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The following examples portray some of the approaches of the CCE via work previously done on other projects and grants and they lay the foundation for investigations possible with the CCE. These research milestones were accomplished through close collaboration between different investigators from a myriad of disciplines, and led to iterative mathematical modeling and experimental parameterization and validation to arrive at evolutionary mathematical frameworks that were used to (i) identify the underlying biology of a cancer type, (ii) develop fundamental evolutionary theory describing tumorigenesis, and ii) determine optimum ways to treat patients that led to clinical trials. These research approaches can be extended from preliminary data to the proposed projects and across projects:



Integrative analysis of intra-tumor heterogeneity and tumor spatial organization

Intra-tumor heterogeneity (ITH) of human tumors is important for tumor progression, treatment response, and drug resistance. However, the spatial distribution of ITH remains incompletely understood. Here, we present spatial analysis of ITH in lung adenocarcinomas from 147 patients using multi-region mass spectrometry of >5,000 regions, single-cell copy number sequencing of 2,000 single cells, and cyclic immunofluorescence of >10 million cells. We identified two distinct spatial patterns among tumors, termed clustered and random geographic diversification (GD). These patterns were observed in the same samples using both proteomic and genomic data. The random proteomic GD pattern, which is characterized by decreased cell adhesion and lower levels of tumor-interacting endothelial cells, was significantly associated with increased risk of recurrence or death in two independent patient cohorts. Our study presents comprehensive spatial mapping of ITH in lung adenocarcinoma and provides insights into the mechanisms and clinical consequences of GD.


Modeling punctuated evolution and timing copy-number alterations with single-cell sequencing data

Our knowledge of copy number evolution during the expansion of primary breast tumours is limited. Using a single-cell, single-molecule DNA-sequencing method and copy number analysis of 16,178 single cells from 8 human triple-negative breast cancers and 4 cell lines, evolutionary analysis suggests that after clonal TP53 mutations, multiple loss-of-heterozygosity events and genome doubling, there was a period of transient genomic instability followed by ongoing copy number evolution during the primary tumour expansion. By subcloning single daughter cells in culture, we show that tumour cells rediversify their genomes and do not retain isogenic properties. These data show that triple-negative breast cancers continue to evolve chromosome aberrations and maintain a reservoir of subclonal diversity during primary tumour growth.

We model copy number alteration accumulation under gradual evolution after a punctured burst or as transient instability after the punctuated burst. The modeling incorporates cell fitness and cell birth and death rates, where cells can acquired heritable breakpoints in their copy-number profiles with a size-dependent probability to account for the transient instability that arises after the punctuated burst. Maximum-likelihood fits for the breakpoint frequency spectra are used to compare the models.


Mathematical modeling of resistance predicts optimum strategies for administering targeted drugs.

(A) Schematic of the stochastic mathematical model. The model considers two subpopulations of cells, sensitive and resistant cells, which are modeled as a branching process. (B) Derivation of an isogenic system of sensitive and resistant non-small cell lung cancer (NSCLC) cells. These cells were then utilized to determine growth and death rates during different concentrations of drug to parameterize the model. (C) Prediction of optimum treatment schedules. The mathematical model, together with in vitro data, was used to identify treatment administration strategies that were predicted to maximally delay the emergence of resistance. A low-dose continuous strategy with high-dose pulses was predicted to be best. (D) This strategy was validated in cell lines and is now being tested in a prospective clinical trial.

(Chmielecki et al, Science Translational Medicine 2011)

Mathematical modeling identifies optimum administration schedules of targeted drugs in non-small cell lung cancer.

We have previously applied a mathematical modeling strategy to identify optimum treatment administration schedules for non–small cell lung cancers (NSCLCs). NSCLCs that harbor mutations within the epidermal growth factor receptor (EGFR) gene are sensitive to the tyrosine kinase inhibitors (TKIs) gefitinib and erlotinib. Unfortunately, all patients treated with these drugs will acquire resistance, most commonly as a result of a secondary mutation within EGFR (T790M). Because both drugs were developed to target wild-type EGFR, we hypothesized that current dosing schedules were not optimized for mutant EGFR or to prevent resistance. To investigate this hypothesis, we developed isogenic TKI-sensitive and TKI-resistant pairs of cell lines that mimic the behavior of human tumors. We determined that the drug-sensitive and drug-resistant EGFR-mutant cells exhibited differential growth kinetics, with the latter cells showing growth in the absence of therapy. We incorporated these data into evolutionary mathematical cancer models with constraints derived from clinical data sets. This modeling predicted alternative therapeutic strategies that could prolong the clinical benefit of TKIs against EGFR-mutant NSCLCs by delaying the development of resistance. We then further expanded on these studies by incorporating pharmacokinetic processes into the model and studying combination administration schedules of chemotherapy and TKIs. These strategies, identified by mathematical modeling, are currently being tested in clinical trials in Asia and the US (http://clinicaltrials.gov/show/NCT01967095), and this research strategy can be extrapolated to optimize treatment strategies for other cancer types as we are proposing to do in the CCE.



A mathematical framework of cancer progression allows the identification of growth and dissemination kinetics.

(A) Schematic overview of mathematical framework. The model considers three cell types: cells which have not yet evolved the ability to metastasize (yellow); they give rise to cells that have evolved the ability to metastasize but still reside in the primary tumor (orange), where they might disseminate to a new metastatic site time unit. This mathematical framework can be used to determine quantities such as response to treatment, the expected number of metastasized cells at death, the risk of metastatic disease at diagnosis, and the effects of different treatment modalities as well as treatment delays on patient survival (B). We found that most patients harbor metastatic cells at the time of diagnosis, and that any treatment delays significantly reduce patient survival.

(Haeno et al, Cell 2012)

Mathematical modeling reveals natural history of pancreatic tumor development.

We developed a mathematical model to describe the dynamics of pancreatic tumor growth and dissemination. We found that pancreatic cancer growth is initially exponential. After estimating the rates of pancreatic cancer cell growth and dissemination, we determined that patients likely harbor metastases at diagnosis and predicted the number and size distribution of metastases as well as patient survival. These findings were validated in an independent database. We also analyzed the effects of different treatment modalities and found that therapies that efficiently reduce the growth rate of primary and metastatic cells earlier in the course of treatment are predicted to be superior to upfront tumor resection. This work has laid the foundation for multiple clinical trials aimed at changing clinical standard of care in pancreatic cancer, as well as follow-up investigations of existing treatment modalities in pancreatic cancer.



Optimized radiation therapy (RT) schedules significantly improve survival in glioma-bearing mice.

(A) Schematic outline of the mathematical model.The model considers stem-like and tumor bulk cells which proliferate and (de)differentiate depending on the amount of RT administered. (B) Kaplan-Meier (KM) analysis of the animals treated with different RT schedules. The schematic indicates the RT schedule for the optimized and scramble control schedules. The optimized schedule had a median survival significantly better than standard (p= 0.001); the scramble control did not (p = 0.23). (C) KM analysis of a 20 Gy, two-week standard RT schedule and 10 Gy standard and optimized schedules. The schematic indicates RT for the 20 Gy standard schedule. Its median survival was significantly longer than the 10 Gy standard median survival (p= 0.0001), but not significantly longer than the optimized 10 Gy median survival (p = 0.3907). (D) Hazard ratios.

(Leder et al, Cell 2014)

Mathematical modeling reveals optimized radiation dosing schedules for brain tumors.

We also developed mathematical modeling approaches to identify optimum administration schedules of radiation therapy (RT). So far, we have applied this approach to primary glioblastomas (GBM), which are the most common and malignant primary tumors of the brain and are frequently treated with RT. GBM is resistant to standard approaches and survival has changed little over the last 50 years. RT is one of the pillars of therapy for GBM but despite treatment, recurrence inevitably occurs. In an attempt to improve tumor control, we employed a novel combined theoretical and experimental strategy that takes into account tumor cellular heterogeneity and the microenvironment to identify radiation delivery strategies that improve survival in an animal model of GBM. The mathematical model considers both stem-like and tumor bulk cells; stem-like cells may self-renew or differentiate to tumor bulk cells and are largely resistant to RT. Tumor bulk cells may de-differentiate to stem-like cells at a rate depending on RT and micro-environmental factors. This model was parameterized using in vivo data. We then used the model to identify an unconventional RT delivery schedule that was predicted to improve survival while keeping the total amount of RT administered the same as standard fractionated therapy (total of 10 Gy). Indeed, this novel schedule nearly doubled the efficacy of each Gray of RT administered when validated in mice and establishes a rationale for future clinical trials. This interdisciplinary approach is also applicable to other GBM subtypes cancer types, and hence may lay the foundation for significantly increasing the effectiveness of RT delivery.