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Comments:	The paper has been withdrawn due to the disagreement with the journal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

Stochastic model for computer simulation of the number of cancer cells and lymphocytes in homogeneous sections of cancer tumors

Arnulfo Castellanos-Moreno, Alejandro Castellanos-Jaramillo, Adalberto Corella-Madueño, Sergio Gutiérrez-López, Rodrigo Rosas-Burgos

(Submitted on 14 Oct 2014)

We deal with a small enough tumor section to consider it homogeneous, such that populations of lymphocytes and cancer cells are independent of spatial coordinates. A stochastic model based in one step processes is developed to take into account natural birth and death rates. Other rates are also introduced to consider medical treatment: natural birth rate of lymphocytes and cancer cells; induced death rate of cancer cells due to self-competition, and other ones caused by the activated lymphocytes acting on cancer cells. Additionally, a death rate of cancer cells due to induced apoptosis is considered. Weakness due to the advance of sickness is considered by introducing a lymphocytes death rate proportional to proliferation of cancer cells.
Simulation is developed considering different combinations of the parameters and its values, so that several strategies are taken into account to study the effect of anti-angiogenic drugs as well the self-competition between cancer cells. Immune response, with the presence of a kind of specialized lymphocytes, is introduced such that they appear once cancer cells are detected. Induced apoptosis of cancer cells is introduced to model the action of several drugs under development right now. Besides, the model predicts the cancer relapse even from a very small number of cells. Simulation is done by using Gillespie algorithm.

link

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

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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