Travelling wave solutions of the reaction-diffusion mathematical model of glioblastoma growth: An Abel equation based approach

Tiberiu Harko, M. K. Mak

(Submitted on 2 Sep 2014)

We consider quasi-stationary (travelling wave type) solutions to a nonlinear reaction-diffusion equation with arbitrary, autonomous coefficients, describing the evolution of glioblastomas, aggressive primary brain tumors that are characterized by extensive infiltration into the brain and are highly resistant to treatment. The second order nonlinear equation describing the glioblastoma growth through travelling waves can be reduced to a first order Abel type equation. By using the integrability conditions for the Abel equation several classes of exact travelling wave solutions of the general reaction-diffusion equation that describes glioblastoma growth are obtained, corresponding to different forms of the product of the diffusion and reaction functions. The solutions are obtained by using the Chiellini lemma and the Lemke transformation, respectively, and the corresponding equations represent generalizations of the classical Fisher--Kolmogorov equation. The biological implications of two classes of solutions are also investigated by using both numerical and semi-analytical methods for realistic values of the biological parameters.

link: http://arxiv.org/abs/1409.0605

Computational Screening of Angiogenesis Model Variants Predicts that Differential Chemotaxis Helps Tip Cells Move to the Sprout Tip and Accelerates Sprouting

Margriet M. Palm, Marchien G. Dallinga, Erik van Dijk, Ingeborg Klaassen, Reinier O. Schlingemann, Roeland M.H. Merks

(Submitted on 20 Sep 2014)

Angiogenesis involves the formation of new blood vessels by sprouting or splitting of existing blood vessels. During sprouting, a highly motile type of endothelial cell, called the tip cell, migrates from the blood vessels followed by stalk cells, an endothelial cell type that forms the body of the sprout. In vitro models and computational models can recapitulate much of the phenomenology of angiogenesis in absence of tip and stalk cell differentiation. Therefore it is unclear how the presence of tip cells contributes to angiogenesis. To get more insight into how tip cells contribute to angiogenesis, we extended an existing computational model of vascular network formation based on the cellular Potts model with tip and stalk differentiation, without making a priori assumptions about the specific rules that tip cells follow. We then screened a range of model variants, looking for rules that make tip cells (a) move to the sprout tip, and (b) change the morphology of the angiogenic networks. The screening predicted that if tip cells respond less effectively to an endothelial chemoattractant than stalk cells, they move to the tips of the sprouts, which impacts the morphology of the networks. A comparison of this model prediction with genes expressed differentially in tip and stalk cells revealed that the endothelial chemoattractant Apelin and its receptor APJ may match the model prediction. To test the model prediction we inhibited Apelin signaling in our model and in an in vitro model of angiogenic sprouting, and found that in both cases inhibition of Apelin or of its receptor APJ reduces sprouting. Based on the prediction of the computational model, we propose that the differential expression of Apelin and APJ yields a "self-generated" gradient mechanisms that accelerates the extension of the sprout.

 link: http://arxiv.org/abs/1409.5895

Glucose-lactate metabolic cooperation in cancer: insights from a spatial mathematical model and implications for targeted therapy

Jessica McGillen, Catherine J Kelly, Alicia Martinez-Gonzalez, Natasha K Martin, Eamonn A Gaffney, Philip KMaini, Victor M Perez-Garcia

doi: http://dx.doi.org/10.1101/008839

ABSTRACT

A recent hypothesis has proposed a glucose-lactate metabolic symbiosis between adjacent hypoxic and oxygenated regions of a developing tumour, and proposed a treatment strategy to target this symbiosis. However, in vivo experimental support remains inconclusive. Here we develop a minimal spatial mathematical model of glucose-lactate metabolism to examine, in principle, whether metabolic symbiosis is plausible in human tumours, and to assess the potential impact of inhibiting it. We find that symbiosis is a robust feature of our model system---although on the length scale at which oxygen supply is diffusion-limited, its occurrence requires very high cellular metabolic activity---and that necrosis in the tumour core is reduced in the presence of symbiosis. Upon simulating therapeutic inhibition of lactate uptake, we predict that targeted treatment increases the extent of tissue oxygenation without increasing core necrosis. The oxygenation effect is correlated strongly with the extent of wildtype hypoxia and only weakly with wildtype symbiotic behaviour, and therefore may be promising for radiosensitisation of hypoxic, lactate-consuming tumours even if they do not exhibit a spatially well-defined symbiosis. Finally, we conduct a set of in vitro experiments on the U87 glioblastoma cell line to facilitate preliminary speculation as to where highly malignant tumours might fall in our parameter space, and find that these experiments suggest a weakly symbiotic regime for U87 cells, which raises the new question of what relationship exists between symbiosis---if indeed it occurs in vivo---and tumour malignancy.

link: http://biorxiv.org/content/early/2014/09/04/008839

#biorxiv

The degenerative evolution from multicellularity to unicellularity during cancer

Han Chen, Fangqin Lin, Xionglei He

(Submitted on 14 Aug 2014)

Theoretical reasoning suggests that human cancer may result from knocking down the genetic constraints evolved for maintenance of the metazoan multicellularity, which, however, requires a critical test. Using xenograft-based experimental evolution we characterized for the first time the full life history from initiation to metastasis of a tumor at the genomic and transcriptomic levels, and observed metastasis-driving positive selection for generally loss-of-function mutations on a set of multicellularity-related genes, which is further supported by large-scale exome data of clinical tumor samples. Subsequent expression analysis revealed mainly expression down-regulation of multicellularity-related genes, which form an evolving expression profile approaching that of embryonic stem cells, the cell type with the most characteristics of unicellular life. The theoretical conjecture predicts that genes born at the emergence of metazoan multicellularity tend to be cancer drivers, which we validated using a rigorous phylostratigraphy analysis on the birth rate of genes annotated by Cancer Gene Census. Also, the number of loss-of-function tumor suppressors often predominates over activated oncogenes in a typical tumor of human patients. These data collectively suggest that, different from typical organismal evolution in which gain of new genes is the mainstream, cancer represents a loss-of-function-driven degenerative evolution back to the unicellular ground state. This cancer evolution model may explain the enormous tumoral genetic heterogeneity in the clinic, underlie how distant-organ metastases originate in primary tumors despite distinct environmental requirements, and hold implications for designing effective cancer therapy.

http://arxiv.org/abs/1408.3236

Stress-Induced Mutagenesis and Complex Adaptation

Yoav Ram, Lilach Hadany

doi: http://dx.doi.org/10.1101/007096

 

Abstract:

Because mutations are mostly deleterious, mutation rates should be reduced by natural selection. However, mutations also provide the raw material for adaptation. Therefore, evolutionary theory suggests that the mutation rate must balance between adaptability - the ability to adapt - and adaptedness - the ability to remain adapted. We model an asexual population crossing a fitness valley and analyze the rate of complex adaptation with and without stress-induced mutagenesis - the increase of mutation rates in response to stress or maladaptation. We show that stress-induced mutagenesis increases the rate of complex adaptation without reducing the population mean fitness, thus breaking the evolutionary trade-off between adaptability and adaptedness. Our theoretical results support the hypothesis that stress-induced mutagenesis promotes adaptation and provide quantitative predictions of the rate of complex adaptation with different mutational strategies.

 

Link: http://www.biorxiv.org/content/early/2014/07/21/007096.abstract?%3Fcollection=

 

Keywords: Adaptation, stress, evolution

Not strictly cancer but the topic is very relevant to many of us trying to understand the emergence of invasiveness.

The Role of Migration in the Evolution of Phenotypic Switching

Oana Carja, Robert E Furrow, Marc W Feldman

 

Stochastic switching is an example of phenotypic bet-hedging, where an individual can switch between different phenotypic states in a fluctuating environment. Although the evolution of stochastic switching has been studied when the environment varies temporally, there has been little theoretical work on the evolution of phenotypic switching under both spatially and temporally fluctuating selection pressures. Here we use a population genetic model to explore the interaction of temporal and spatial variation in the evolutionary dynamics of phenotypic switching. We find that spatial variation in selection is important; when selection pressures are similar across space, migration can decrease the rate of switching, but when selection pressures differ spatially, increasing migration between demes can facilitate the evolution of higher rates of switching. These results may help explain the diverse array of non-genetic contributions to phenotypic variability and phenotypic inheritance observed in both wild and experimental populations.

 

Source: bioRxiv

 

Investigating the development of chemotherapeutic drug resistance in cancer: A multiscale computational study

Investigating the development of chemotherapeutic drug resistance in cancer: A multiscale computational study

 By: Gibin G Powathil, Mark AJ Chaplain, Maciej Swat

Chemotherapy is one of the most important therapeutic options used to treat human cancers, either alone or in combination with radiation therapy and surgery. Recent studies have indicated that intra-tumoural heterogeneity has a significant role in driving resistance to chemotherapy in many human malignancies. Multiple factors including the internal cell-cycle dynamics and the external microenvironement contribute to the intra-tumoural heterogeneity. In this paper we present a hybrid, multiscale, individual-based mathematical model, incorporating internal cell-cycle dynamics and changes in oxygen concentration, to study the effects of delivery of several different chemotherapeutic drugs on the heterogeneous subpopulations of cancer cells with varying cell-cycle dynamics. The computational simulation results from the multiscale model are in good agreement with available experimental data and support the hypothesis that slow-cycling sub-populations of tumour cells within a growing tumour mass can induce drug resistance to chemotherapy and thus the use of conventional chemotherapy may actually result in the emergence of dominant, therapy-resistant, slow-cycling subpopulations of tumour cells. Our results indicate that the appearance of this chemotherapeutic resistance is mainly due to the inability of the administered drug to target all cancer cells irrespective of the stage in the cell-cycle they are in i.e. most chemotherapeutic drugs target cells in a particular phase/phases of the cell-cycle, and hence always spare some cancer cells that are not in the targeted cell-cycle phase/phases. The results also suggest that this cell-cycle-mediated drug resistance may be overcome by using multiple doses of cell-cycle, phase-specific chemotherapy that targets cells in all phases and its appropriate sequencing and scheduling.   

http://arxiv.org/abs/1407.0865