Prediction of drug pair forming an “evolutionary trap” for breast cancer

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Robustness and Evolvability of a Heterogeneous Cell Populations

While the model introduced in the Chapter 2 allowed us to explain the experimentally observed relative fitness distributions across stress environments for aneuploid yeast, its relationship to existing models, as well as meaning and influence on the model’s behavior of some of the parameters remained insufficiently explored. In addition, while we suggested that our model could be applied to other biological systems beyond yeast, notably cancer, the reference euploid population was not necessarily clearly defined.
Chapter 3 presents a more in-depth work on exploring the model from a theoretical perspective. Here, we derive a closed formula solutions as well as approximate closed form solutions for the standard deviation and mean of the relative fitness. We as well define the properties of a phenotypical reference population and offer an algorithm describing how to detect a reference population. Here, we explore more in depth how our model behavior depends on the convexity of the function mapping the traits deviation from the environment optimum to the fitness (robustness factor) and establishes the link between our model and the well-known Fisher’s geometric model in population genetics, introduced by sir Ronald Fisher to reconcile Mendelian genetics and Biostatistics in the early 1930th.
The impact of this modelling work however goes beyond the confines of aneuploidy and adaptation to stress. Due to its formal similarity with Fisher’s Geometrical model, our model provides an insight as well for the field of population genetics, especially with regards to measuring the complexity of the phenotypic space experimentally, as well as estimate the robustness of the organism. Due to the heterogeneity of cancer and the importance that this heterogeneity plays in allowing it to acquire drug resistance, our search for a reference population in a cancer cell line population yielded a likely candidate to model a multidrug resistant cancer cell line.
For this article, I have contributed to the article writing, figure generation, conceptualization of the model, review of articles in population genetics, mathematical model formalization, raw data extraction through code as well as invention and implementation of the algorithm for phenotypic reference population detection based on the fitness in a set of environments data. Boris Rubinstein provided help with closed form solution derivation and parts of Mathematica code used for regression. Jin Zhu provided previously unpublished data for non-normalized yeast aneuploid fitness in a large set of environments. The article is in submission and its prior publication is contrary to the journal policies.

Prediction of drug pair forming an “evolutionary trap” for breast cancer

In this chapter, we attempted to apply our mathematical model of adaptation to a concrete rapidly evolving biological system – breast cancer. Our goal is to design an “evolutionary trap”, as described in the chapter 2 – a pair of drugs that would efficiently cover the entire trait space available for the breast cancer cell lines and hence ensure that even multidrug resistant breast cancer cell populations can be targeted and eliminated.
To do this, we rely on the data from the cancer pharmacogenomics screen assay performed and published previously (Daemen et al., 2013; Heiser and Sadanandam, 2012). In their screen, authors use a collection of 70 breast cancer cell lines, which they tested for growth inhibition by a palette of concentration of 90 different therapeutic compounds, ranging from 10e-8 10e-3 molar for 72 hours. Their screen included several lines of non-tumor-inducing immortalized breast epithelia as a reference population, as well as pulled together a highly diverse therapeutic compound set, with vastly different modes of action, for a number of them not even targeting cancer specifically. We were interested in finding the combination of drugs that, at given concentrations, would have had a complementary killing effect on the breast cancer cells, while leaving non-tumorigenic cells grow. To find such a pair of drugs, we made three assumptions. First, we assumed that the breast cancer cell lines, as well as immortalized non-tumorigenic epithelial cell lines responded to the drugs similarly to the breast cancer cells inside patients. Second, we assumed that the breast cancer cell lines were sampling the available trait space in a saturating manner – in other terms they were representing all the space breast cancer cell lines could explore to escape from evolutionary pressure imposed by drugs. Our final assumption was that the action of drugs on the breast cancer for the successive application of two drugs to a cancer cell lines for 72 hours each could be represented as a product of the factor (f) by which the cells grew (f>1) or were killed (f<1) during that period.
First, we needed to process the raw data supplied by (Damien et al. 2013). The data contained a different number of replicates for each compound – cell line pair, as shown in the Figure 2 below. Given that the proxy for cell proliferation and fitness chosen by authors was change in optical density, we needed to account for the acquisition error margin of the instruments. To do this, for each 96 well plate in which the assays were performed, we calculated the Optical Density (OD) of four empty wells. Ideally, their OD would all be set to 0, but in reality, we observed a curve centered about 100 OD units (figure 3, black), that was approximately gaussian (figure 3, green, distortion due to binning). We also noticed that several plates had control wells contaminated, with ODs in the range of several thousands. We discarded those plates from further analysis. In addition to that, we transformed our OD measurements from arbitrary OD units into the units corresponding to the SD of the instrument precision.

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Information flow framework for biological network analysis

Our quantitative models explaining the beneficial effect of aneuploidy on the robustness were a promising start. However, we knew that in yeast, adaptation to specific stresses is mediated by aneuploidies with specific patterns. For instance, Radicicol resistance in S. Cerevisiae is conferred specifically by the chromosome 15 gain (Chen et al. 2012). In cancers, specific segmental aneuploidies are associated to specific cancers, such as Chromosome 10 loss to glioblastoma multiforma (von Deimling et al. 1992).
Thanks to the genomic characterization of the breast cancer cell lines throughout the last 15 years, both from the sequencing and DNA CHIPs, we can quantify large-scale segmental aneuploidy in cancer with HMM, as represented in the figure 9 below (code used to generate it available at Once we separate the large-scale segmental aneuploidy in a collection of 53 breast cancer or breast epithelia immortalized cell lines (Neve et al. 2006) from the local amplification, and look at the former (figure 10 below), we can see a specific pattern of common losses and gains of chromosomes.

Table of contents :

Table of Contents
Published content
Chapter 1: General Introduction:
Chapter 2: Targeting the adaptability of heterogeneous aneuploids – Geometrical model of adaptation
Chapter 3: Robustness and Evolvability of a Heterogeneous Cell Populations
Chapter 4: Prediction of drug pair forming an “evolutionary trap” for breast cancer
Chapter 5: Information flow framework for biological network analysis
Chapter 6: Essential genes as evolutionary dead-ends in biomolecular networks
Chapter 7: Experimental investigation of aneuploidy evolvability enhancing potential
Chapter 8: Experimental investigation of aneuploidy impact on intra-nuclear chromosome localization and motility
Chapter 9: ImagePipe: a Python Framework for Biological Microscopy Analysis Pipelines .
Chapter 10: Example of application of ImagePipe: import of HS-aggregate related proteins into mitochondria
Chapter 11: General conclusion


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