Spatial metrics of tumour vascular organisation predict radiation efficacy in a computational model

Jacob G Scott, Alexander George Fletcher, Alexander RA Anderson, Philip K Maini

doi: http://dx.doi.org/10.1101/029595

Abstract

Intratumoural heterogeneity is known to contribute to heterogeneity in therapeutic response. Variations in oxygen tension in particular have been correlated with changes in radiation response in vitro and at the clinical scale with overall survival. Heterogeneity at the microscopic scale in tumour blood vessel architecture has been described, and is one source of the underlying variations in oxygen tension. We endeavour to determine whether histologic scale measures of the erratic distribution of blood vessels within a tumour can be used to predict differing radiation response. Using a two-dimensional hybrid cellular automaton model of tumour growth, we evaluate the effect of vessel distribution on cell survival outcomes of simulated radiation therapy. Using the standard equations for the oxygen enhancement ratio for cell survival probability under differing oxygen tensions, we calculate average radiation effect in simulated, random, vessel organizations. We go on to quantify the vessel distribution heterogeneity and measure spatial organization using Ripley's L function, a measure designed to detect deviations from spatial homogeneity. We find that under differing regimes of vessel density the correlation coefficient between the measure of spatial organization and radiation effect changes sign. This provides not only a useful way to understand the differences seen in radiation effect for tissues based on vessel architecture, but also an alternate explanation for the vessel normalization hypothesis.

http://biorxiv.org/content/early/2015/10/26/029595

Computational modelling of metastasis development in renal cell carcinoma 

Etienne Baratchart 1, 2 Sébastien Benzekry 1, 2, * Andreas Bikfalvi 3, * Thierry Colin 1, 4, 2, * Lindsay S. Cooley 3 Raphäel Pineau 3 Emeline Ribot 5 Olivier Saut 1, 2 Wilfried Souleyreau 3 

* Corresponding author

1 MONC - Modélisation Mathématique pour l'Oncologie 

IMB - Institut de Mathématiques de Bordeaux, INRIA Bordeaux - Sud-Ouest, Institut Bergonié - CRLCC Bordeaux

2 IMB - Institut de Mathématiques de Bordeaux 

3 LAMC - Laboratoire Angiogenèse et Micro-environnement des Cancers 

4 UB - Université de Bordeaux 

5 RMSB - Résonance magnétique des systèmes biologiques 

Abstract : To improve our understanding of the biology of the metastatic colonization process, we conducted a modelling study based on multi-modal data from an orthotopic murine experimental system of metastatic renal cell carcinoma. The standard theory of metastatic colonization usually assumes that secondary tumours, once established at a distant site, grow independently from each other and from the primary tumour. Using a mathematical model describing the metastatic population dynamics under this assumption, we challenged the theory against our data that included: 1) dynamics of primary tumour cells in the kidney and metastatic cells in the lungs, retrieved by green fluorescent protein tracking, and 2) magnetic resonance images (MRI) informing on the number and size of macroscopic lesions. While the model could fit the primary tumour and total metastatic burden, the predicted size distribution was not in agreement with the MRI observations. Moreover, the model was incompatible with the growth rates of individual metastatic tumours. To explain the observed metastatic patterns, we hypothesised that metastatic foci derived from one or a few cells could aggregate, resulting in a similar total mass but a smaller number of metastases. This was indeed observed in our data and led us to investigate the effect of spatial interactions on the dynamics of the global metastatic burden. We derived a novel mathematical model for spatial tumour growth, where the intra-tumour increase in pressure is responsible for the slowdown of the growth rate. The model could fit the growth of lung metastasis visualized by magnetic resonance imaging. As a non-trivial outcome from this analysis, the model predicted that the net growth of two neighbouring tumour lesions that enter in contact is considerably impaired (of 31% ± 1.5%, mean ± standard deviation), as compared to the growth of two independent tumours. Together, our results have implications for theories of metastatic development and suggest that global dynamics of metastasis development is dependent on spatial interactions between metastatic lesions.

https://hal.inria.fr/hal-01164834

Towards a standard model for research in agent-based modeling and simulation

Towards a standard model for research in agent-based modeling and simulation

Nuno Fachada 1, Vitor V Lopes2, Rui C Martins3, Agostinho C Rosa

Agent-based modeling (ABM) is a bottom-up modeling approach, where each entity of the system being modeled is uniquely represented as an independent decision-making agent. ABMs are very sensitive to implementation details. Thus, it is very easy to inadvertently introduce changes which modify model dynamics. Such problems usually arise due to the lack of transparency in model descriptions, which constrains how models are assessed, implemented and replicated. In this paper, we present PPHPC, a model which aims to serve as a standard in agent based modeling research, namely, but not limited to, conceptual model specification, statistical analysis of simulation output, model comparison and parallelization studies. This paper focuses on the first two aspects (conceptual model specification and statistical analysis of simulation output), also providing a canonical implementation of PPHPC. The paper serves as a complete reference to the presented model, and can be used as a tutorial for simulation practitioners who wish to improve the way they communicate their ABMs.

Link (PeerJ): https://peerj.com/preprints/1440/

Population heterogeneity in the epithelial to mesenchymal transition is controlled by NFAT and phosphorylated Sp1

Population heterogeneity in the epithelial to mesenchymal transition is controlled by NFAT and phosphorylated Sp1

Russell Gould, Anirikh Chakrabarti, Jeffrey Varner, Jonathan Butcher

Link: http://biorxiv.org/content/early/2015/10/13/028993

Epithelial to mesenchymal transition (EMT) is an essential differentiation program during tissue morphogenesis and remodeling. EMT is induced by soluble transforming growth factor β (TGF-β) family members, and restricted by vascular endothelial growth factor family members. While many downstream molecular regulators of EMT have been identified, these have been largely evaluated individually without considering potential crosstalk. In this study, we created an ensemble of dynamic mathematical models describing TGF-β induced EMT to better understand the operational hierarchy of this complex molecular program. These models incorporate mass action kinetics within an ordinary differential equation (ODE) framework to describe the transcriptional and post-translational regulatory events driving EMT. Model parameters were estimated from multiple data sets using multiobjective optimization, in combination with cross-validation. TGF-β exposure drove the model population toward a mesenchymal phenotype, while an epithelial phenotype was maintained following vascular endothelial growth factor A (VEGF-A) exposure. Simulations predicted that the transcription factors phosphorylated SP1 and NFAT were master regulators promoting or inhibiting EMT, respectively. Surprisingly, simulations also predicted that a cellular population could exhibit phenotypic heterogeneity (characterized by a significant fraction of the population with both high epithelial and mesenchymal marker expression) if treated simultaneously with TGF-β and VEGF-A. We tested this prediction experimentally in both MCF10A and DLD1 cells and found that upwards of 45% of the cellular population acquired this hybrid state in the presence of both TGF-β and VEGF-A. We experimentally validated the predicted NFAT/Sp1 signaling axis for each phenotype response. Lastly, we found that cells in the hybrid state had significantly different functional behavior when compared to VEGF-A or TGF-β treatment alone. Together, these results establish a predictive mechanistic model of EMT susceptibility, and potentially reveal a novel signaling axis which regulates carcinoma progression through an EMT versus tubulogenesis response.

DOI: http://dx.doi.org/10.1101/028993

The evolutionary advantage of heritable phenotypic heterogeneity

The evolutionary advantage of heritable phenotypic heterogeneity

Oana Carja, Joshua B Plotkin

doi: http://biorxiv.org/content/early/2015/10/09/028795 

Abstract:

Phenotypic plasticity is an evolutionary driving force in diverse biological processes, including the adaptive immune system, the development of neoplasms, and the bacterial acquisition of drug resistance. It is essential, therefore, to understand the evolutionary advantage of an allele that confers cells the ability to express a range of phenotypes. Of particular importance is to understand how this advantage of phenotypic plasticity depends on the degree of heritability of non-genetically encoded phenotypes between generations, which can induce irreversible evolutionary changes in the population. Here, we study the fate of a new mutation that allows the expression of multiple phenotypic states, introduced into a finite population otherwise composed of individuals who can express only a single phenotype. We analyze the fixation probability of such an allele as a function of the strength of inter-generational phenotypic heritability, called memory, the variance of expressible phenotypes, the rate of environmental changes, and the population size. We find that the fate of a phenotypically plastic allele depends fundamentally on the environmental regime. In a constant environment, the fixation probability of a plastic allele always increases with the degree of phenotypic memory. In periodically fluctuating environments, by contrast, there is an optimum phenotypic memory that maximizes the probability of the plastic allele's fixation. This same optimum value of phenotypic memory also maximizes geometric mean fitness, in steady state. We interpret these results in the context of previous studies in an infinite-population framework. We also discuss the implications of our results for the design of therapies that can overcome resistance, in a variety of diseases.

Cell-cell interactions and evolution using evolutionary game theory

David Basanta

Cancers arise from genetic aberrations but also consistently display high levels of intra-tumor heterogeneity and evolve according to Darwinian dynamics. This makes evolutionary game theory an ideal tool in which to mathematically capture these cell-cell interactions and in which to investigate how they impact evolutionary dynamics. In this chapter we present some examples of how evolutionary game theory can elucidate cancer evolution.

Link: http://dx.doi.org/10.1101/028746

 

From concept to clinic: mathematically informed immunotherapy

Rachel Walker, Heiko Enderling

doi: http://dx.doi.org/10.1101/027979

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Abstract

Mathematical modeling has become a valuable tool in the continued effort to understand, predict and ultimately treat a wide range of cancers in recent years. By describing biological phenomena in the concise and formal language of mathematics, it is possible to elucidate key components of complex systems and ultimately develop tools capable of quantifying and predicting system behavior under given conditions. When these tools are applied as a complement to the detailed understanding of cancer biology provided by biological scientists and clinicians, new insights can be gained into the mechanisms and first-order principles of cancer development and control. To date, although mathematical tools have been applied extensively in understanding tumor growth and dynamic interactions between cancer and host, studies involving the theoretical modeling of patient response to treatment and the contribution of such findings to the development of clinically-actionable therapeutic protocols remain strikingly limited. In particular, despite the rising emergence of immunotherapy as a promising cancer treatment, knowledge gained from mathematical modeling of tumor-immune interactions often still eludes application to the clinic. The currently underutilized potential of such techniques to forecast response to treatment, aid the development of immunotherapeutic regimes and ultimately streamline the transition from innovative concept to clinical practice is hence the focus of this review.

http://biorxiv.org/content/early/2015/10/01/027979

Algorithmic Methods to Infer the Evolutionary Trajectories in Cancer Progression

Giulio Caravagna, Alex Graudenzi, Daniele Ramazzotti, Rebeca Sanz-Pamplona, Luca De Sano, Giancarlo Mauri, Victor Moreno, Marco Antoniotti, Bud Mishra

The evolutionary nature of cancer relates directly to a renewed focus on the voluminous NGS (next generation sequencing) data, aiming at the identification of explanatory models of how the (epi)genomic events are choreographed in cancer initiation and development. However, despite the increasing availability of multiple additional -omics data, this quest has been frustrated by various theoretical and technical hurdles, mostly related to the dramatic heterogeneity and temporality of the disease. In this paper, we build on our recent works on selectivity relation among driver mutations in cancer progression and investigate their applicability to the modeling problem - both at the population and individual levels. On one hand, we devise an optimal, versatile and modular pipeline to extract ensemble-level progression models from cross sectional sequenced cancer genomes. The pipeline combines state-of-the-art techniques for sample stratification, driver selection, identification of fitness-equivalent exclusive alterations and progression model inference. We demonstrate this pipeline's ability to reproduce much of the current knowledge on colorectal cancer progression, as well as to suggest novel experimentally verifiable hypotheses. On the other hand, we prove that our framework can be applied, mutatis mutandis, in reconstructing the evolutionary history of cancer clones in single patients, as illustrated by an example with multiple biopsy data from clear cell renal carcinomas.

bioRXiv: http://dx.doi.org/10.1101/027359

Robust Parameter Estimation for Biological Systems: A Study on the Dynamics of Microbial Communities 

Matthias Chung, Justin Krueger, Mihai Pop
http://arxiv.org/abs/1509.06926 

Abstract 

Interest in the study of in-host microbial communities has increased in recent years due to our improved understanding of the communities' significant role in host health. As a result, the ability to model these communities using differential equations, for example, and analyze the results has become increasingly relevant. The size of the models and limitations in data collection among many other considerations require that we develop new parameter estimation methods to address the challenges that arise when using traditional parameter estimation methods for models of these in-host microbial communities. In this work, we present the challenges that appear when applying traditional parameter estimation techniques to differential equation models of microbial communities, and we provide an original, alternative method to those techniques. We show the derivation of our method and how our method avoids the limitations of traditional techniques while including additional benefits. We also provide simulation studies to demonstrate our method's viability, the application of our method to a model of intestinal microbial communities to demonstrate the insights that can be gained from our method, and sample code to give readers the opportunity to apply our method to their own research.