Reconstructing phylogenies of metastatic cancers

Johannes G Reiter, Alvin P Makohon-Moore, Jeffrey M Gerold, Ivana Bozic, Krishnendu Chatterjee, Christine A Iacobuzio-Donahue, Bert Vogelstein, Martin A Nowak

Abstract

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.

Link: http://biorxiv.org/content/early/2016/04/11/048157

Universal asymptotic clone size distribution for general population growth

Michael D. Nicholson, Tibor Antal

Deterministically growing (wild-type) populations which seed stochastically developing mutant clones have found an expanding number of applications from microbial populations to cancer. The special case of exponential wild-type population growth, usually termed as the Luria-Delbruck or Lea-Coulson model, is often assumed but seldom realistic. In this article we generalise the model to different types of wild-type population growth, with mutants evolving as a birth-death branching process. Our focus is on the size distribution of clones after some time, which can be mapped to the total number of mutants. Exact expressions are derived for exponential, power-law and logistic population growth. We prove that the large time limit of the clone size distribution has a general two-parameter form for a large class of population growth. The large time clone size distribution always has a power-law tail, and for subexponential wild-type growth the probability of a given clone size is inversely proportional to the clone size. We support our results by analysing a data-set on tumour metastasis sizes, and we find that a power-law tail is more likely than an exponential one, in agreement with our predictions.

Link: http://arxiv.org/abs/1604.04936#

A Hydrodynamic Approach To Cancer

Abstract

This is the pre-print version of a paper submitted to Technische Mechanik (ISSN 0232-3869) Hydrodynamic analysis suggests that the injection of drag-reducing agents (DRA) in nanomolar concentrations may hinder metastasizing of circulating tumor cells and serve this way as a complementary post-operative treatment for cancer patients. Our conclusion is based on the following considerations: - Tumor cells need an extra nutrient supply in order to survive and grow. - The attachment of circulating tumor cells therefore tends to occur at sites in the human circulatory system characterized by localized turbulence, which enhances the mass transfer of nutrients, e.g., at sites of vessel branching and bending with plasma skimming. - Also obstacles to blood flow, such as plaques (atherosclerosis), tumors, and red blood cell (RBC) rouleaux, produce local vortices that increase mass transfer, i.e., food supply. - DRA have the ability to smooth (laminarise) localized turbulence in the circulatory system and to reduce mass transfer. - Depriving tumor cells of their required nutrient levels will reduce the probability of creating metastatic tumors, and may lead to their starvation-induced death. In the first part of our essay we demonstrate how flow constrictions decrease mean blood flow velocity, wall shear rates, and Reynolds numbers respectively, and increase the friction factor. Experimentally derived apparent viscosity data from literature will be used to determine the probability of RBC rouleaux formation. This is of importance since RBC rouleaux are typically associated with turbulent blood flow patterns. An increase in apparent viscosity at low flow rates will be attributed to the formation of RBC rouleaux. In part two we discuss the application of the Lockhart/Martinelli method to determine the pressure drop in blood vessels. The objective is to determine a mass transfer coefficient characterizing the mass transfer between the center and the wall of both healthy and cancerous blood vessels. This coefficient indicates the nutrient supply available to tumor cells under different flow conditions and shows the effect of DRA. Our hydrodynamic approach contrasts with previous studies of the possible benefits of DRA injection, which were focused on improving blood supply. We emphasize the reduction of the mass transfer rate as a tool to withhold turbulence induced supplementary food supply to tumor cells. Due to the possibility of unexpected side effects when using DRA (including their mechanical degradation products) animal models are indispensable before clinical trials.

link: http://biorxiv.org/content/early/2015/02/03/014696

Cancer Metastasis: Collective Invasion in Heterogeneous Multicellular Systems

Adrien Hallou, Joel Jennings, Alexandre Kabla

(Submitted on 31 Dec 2014)

Heterogeneity within tumour cell populations is associated with an increase in malignancy and appears to play an important role during cancer metastasis. Using in silico experiments, we study the interplay between collective behaviours and cell motility heterogeneities in a model system. Working with tumour spheroids that contain two non-proliferating cell populations of different motile properties, we explore the conditions required for maximal invasion into surrounding tissues. We show emerging spatial patterns of cellular organisation and invasion which are consistent with in vitro and in vivo observations. This demonstrates that mechanical interactions at the cellular level are sufficient to account for many of the observed morphologies of invasion and that heterogeneity in cell motility can be more important than average mechanical properties in controlling the fate of large cell populations.

link: http://arxiv.org/abs/1501.00065

Niche inheritance: a cooperative pathway to enhance cancer cell fitness though ecosystem engineering

Kimberline R. Yang, Steven Mooney, Jelani C. Zarif, Donald S. Coffey, Russell S. Taichman, Kenneth J. Pienta

(Submitted on 28 Mar 2014)

Cancer cells can be described as an invasive species that is able to establish itself in a new environment. The concept of niche construction can be utilized to describe the process by which cancer cells terraform their environment, thereby engineering an ecosystem that promotes the genetic fitness of the species. Ecological dispersion theory can then be utilized to describe and model the steps and barriers involved in a successful diaspora as the cancer cells leave the original host organ and migrate to new host organs to successfully establish a new metastatic community. These ecological concepts can be further utilized to define new diagnostic and therapeutic areas for lethal cancers.

link: http://arxiv.org/abs/1403.7413 

Minimizing Metastatic Risk in Radiotherapy Fractionation Schedules

Kevin Leder, Jagdish Ramakrishnan

(Submitted on 27 Dec 2013)

Metastasis is the process by which cells from a primary tumor disperse and form new tumors at distant anatomical locations. The treatment and prevention of metastatic cancer remains an extremely challenging problem. In this work, we consider the problem of developing fractionated irradiation schedules that minimize production of metastatic cancer cells. Interestingly we observe that the resulting fractionation schedules are significantly different than those that result from more standard objectives such as minimization of final primary tumor volume. Hypo-fractionation is suggested even in cases when the α/β value of the tumor is large. This work introduces a novel biologically motivated objective function to the radiation optimization community that takes into account metastatic risk instead of the status of the primary tumor.

http://arxiv.org/abs/1312.7337

Global Dormancy of Metastases due to Systemic Inhibition of Angiogenesis

Cancer does not always develop to become a clinically manifest disease. Most of the population actually carries small occult tumors that remain asymptomatic and undetectable. Here, we propose a theoretical study of this phenomenon by defining and simulating a novel mathematical model able to describe the development of a population of tumors at the organism scale. After demonstrating the model can explain experimental data on metastatic development, we go on to test the hypothesis of global dormancy resulting from inhibitory signaling interactions among the tumors. These interactions are targeted against the tumor's vascular support development (angiogenesis), known to be essential for tumor growth, by means of inhibitory molecules released in the circulation. By quantifying their consequences on the establishment of metastases and maintenance of the dormant state, our model shows for the first time how a previously unrecognized phenomenon - systemic inhibition of angiogenesis (SIA) - regulates tumor development. We show SIA alone is not sufficient for global dormancy but can suppress the growth of the total metastatic burden, even to the point of producing an equilibrium state with low and stable total cancerous mass.

Sebastien Benzekry, Alberto Gandolfi, Philip Hahnfeldt

Link: http://hal.inria.fr/hal-00868592/

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

The Cancer Diaspora: Metastasis beyond the seed and soil hypothesis

Kenneth J. Pienta, Bruce Robertson, Donald S. Coffey, Russell S. Taichman

(Submitted on 8 Aug 2013)

Do cancer cells escape their confinement of their original habitat in the primary tumor or are they forced out by ecological changes in their home niche? Describing metastasis in terms of a simple one-way migration of cells from the primary to target organs is an insufficient concept to cover the nuances of cancer spread. A diaspora is the scattering of people away from an established homeland. To date, diaspora has been a uniquely human term utilized by social scientists, however, the application of the diaspora concept to metastasis may yield new biological insights as well as therapeutic paradigms. The diaspora paradigm takes into account and models several variables: the quality of the primary tumor microenvironment, the fitness of individual cancer cell migrants as well as migrant populations, the rate of bidirectional migration of cancer and host cells between cancer sites, and the quality of the target microenvironments to establish metastatic sites. Ecological scientific principles can be applied to the cancer diaspora to develop new therapeutic strategies. For example, ecological traps, habitats that lead to the extinction of a species, can be developed to attract cancer cells to a place where they can be better exposed to treatments or to cells of the immune system for improved antigen presentation. Merging the social science concept of diaspora with ecological and population sciences concepts can inform the cancer field to understand the biology of tumorigenesis and metastasis and inspire new ideas for therapy.

http://arxiv.org/abs/1308.1938

This preprint presents a model which looks like a merge of two previous models on different biological scales: one is a tumour growth model by Hahnfeldt et al. the other is a model of metastatic spread in terms of a transport equation originally formulated by Iwata et al. With this new model the authors investigate the efficacy of different schedules for chemotherapy.

Quantitative Analysis of the Tumor/Metastasis System and its Optimal Therapeutic Control

Sebastien Benzekry (CCSB, INRIA Bordeaux - Sud-Ouest), Dominique Barbolosi (CRO2), Assia Benabdallah (LATP), Florence Hubert (LATP), Philip Hahnfeldt (CCSB)

(Submitted on 20 Jun 2013)

A mathematical model for time development of metastases and their distribution in size and carrying capacity is presented. The model is used to theoretically investigate anti-cancer therapies such as surgery and chemical treatments (cytotoxic or anti-angiogenic), in monotherapy or in combination. Quantification of the effect of surgery on the size distribution of metastatic colonies is derived. For systemic therapies, emphasis is placed on the differences between the treatment of an isolated lesion and a population of metastases. Combination therapy is addressed, in particular the problem of the drugs administration sequence. Theoretical optimal schedules are derived that show the superiority of a metronomic administration scheme (defined as a continuous administration of a given amount of drug spread during the whole therapeutic cycle) on a classical Maximum Tolerated Dose scheme (where the dose is given as a few concentrated administrations at the beginning of the cycle), for the total metastatic burden in the organism.

Maximum Tolerated Dose Versus Metronomic Scheduling in the Treatment of Metastatic Cancers

This paper was posted to the arxiv along with another paper, titled

Quantitative Analysis of the Tumor/Metastasis 

System and its Optimal Therapeutic Control

The authors are clearly interested in the implications of optimal control in the metastatic setting. The paper below leaves me wondering from an evolutionary selection point of view, if metronomic therapy is actually increasing the probability of metastasis.

Maximum Tolerated Dose Versus Metronomic Scheduling in the Treatment of Metastatic Cancers

Authors

Sébastien Benzekry, Philip Hahnfeldt

Abstract

Although optimal control theory has been used for the theoretical study of anticancerous drugs scheduling optimization,with the aim of reducing the primary tumor volume, the effect on metastases is often ignored. Here, we use a previously published model for metastatic development to define an optimal control problem at the scale of the entire organism of the patient. In silico study of the impact of different scheduling strategies for anti-angiogenic and cytotoxic agents (either in monotherapy or in combination) is performed to compare a low-dose, continuous, metronomic administration scheme with a more classical maximum tolerated dose schedule. Simulation results reveal differences between primary tumor reduction and control of metastases but overall suggest use of the metronomic protocol.

Link to the arxiv