underlying intratumor heterogeneity have been poorly understood. Here, to explore the principles, we built a cellular automaton model, termed the BEP model, which can reproduce the branching cancer evolution in silico. We then extensively searched for conditions leading to high intratumor heterogeneity by performing simulations with various parameter settings on a supercomputer. Our result suggests that multiple driver genes of moderate strength can shape subclonal structures by positive natural selection. Moreover, we found that high mutation rate and a stem cell hierarchy can contribute to extremely high intratumor heterogeneity, which is characterized by fractal patterns, through neutral evolution. Collectively, This study identified the possible principles underlying intratumor heterogeneity, which provide novel insights into the origin of cancer robustness and evolvability.

http://biorxiv.org/content/early/2015/07/17/022806

 

The Universality of Cancer

Carson C. Chow, Yanjun Li, Vipul Periwal

Cancer has been characterized as a constellation of hundreds of diseases differing in underlying mutations and depending on cellular environments. Carcinogenesis as a stochastic physical process has been studied for over sixty years, but there is no accepted standard model. We show that the hazard rates of all cancers are characterized by a simple dynamic stochastic process on a half-line, with a universal linear restoring force balancing a universal simple Brownian motion starting from a universal initial distribution. Only a critical radius defining the transition from normal to tumorigenic genomes distinguishes between different cancer types when time is measured in cell–cycle units. Reparametrizing to chronological time units introduces two additional parameters: the onset of cellular senescence with age and the time interval over which this cessation in replication takes place. This universality implies that there may exist a finite separation between normal cells and tumorigenic cells in all tissue types that may be a viable target for both early detection and preventive therapy.

http://arxiv.org/abs/1506.00597v1

Cancer therapeutic potential of combinatorial immuno- and vaso-modulatory interventions

Cancer therapeutic potential of combinatorial immuno- and vaso-modulatory interventions 

H. Hatzikirou, J. C. L. Alfonso, S. Muhle, C. Stern, S. Weiss, M. Meyer-Hermann

Currently, most of the basic mechanisms governing tumor-immune system interactions, in combination with modulations of tumor-associated vasculature, are far from being completely understood. Here, we propose a mathematical model of vascularized tumor growth, where the main novelty is the modelling of the interplay between functional tumor vasculature and effector recruitment dynamics. Parameters are calibrated on the basis of different in vivo Rag1-/- and wild-type (WT) BALB/c murine tumor growth experiments. The model analysis supports that vasculature normalization can be a plausible and effective strategy to treat cancer when combined with appropriate immuno-stimulation. We find that improved levels of functional vasculature, potentially mediated by vascular normalization or stress alleviation strategies, can provide beneficial outcomes in terms of tumor burden reduction and control. Normalization of tumor blood vessels opens a therapeutic window of opportunity to augment the anti- tumor immune responses, as well as to reduce the intratumoral immunosuppression and hypoxia due to vascular abnormalities. The potential success of normalizing tumor vasculature closely depends on the effector cell recruitment dynamics and tumor sizes. Furthermore, an arbitrary increase of initial effector cell concentration does not necessarily imply tumor control, and we evidence the existence of an optimal effector concentration range for tumor shrinkage. Based on these findings, we suggest a theory-driven therapeutic proposal that optimally combines immune- and vaso-modulatory interventions.

http://arxiv.org/abs/1505.05670

A stochastic individual-based model for immunotherapy of cancer

Martina Baar, Loren Coquille, Hannah Mayer, Michael Hölzel, Meri Rogava, Thomas Tüting, Anton Bovier 

 

We propose an extension of a standard stochastic individual-based model in population dynamics which broadens the range of biological applications. Our primary motivation is modelling of immunotherapy for malignant tumors. The main characteristics of the model are distinguishing phenotype and genotype, including environment-dependent transitions between phenotypes that do not affect the genotype, and the introduction of a competition term which lowers the reproduction rate of an individual in addition to the usual term that increases its death rate. We prove that this stochastic process converges in the limit of large populations to a deterministic limit which is the solution to a system of quadratic differential equations. We illustrate the new setup by using it to model various phenomena arising in immunotherapy. Our aim is twofold: on the one hand, we show that the interplay of genetic mutations and phenotypic switches on different timescales as well as the occurrence of metastability phenomena raise new mathematical challenges. On the other hand, we argue why understanding purely stochastic events (which cannot be obtained with deterministic systems) may help to understand the resistance of tumors to various therapeutic approaches and may have non-trivial consequences on tumor treatment protocols and demonstrate this through numerical simulations.

http://arxiv.org/abs/1505.00452 

Edge effects in game theoretic dynamics of spatially structured tumors

Edge effects in game theoretic dynamics of spatially structured tumours

Artem Kaznatcheev, Jacob G Scott, DavidBasanta

doi: http://dx.doi.org/10.1101/014233

Abstract

Background: Analysing tumour architecture for metastatic potential usually focuses on phenotypic differences due to cellular morphology or specific genetic mutations, but often ignore the cell's position within the heterogeneous substructure. Similar disregard for local neighborhood structure is common in mathematical models. Methods: We view the dynamics of disease progression as an evolutionary game between cellular phenotypes. A typical assumption in this modeling paradigm is that the probability of a given phenotypic strategy interacting with another depends exclusively on the abundance of those strategies without regard local heterogeneities. We address this limitation by using the Ohtsuki-Nowak transform to introduce spatial structure to the go vs. grow game. Results: We show that spatial structure can promote the invasive (go) strategy. By considering the change in neighbourhood size at a static boundary -- such as a blood-vessel, organ capsule, or basement membrane -- we show an edge effect that allows a tumour without invasive phenotypes in the bulk to have a polyclonal boundary with invasive cells. We present an example of this promotion of invasive (EMT positive) cells in a metastatic colony of prostate adenocarcinoma in bone marrow. Interpretation: Pathologic analyses that do not distinguish between cells in the bulk and cells at a static edge of a tumour can underestimate the number of invasive cells. We expect our approach to extend to other evolutionary game models where interaction neighborhoods change at fixed system boundaries.

Link: http://biorxiv.org/content/early/2015/01/23/014233

Model for Acid-Mediated Tumour Invasion with Chemotherapy Intervention I: Homogeneous Populations

Andrew B. Holder, Marianito R. Rodrigo

(Submitted on 2 Dec 2014)

The acid-mediation hypothesis, that is, the hypothesis that acid produced by tumours, as a result of aerobic glycolysis, provides a mechanism for invasion, has so far been considered as a relatively closed system. The focus has mainly been on the dynamics of the tumour, normal-tissue, acid and possibly some other bodily components, without considering the effect of an external intervention such as a cytotoxic treatment. This article aims to examine the effect that a cytotoxic treatment has on a tumour growing under the acid-mediation hypothesis by using a simple set of ordinary differential equations that consider the interaction between normal-tissue, tumour-tissue, acid and chemotherapy drug.

link: http://arxiv.org/abs/1412.0748 

Dynamics and bifurcations in a simple quasispecies model of tumorigenesis

V. Castillo, J. Tomas Lazaro, J. Sardanyes 

Submitted on 24 Nov 2014

 

Cancer is a complex disease and thus is complicated to model. However, simple models that describe the main processes involved in tumoral dynamics, e.g., competition and mutation, can give us clues about cancer behaviour, at least qualitatively, also allowing us to make predictions. Here we analyze a simplified quasispecies mathematical model given by differential equations describing the time behaviour of tumor cells populations with different levels of genomic instability. We find the equilibrium points, also characterizing their stability and bifurcations focusing on replication and mutation rates. We identify a transcritical bifurcation at increasing mutation rates of the tumor cells population. Such a bifurcation involves an scenario with dominance of healthy cells and impairment of tumor populations. Finally, we characterize the transient times for this scenario, showing that a slight increase beyond the critical mutation rate may be enough to have a fast response towards the desired state (i.e., low tumor populations) during directed mutagenic therapies. 

Link: http://arxiv.org/abs/1411.6531

Cancer initiation with epistatic interactions between driver and passenger mutations

Benedikt Bauer, Arne Traulsen

(Submitted on 4 Oct 2013)

We investigate the dynamics of cancer initiation in a model with one driver mutation and several passenger mutations. In contrast to previous models, the change in fitness induced by the driver mutation depends on the genetic background of the cell, in our case on the number of passenger mutations. The passenger mutations themselves have no or only a very small impact on the cell's fitness. This approach is motivated by the Burkitt Lymphoma, where the hallmark mutation, a translocation between the MYC gene and an immunoglobulin gene, alters the rate of apoptosis, but also the proliferation rate of cells. This way we obtain an epistatic fitness landscape, where the fitness of cells with the driver mutation is advantageous only if enough passenger genes have mutated. Otherwise the fitness might even be deleterious. Our analysis is based on an individual cell model in which the cells can divide or undergo apoptosis. In case of division the two daughter cells can mutate. This model shows a very interesting dynamical behavior. Since the driver mutation is deleterious on a background with only a few passenger mutations, there is a long period of stasis in the number of cells until a clone of cells has evolved with enough passenger mutations. Only when the driver mutation occurs in one of those cells, the cell population starts to grow exponentially.

Link: http://arxiv.org/abs/1310.1853

A filter-flow perspective of hematogenous metastasis offers a non-genetic paradigm for personalized cancer therapy

This is a rather short paper authored by some of us who maintain Warburg's Lens. The focus is on metastatic spread and how it can be understood from a filter-flow perspective, i.e. how the blood flow and filtration that occurs in capillary beds affects the efficiency of the process. This method builds on the work of Leonard Weiss, who was a leading figure in research into metastatic spread for many years.

Jacob G. Scott, Alexander G. Fletcher, Philip K. Maini, Alexander R. A. Anderson, Philip Gerlee

Research into mechanisms of hematogenous metastasis has largely become genetic in focus, attempting to understand the molecular basis of `seed-soil' relationships. Preceding this biological mechanism is the physical process of dissemination of circulating tumour cells (CTCs). We utilize a `filter-flow' paradigm to show that assumptions about CTC dynamics strongly affect metastatic efficiency: without data on CTC dynamics, any attempt to predict metastatic spread in individual patients is impossible.

link: http://arxiv.org/abs/1309.5078

Adaptation and learning of molecular networks as a description of cancer development at the systems-level: Potential use in anti-cancer therapies

David M. Gyurko, Daniel V. Veres, Dezso Modos, Katalin Lenti, Tamas Korcsmaros, Peter Csermely

(Submitted on 14 Jun 2013)

There is a widening recognition that cancer cells are products of complex developmental processes. Carcinogenesis and metastasis formation are increasingly described as systems-level, network phenomena. Here we propose that malignant transformation is a two-phase process, where an initial increase of system plasticity is followed by a decrease of plasticity at late stages of carcinogenesis as a model of cellular learning. We describe the hallmarks of increased system plasticity of early, tumor initiating cells, such as increased noise, entropy, conformational and phenotypic plasticity, physical deformability, cell heterogeneity and network rearrangements. Finally, we argue that the large structural changes of molecular networks during cancer development necessitate a rather different targeting strategy in early and late phase of carcinogenesis. Plastic networks of early phase cancer development need a central hit, while rigid networks of late stage primary tumors or established metastases should be attacked by the network influence strategy, such as by edgetic, multi-target, or allo-network drugs. Cancer stem cells need special diagnosis and targeting, since their dormant and rapidly proliferating forms may have more rigid, or more plastic networks, respectively. The extremely high ability to change their rigidity/plasticity may be a key differentiating hallmark of cancer stem cells. The application of early stage-optimized anti-cancer drugs to late-stage patients may be a reason of many failures in anti-cancer therapies. Our hypotheses presented here underlie the need for patient-specific multi-target therapies applying the correct ratio of central hits and network influences -- in an optimized sequence.

Symmetric vs asymmetric stem cell divisions: an adaptation against cancer?

Interesting paper on the effect of different division patterns on the accumulation of mutations in tissue cells. In particular, symmetric vs asymmetric divisions are compared, and it is found that symmetric cell divisions could delay the accumulation or carcinogenic mutations and thus the development of cancer. 

Symmetric vs asymmetric stem cell divisions: an adaptation against cancer?

Leili Shahriyari, Natalia L. Komarova

 

Traditionally, it has been held that a central characteristic of stem cells is their ability to divide asymmetrically. Recent advances in inducible genetic labeling provided ample evidence that symmetric stem cell divisions play an important role in adult mammalian homeostasis. It is well understood that the two types of cell divisions differ in terms of the stem cells' flexibility to expand when needed. On the contrary, the implications of symmetric and asymmetric divisions for mutation accumulation are still poorly understood. In this paper we study a stochastic model of a renewing tissue, and address the optimization problem of tissue architecture in the context of mutant production. Specifically, we study the process of tumor suppressor gene inactivation which usually takes place as a sequence of two consecutive "hits", and which is one of the most common patterns in carcinogenesis. We compare and contrast symmetric and asymmetric (and mixed) stem cell divisions, and focus on the rate at which double-hit mutants are generated. It turns out that symmetrically-dividing cells generate such mutants at a rate which is significantly lower than that of asymmetrically-dividing cells. This result holds whether single-hit (intermediate) mutants are disadvantageous, neutral, or advantageous. It is also independent on whether the carcinogenic double-hit mutants are produced only among the stem cells or also among more differentiated cells. We argue that symmetric stem cell divisions in mammals could be an adaptation which helps delay the onset of cancers. We further investigate the question of the optimal fraction of stem cells in the tissue, and quantify the contribution of non-stem cells in mutant production. Our work provides a hypothesis to explain the observation that in mammalian cells, symmetric patterns of stem cell division seem to be very common.

Preprint: http://arxiv.org/abs/1305.0100