Spatial model predicts dispersal and cell turnover cause reduced intra-tumor heterogeneity

Spatial model predicts dispersal and cell turnover cause reduced intra-tumor heterogeneity

Bartlomiej Waclaw , Ivana Bozic , Meredith E Pittman , Ralph H Hruban , Bert Vogelstein , Martin A Nowak

 

Most cancers in humans are large, measuring centimeters in diameter, composed of many billions of cells. An equivalent mass of normal cells would be highly heterogeneous as a result of the mutations that occur during each cell division. What is remarkable about cancers is their homogeneity - virtually every neoplastic cell within a large cancer contains the same core set of genetic alterations, with heterogeneity confined to mutations that have emerged after the last clonal expansions. How such clones expand within the spatially-constrained three dimensional architecture of a tumor, and come to dominate a large, pre-existing lesion, has never been explained. We here describe a model for tumor evolution that shows how short-range migration and cell turnover can account for rapid cell mixing inside the tumor. With it, we show that even a small selective advantage of a single cell within a large tumor allows the descendants of that cell to replace the precursor mass in a clinically relevant time frame. We also demonstrate that the same mechanisms can be responsible for the rapid onset of resistance to chemotherapy. Our model not only provides novel insights into spatial and temporal aspects of tumor growth but also suggests that targeting short range cellular migratory activity could have dramatic effects on tumor growth rates.

 

BioRXiv: link 

The overshoot and phenotypic equilibrium in characterizing cancer dynamics of reversible phenotypic plasticity

Xiufang Chen, Yue Wang, Tianquan Feng, Ming Yi, Xingan Zhang, Da Zhou

(Submitted on 16 Mar 2015)

The paradigm of phenotypic plasticity indicates reversible relations of different cancer cell phenotypes, which challenges the cellular hierarchy proposed by the conventional cancer stem cell (CSC) theory. Since the validity of the reversible model versus the hierarchical model of cancer cells is still experimentally debated, it is worthwhile to theoretically explore the dynamic behavior characterizing the reversible model in comparison of the hierarchical model. By comparing the two models in predicting the cell-state dynamics observed in biological experiments, our results imply that the reversible model has advantages over the hierarchical model in predicting both long-term stable and short-term transient dynamics of cancer cells. In particular, it is found that i) the reversible model can predict the phenotypic equilibrium better than the hierarchical model, namely, the stability of the phenotypic mixture of cancer cells is more rooted in the reversible model; ii) the reversible model can perform various types of overshoot behavior, whereas the hierarchical model can never predict the overshoot of CSCs proportion. These also indicate that the phenotypic equilibrium and overshoot can be good candidates to characterize the models with the reversible phenotypic plasticity.

http://arxiv.org/abs/1503.04558

Phase i trials in melanoma: A framework to translate preclinical findings to the clinic

Eunjung Kim , Vito W. Rebecca , Keiran S.M. Smalley , Alexander R.A. Anderson

doi: http://dx.doi.org/10.1101/015925 

Abstract

The combination of chemotherapy and an AKT inhibitor in patients with metastatic solid tumors including melanomas was tested in a recently completed phase 1 clinical trial. Our experiments showed that such regimens differentially induce autophagy in melanoma cells and autophagy modulates the response to treatment. Motivated by these observations, we formulated a mathematical model comprised of a system of ordinary differential equations that explains the dynamics of the response of melanoma cells to different mono and combination therapies. Model parameters were estimated using an optimization algorithm that minimizes differences between predicted cell populations and experimentally measured cell numbers. The model predicts that the combination therapy treatment protocol used in the trial is effective in short term tumor control but that the treatment will eventually fail, although smarter schedules can be applied to extend response. To move this model forward into a more clinically relevant setting, we implemented a phase i trial (a virtual/imaginary yet informed clinical trial), where a genetic algorithm was used to generate a cohort of virtual patients that captured the diversity of disease response observed in a comparable clinical trial. Simulated clinical trials with the cohort and sensitivity analysis defined parameters that discriminated virtual patients having more favorable versus less favorable outcomes. These analyses established the relevance of selecting patients based on rates of tumor growth and autophagic flux. Finally, the model predicts optimal therapeutic approaches across all virtual patients, laying the foundation for phase i-informed clinical melanoma trials. The specific melanoma model developed here is just one example of the much broader potential of the phase i framework, which can be applied to almost any parameterized cancer model.  

Link: http://biorxiv.org/content/early/2015/03/02/015925

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

A pan-cancer signature of neutral tumor evolution

Andrea Sottoriva , Trevor Graham 

 

Despite extraordinary efforts to profile cancer genomes on a large scale, interpreting the vast amount of genomic data in the light of cancer evolution and in a clinically relevant manner remains challenging. Here we demonstrate that cancer next-generation sequencing data is dominated by the signature of growth governed by a power-law distribution of mutant allele frequencies. The power-law signature is common to multiple tumor types and is a consequence of the effectively-neutral evolutionary dynamics that underpin the evolution of a large proportion of cancers, giving rise to the abundance of mutations responsible for intra-tumor heterogeneity. Importantly, the law allows the measurement, in each individual cancer, of the in vivo mutation rate and the timing of mutations with remarkable precision. This result provides a new way to interpret cancer genomic data by considering the physics of tumor growth in a way that is both patient-specific and clinically relevant.

 

bioRXiv: http://biorxiv.org/content/early/2015/02/11/014894

 

Imperfect drug penetration leads to spatial monotherapy and rapid evolution of multi-drug resistance

Stefany Moreno-Gamez , Alison L Hill , Daniel I.S. Rosenbloom , Dmitri A. Petrov , Martin A Nowak , PleuniPennings

doi: http://dx.doi.org/10.1101/013003

• Abstract
• Info/History
• Metrics
• Data Supplements
•  Preview PDF

Abstract

Infections with rapidly evolving pathogens are often treated using combinations of drugs with different mechanisms of action. One of the major goals of combination therapy is to reduce the risk of drug resistance emerging during a patient's treatment. While this strategy generally has significant benefits over monotherapy, it may also select for multi-drug resistant strains, which present an important clinical and public health problem. For many antimicrobial treatment regimes, individual drugs have imperfect penetration throughout the body, so there may be regions where only one drug reaches an effective concentration. Here we propose that mismatched drug coverage can greatly speed up the evolution of multi-drug resistance by allowing mutations to accumulate in a stepwise fashion. We develop a mathematical model of within-host pathogen evolution under spatially heterogeneous drug coverage and demonstrate that even very small single-drug compartments lead to dramatically higher resistance risk. We find that it is often better to use drug combinations with matched penetration profiles, although there may be a trade-off between preventing eventual treatment failure due to resistance in this way, and temporarily reducing pathogen levels systemically. Our results show that drugs with the most extensive distribution are likely to be the most vulnerable to resistance. We conclude that optimal combination treatments should be designed to prevent this spatial effective monotherapy. These results are widely applicable to diverse microbial infections including viruses, bacteria and parasites.

link: http://biorxiv.org/content/early/2014/12/19/013003

Statistical interpretations and new findings on Variation in Cancer Risk Among Tissues

Robert Noble, Oliver Kaltz, Michael E Hochberg

(Submitted on 3 Feb 2015)

Tomasetti and Vogelstein (2015a) find that the incidence of a set of cancer types is correlated with the total number of normal stem cell divisions. Here, we separate the effects of standing stem cell number (i.e., organ or tissue size) and per stem cell lifetime replication rate. We show that each has a statistically significant and independent effect on explaining variation in cancer incidence over the 31 cases considered by Tomasetti and Vogelstein. When considering the total number of stem cell divisions and when removing cases associated with disease or carcinogens, we find that cancer incidence attains a plateau of approximately 0.6% incidence for the cases considered by these authors. We further demonstrate that grouping by anatomical site explains most of the remaining variation in risk between cancer types. This new analysis suggests that cancer risk depends not only on the number of stem cell divisions but varies enormously ($\sim$10,000 times) depending on the stem cell's environment. Future research should investigate how tissue characteristics (anatomical site, type, size, stem cell divisions) explain cancer incidence over a wider range of cancers, to what extent different tissues express specific protective mechanisms, and whether any differential protection can be attributed to natural selection.

link:  http://arxiv.org/abs/1502.01061