Person:

Nowak, Martin

Major efforts to sequence cancer genomes are now occurring throughout the world. Though the emerging data from these studies are illuminating, their reconciliation with epidemiologic and clinical observations poses a major challenge. In the current study, we provide a novel mathematical model that begins to address this challenge. We model tumors as a discrete time branching process that starts with a single driver mutation and proceeds as each new driver mutation leads to a slightly increased rate of clonal expansion. Using the model, we observe tremendous variation in the rate of tumor development - providing an understanding of the heterogeneity in tumor sizes and development times that have been observed by epidemiologists and clinicians. Furthermore, the model provides a simple formula for the number of driver mutations as a function of the total number of mutations in the tumor. Finally, when applied to recent experimental data, the model allows us to calculate, for the first time, the actual selective advantage provided by typical somatic mutations in human tumors in situ. This selective advantage is surprisingly small, 0.005 +- 0.0005, and has major implications for experimental cancer research.

Background: Interstitial brachytherapy for localised prostate cancer may be followed by transient increases in prostate-specific antigen (PSA) that resolve without therapy. Such PSA bounces may be associated with an improved outcome but often cause alarm in the patient and physician, and have defied explanation. Methods: We developed a mathematical model to capture the interactions between the tumour, radiation and anti-tumour immune response. The model was fitted to data from a large cohort of patients treated exclusively with interstitial brachytherapy. Immunohistological analysis for T-cell infiltration within the same tumours was also performed. Results: Our minimal model captures well the dynamics of the tumour after therapy, and suggests that a strong anti-tumour immune response coupled with the therapeutic effect of radiation on the tumour is responsible for the PSA bounce. Patients who experience a PSA bounce had a higher density of CD3 and CD8 cells within the tumour that likely contribute to the PSA bounce and the overall better outcomes observed. Conclusions: Our observations provide a novel and unifying explanation for the PSA bounce in patients with early prostate cancer and also have implications for the use of immune-based therapies in such patients to improve outcomes.

Tumor growth is caused by the acquisition of driver mutations, which enhance the net reproductive rate of cells. Driver mutations may increase cell division, reduce cell death, or allow cells to overcome density-limiting effects. We study the dynamics of tumor growth as one additional driver mutation is acquired. Our models are based on two-type branching processes that terminate in either tumor disappearance or tumor detection. In our first model, both cell types grow exponentially, with a faster rate for cells carrying the additional driver. We find that the additional driver mutation does not affect the survival probability of the lesion, but can substantially reduce the time to reach the detectable size if the lesion is slow growing. In our second model, cells lacking the additional driver cannot exceed a fixed carrying capacity, due to density limitations. In this case, the time to detection depends strongly on this carrying capacity. Our model provides a quantitative framework for studying tumor dynamics during different stages of progression. We observe that early, small lesions need additional drivers, while late stage metastases are only marginally affected by them. These results help to explain why additional driver mutations are typically not detected in fast-growing metastases.

In solid tumors, targeted treatments can lead to dramatic regressions, but responses are often short-lived because resistant cancer cells arise. The major strategy proposed for overcoming resistance is combination therapy. We present a mathematical model describing the evolutionary dynamics of lesions in response to treatment. We first studied 20 melanoma patients receiving vemurafenib. We then applied our model to an independent set of pancreatic, colorectal, and melanoma cancer patients with metastatic disease. We find that dual therapy results in long-term disease control for most patients, if there are no single mutations that cause cross-resistance to both drugs; in patients with large disease burden, triple therapy is needed. We also find that simultaneous therapy with two drugs is much more effective than sequential therapy. Our results provide realistic expectations for the efficacy of new drug combinations and inform the design of trials for new cancer therapeutics. DOI: http://dx.doi.org/10.7554/eLife.00747.001

Reconstructing the evolutionary history of metastases is critical for understanding their basic biological principles and has profound clinical implications. Genome-wide sequencing data has enabled modern phylogenomic methods to accurately dissect subclones and their phylogenies from noisy and impure bulk tumor samples at unprecedented depth. However, existing methods are not designed to infer metastatic seeding patterns. Here we develop a tool, called Treeomics, to reconstruct the phylogeny of metastases and map subclones to their anatomic locations. Treeomics infers comprehensive seeding patterns for pancreatic, ovarian, and prostate cancers. Moreover, Treeomics correctly disambiguates true seeding patterns from sequencing artifacts; 7% of variants were misclassified by conventional statistical methods. These artifacts can skew phylogenies by creating illusory tumor heterogeneity among distinct samples. In silico benchmarking on simulated tumor phylogenies across a wide range of sample purities (15-95%) and sequencing depths (25-800x) demonstrates the accuracy of Treeomics compared to existing methods.

Reconstructing the evolutionary history of metastases is critical for understanding their basic biological principles and has profound clinical implications. Genome-wide sequencing data has enabled modern phylogenomic methods to accurately dissect subclones and their phylogenies from noisy and impure bulk tumor samples at unprecedented depth. However, existing methods are not designed to infer metastatic seeding patterns. We have developed a tool, called Treeomics, that utilizes Bayesian inference and Integer Linear Programming to reconstruct the phylogeny of metastases. Treeomics allowed us to infer comprehensive seeding patterns for pancreatic, ovarian, and prostate cancers. Moreover, Treeomics correctly disambiguated true seeding patterns from sequencing artifacts; 7% of variants were misclassified by conventional statistical methods. These artifacts can skew phylogenies by creating illusory tumor heterogeneity among distinct samples. Last, we performed in silico benchmarking on simulated tumor phylogenies across a wide range of sample purities (30-90%) and sequencing depths (50-800x) to demonstrate the high accuracy of Treeomics compared to existing methods.

Molecular targeted drugs are clinically effective anti-cancer therapies. However, tumours treated with single agents usually develop resistance. Here we use colorectal cancer (CRC) as a model to study how the acquisition of resistance to EGFR-targeted therapies can be restrained. Pathway-oriented genetic screens reveal that CRC cells escape from EGFR blockade by downstream activation of RAS-MEK signalling. Following treatment of CRC cells with anti-EGFR, anti-MEK or the combination of the two drugs, we find that EGFR blockade alone triggers acquired resistance in weeks, while combinatorial treatment does not induce resistance. In patient-derived xenografts, EGFR-MEK combination prevents the development of resistance. We employ mathematical modelling to provide a quantitative understanding of the dynamics of response and resistance to these single and combination therapies. Mechanistically, we find that the EGFR-MEK Combo blockade triggers Bcl-2 and Mcl-1 downregulation and initiates apoptosis. These results provide the rationale for clinical trials aimed at preventing rather than intercepting resistance.

SUMMARY Which genetic alterations drive tumorigenesis and how they evolve over the course of disease and therapy are central questions in cancer biology. We identify 44 recurrently mutated genes and 11 recurrent somatic copy number variations through whole-exome sequencing of 538 chronic lymphocytic leukemia (CLL) and matched germline DNA samples, 278 of which were collected in a prospective clinical trial. These include previously unrecognized cancer drivers (RPS15, IKZF3) and collectively identify RNA processing and export, MYC activity and MAPK signaling as central pathways involved in CLL. Clonality analysis of this large dataset further enabled reconstruction of temporal relationships between driver events. Direct comparison between matched pre-treatment and relapse samples from 59 patients demonstrated highly frequent clonal evolution. Thus, large sequencing datasets of clinically informative samples enable the discovery of novel cancer genes and the network of relationships between the driver events and their impact on disease relapse and clinical outcome.

The vast majority of mutations in the exome of cancer cells are passengers, which do not affect the reproductive rate of the cell. Passengers can provide important information about the evolutionary history of an individual cancer, and serve as a molecular clock. Passengers can also become targets for immunotherapy or confer resistance to treatment. We study the stochastic expansion of a population of cancer cells describing the growth of primary tumors or metastatic lesions. We first analyze the process by looking forward in time and calculate the fixation probabilities and frequencies of successive passenger mutations ordered by their time of appearance. We compute the likelihood of specific evolutionary trees, thereby informing the phylogenetic reconstruction of cancer evolution in individual patients. Next, we derive results looking backward in time: for a given subclonal mutation we estimate the number of cancer cells that were present at the time when that mutation arose. We derive exact formulas for the expected numbers of subclonal mutations of any frequency. Fitting this formula to cancer sequencing data leads to an estimate for the ratio of birth and death rates of cancer cells during the early stages of clonal expansion.

Molecular targeted drugs are clinically effective anti-cancer therapies. However, tumours treated with single agents usually develop resistance. Here we use colorectal cancer (CRC) as a model to study how the acquisition of resistance to EGFR-targeted therapies can be restrained. Pathway-oriented genetic screens reveal that CRC cells escape from EGFR blockade by downstream activation of RAS-MEK signalling. Following treatment of CRC cells with anti-EGFR, anti-MEK or the combination of the two drugs, we find that EGFR blockade alone triggers acquired resistance in weeks, while combinatorial treatment does not induce resistance. In patient-derived xenografts, EGFR-MEK combination prevents the development of resistance. We employ mathematical modelling to provide a quantitative understanding of the dynamics of response and resistance to these single and combination therapies. Mechanistically, we find that the EGFR-MEK Combo blockade triggers Bcl-2 and Mcl-1 downregulation and initiates apoptosis. These results provide the rationale for clinical trials aimed at preventing rather than intercepting resistance.