Dynamics and bifurcations in a simple quasispecies model of tumorigenesis

V. Castillo, J. Tomas Lazaro, J. Sardanyes 

Submitted on 24 Nov 2014

 

Cancer is a complex disease and thus is complicated to model. However, simple models that describe the main processes involved in tumoral dynamics, e.g., competition and mutation, can give us clues about cancer behaviour, at least qualitatively, also allowing us to make predictions. Here we analyze a simplified quasispecies mathematical model given by differential equations describing the time behaviour of tumor cells populations with different levels of genomic instability. We find the equilibrium points, also characterizing their stability and bifurcations focusing on replication and mutation rates. We identify a transcritical bifurcation at increasing mutation rates of the tumor cells population. Such a bifurcation involves an scenario with dominance of healthy cells and impairment of tumor populations. Finally, we characterize the transient times for this scenario, showing that a slight increase beyond the critical mutation rate may be enough to have a fast response towards the desired state (i.e., low tumor populations) during directed mutagenic therapies. 

Link: http://arxiv.org/abs/1411.6531

Replicator Dynamics of of Cancer Stem Cell; Selection in the Presence of Differentiation and Plasticity

Kamran Kaveh, Mohammad Kohandel, Siv Sivaloganathan

(Submitted on 5 Nov 2014)

Stem cells have the potential to produce lineages of non-stem cell populations (differentiated cells) via a ubiquitous hierarchal division scheme. Differentiation of a stem cell into (partially) differentiated cells can happen either symmetrically or asymmetrically. The selection dynamics of a mutant cancer stem cell should be investigated in the light of a stem cell proliferation hierarchy and presence of a non-stem cell population. By constructing a three-compartment Moran-type model composed of normal stem cells, mutant (cancer) stem cells and differentiated cells, we derive the replicator dynamics of stem cell frequencies where asymmetric differentiation and differentiated cell death rates are included in the model. We determine how these new factors change the conditions for a successful mutant invasion and discuss the variation on the steady state fraction of the population as different model parameters are changed. By including the phenotypic plasticity/dedifferentiation, in which a progenitor/differentiated cell can transform back into a cancer stem cell, we show that the effective fitness of mutant stem cells is not only determined by their proliferation and death rates but also according to their dedifferentiation potential. By numerically solving the model we derive the phase diagram of the advantageous and disadvantageous phases of cancer stem cells in the space of proliferation and dedifferentiation potentials. The result shows that at high enough dedifferentiation rates even a previously disadvantageous mutant can take over the population of normal stem cells. This observation has implications in different areas of cancer research including experimental observations that imply metastatic cancer stem cell types might have lower proliferation potential than other stem cell phenotypes while showing much more phenotypic plasticity and can undergo clonal expansion.

link: http://arxiv.org/abs/1411.1399 

Modeling and simulation of a low grade urinary bladder carcinoma

Svetlana Bunimovich-Mendrazitsky, Vladimir Pisarev, Eugene Kashdan

(Submitted on 11 Oct 2013 (v1), last revised 8 Nov 2014 (this version, v3))

In this work, we present a mathematical model of the initiation and progression of a low-grade urinary bladder carcinoma. We simulate the crucial processes involved in tumor growth, such as oxygen diffusion, carcinogen penetration, and angiogenesis, within the framework of the urothelial cell dynamics. The cell dynamics are modeled using the discrete technique of Cellular Automata, while the continuous processes of carcinogen penetration and oxygen diffusion are described by nonlinear diffusion-absorption equations. As the availability of oxygen is necessary for tumor progression, processes of oxygen transport to the tumor growth site seem most important. Our model yields a theoretical insight into the main stages of development and growth of urinary bladder carcinoma with emphasis on two most common types: bladder polyps and carcinoma {\it in situ}. Analysis of histological structure of bladder tumor is important to avoid misdiagnosis and wrong treatment and we expect our model to be a valuable tool in the prediction of tumor grade and progression patterns, based on the exposure to carcinogens and an oxygen dependent expression of genes promoting tumor growth. Our numerical simulations have good qualitative agreement with {\it in vivo} results reported in the corresponding medical literature.

Comments:	The paper has been withdrawn due to the disagreement with the journal
Subjects:	Quantitative Methods (q-bio.QM); Tissues and Organs (q-bio.TO)
Cite as:	arXiv:1310.3301 [q-bio.QM]
	(or arXiv:1310.3301v3 [q-bio.QM] for this version) link: http://arxiv.org/abs/1310.3301 CAN THE AUTHORS ELABORATE ON THE WITHDRAWAL FROM THE JOURNAL?

A pedagogical walkthrough of computational modeling and simulation of Wnt signaling pathway using static causal models in Matlab

Shriprakash Sinha

doi: http://dx.doi.org/10.1101/011064

A tutorial introduction to computational modeling of Wnt signaling pathway in a human colorectal cancer dataset using static Bayesian network models is provided. This work endeavours to expound in detail the simulation study in Matlab along with the code while explaining the concepts related to Bayesian networks. This is done in order to ease the understanding of beginner students and researchers in transition to computational signaling biology, who intend to work in the field of modeling of signaling pathways. The case study is based on the contents of the advance article by Sinha (2014) and takes the reader in a step by step process of how (1) the collection and the transformation of the available biological information from literature is done, (2) the integration of the heterogeneous data and prior biological knowledge in the network is achieved, (3) the simulation study is designed, (4) the hypothesis regarding a biological phenomena is transformed into computational framework, and (5) results and inferences drawn using d-connectivity/separability are reported. It is hoped that the walkthrough will aid biologists understand the design of the computational experiments using causal models. The manuscript finally ends with a programming assignment to help the readers get hands on experience of a perturbation project. Matlab code with dataset is made available under GNU GPL v3 license at google code project on https://code.google.com/p/static-bn-for-wnt-signaling-pathway

link to bioarXiv