- Evolutionary Biology, Cancer, Evolutionary Computation, Evolutionary Ecology, Biology, Ecology, and 14 moreEvolution, Mathematical Biology, Molecular Biology, Immunology, Spatial Heterogeneity, Tumor microenvironment, Cell Biology, Human-wildlife conflicts, Science Communication, Morphological evolution, Cancer Biology, Modeling, Evolutionary Developmental Biology, and Biomathematicsedit
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The proper structure and function of multi- cellular organisms is a result of interactions of the individual cells in the body, and is controlled and guided by various signals interchanged be- tween the neighbouring cells or sensed from... more
The proper structure and function of multi- cellular organisms is a result of interactions of the individual cells in the body, and is controlled and guided by various signals interchanged be- tween the neighbouring cells or sensed from the cell local microenvironment. We are interested in building a bio-mechanical model that can be used to investigate cell collaborative or compet-
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The increasing rate of antibiotic resistance and slowing discovery of novel antibiotic treatments presents a growing threat to public health. Here, we consider a simple model of evolution in asexually reproducing populations which... more
The increasing rate of antibiotic resistance and slowing discovery of novel antibiotic treatments presents a growing threat to public health. Here, we consider a simple model of evolution in asexually reproducing populations which considers adaptation as a biased random walk on a fitness landscape. This model associates the global properties of the fitness landscape with the algebraic properties of a Markov chain transition matrix and allows us to derive general results on the non-commutativity and irreversibility of natural selection as well as antibiotic cycling strategies. Using this formalism, we analyze 15 empirical fitness landscapes of E. coli under selection by different β-lactam antibiotics and demonstrate that the emergence of resistance to a given antibiotic can be either hindered or promoted by different sequences of drug application. Specifically, we demonstrate that the majority, approximately 70%, of sequential drug treatments with 2-4 drugs promote resistance to the ...
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Histopathologic knowledge that extensive heterogeneity exists between and within tumors has been confirmed and deepened recently by molecular studies. However, the impact of tumor heterogeneity on prognosis and treatment remains as poorly... more
Histopathologic knowledge that extensive heterogeneity exists between and within tumors has been confirmed and deepened recently by molecular studies. However, the impact of tumor heterogeneity on prognosis and treatment remains as poorly understood as ever. Using a hybrid multiscale mathematical model of tumor growth in vascularized tissue, we investigated the selection pressures exerted by spatial and temporal variations in tumor microenvironment and the resulting phenotypic adaptations. A key component of this model is normal and tumor metabolism and its interaction with microenvironmental factors. The metabolic phenotype of tumor cells is plastic, and microenvironmental selection leads to increased tumor glycolysis and decreased pH. Once this phenotype emerges, the tumor dramatically changes its behavior due to acid-mediated invasion, an effect that depends on both variations in the tumor cell phenotypes and their spatial distribution within the tumor. In early stages of growth,...
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Page 1. SINGLE-CELL-BASED MODELS BIOLOGYnnd MEDICINE Alexander RA Anderson Mark AJ Chaplain Katarzyna A. Rejniak Page 2. Page 3. Mathematics and Biosciences in Interaction Managing Editor Wolfgang Alt ...
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Research Interests: Genetics, Applied Mathematics, Computational Biology, Cell Migration, Cytokines, and 20 moreCell Adhesion, Mathematical Modelling, Theoretical biology, Temporal dynamics, Extracellular Matrix, Biological Sciences, Humans, Mathematical Sciences, PARTIAL DIFFERENTIAL EQUATION, Enzyme, Potential Function, Neoplasm Invasiveness, Neoplasms, Biological Process, Mathematical and Computer Modelling, Numerical Analysis and Computational Mathematics, Computer Modelling, Cell Proliferation, Hybrid Model, and Cell Motility
Research Interests: Wound Healing, Extracellular Matrix, Discrete Mathematics, Cell Division, Stochastic processes, and 16 moreBiological Sciences, Mitosis, Numerical Simulation, Humans, Computer Simulation, Capillaries, Random Walk, Mathematical Sciences, Animals, Vascular endothelium, PARTIAL DIFFERENTIAL EQUATION, Endothelial cell, Cell Proliferation, Cell communication, Experimental Data, and Blood Vessel
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Research Interests: Mathematical Biology, Nonlinear dynamics, Multiscale Modelling, Extracellular Matrix, Biological Sciences, and 13 moreHumans, Capillaries, Mathematical Sciences, Animals, Mathematical, Mathematical Model, Mathematical Concepts, Neoplasm Invasiveness, Blood Flow, Neoplasms, Cell Proliferation, Blood Flow Velocity, and Biomechanical Phenomena
Research Interests: Chemical Engineering, Applied Mathematics, Biomedical Engineering, Mathematical Modelling, Humans, and 15 moreComputer Simulation, Endothelial Cells, Reaction-Diffusion Systems, Mathematical, Endothelial cell, Neoplasms, Stromal Cells, Growth rate, Interactive application, Tumor Growth, Antineoplastic Agents, Quantitative Method, Blood Vessel, Vascular Endothelial Growth Factor, and Spatial Model
Research Interests: Electron Microscopy, Fluorescence Microscopy, Biophysical Chemistry, Extracellular Matrix, Biological Sciences, and 11 moreHumans, Computer Simulation, Basement Membrane, Collagen, Computer Model, Physical sciences, Gelatin, Live cell Imaging, CHEMICAL SCIENCES, Experimental Validation, and Cellular automaton
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We study the interface morphology of a 2D simulation of an avascular tumor composed of identical cells growing in an homogeneous healthy tissue matrix (TM), in order to understand the origin of the morphological changes often observed... more
We study the interface morphology of a 2D simulation of an avascular tumor composed of identical cells growing in an homogeneous healthy tissue matrix (TM), in order to understand the origin of the morphological changes often observed during real tumor growth. We use the Glazier–Graner–Hogeweg model, which treats tumor cells as extended, deformable objects, to study the effects of two parameters: a dimensionless diffusion-limitation parameter defined as the ratio of the tumor consumption rate to the substrate transport rate, and the tumor-TM surface tension. We model TM as a nondiffusing field, neglecting the TM pressure and haptotactic repulsion acting on a real growing tumor; thus, our model is appropriate for studying tumors with highly motile cells, e.g., gliomas. We show that the diffusion-limitation parameter determines whether the growing tumor develops a smooth (noninvasive) or fingered (invasive) interface, and that the sensitivity of tumor morphology to tumor-TM surface tension increases with the size of the dimensionless diffusion-limitation parameter. For large diffusion-limitation parameters, we find a transition (missed in previous work) between dendritic structures, produced when tumor-TM surface tension is high, and seaweed-like structures, produced when tumor-TM surface tension is low. This observation leads to a direct analogy between the mathematics and dynamics of tumors and those observed in nonbiological directional solidification. Our results are also consistent with the biological observation that hypoxia promotes invasive growth of tumor cells by inducing higher levels of receptors for scatter factors that weaken cell-cell adhesion and increase cell motility. These findings suggest that tumor morphology may have value in predicting the efficiency of antiangiogenic therapy in individual patients.
Research Interests: Engineering, Physics, Chemistry, Metabolism, Computational Biology, and 23 moreBiology, Cell Adhesion, Hypoxia, Medicine, Multidisciplinary, Extracellular Matrix, Biological Sciences, Motility, Humans, Computer Simulation, Mathematical Sciences, Animals, Deformable Objects, PLoS one, Mathematical Concepts, Neoplasm Invasiveness, Surface Tension, Time Factors, Neoplasms, Three Dimensional, Cell Proliferation, Tumor Growth, and Cell Motility
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Cancer is a complex, multiscale process in which genetic mutations occurring at a subcellular level manifest themselves as functional changes at the cellular and tissue scale. The multiscale nature of cancer requires mathematical modeling... more
Cancer is a complex, multiscale process in which genetic mutations occurring at a subcellular level manifest themselves as functional changes at the cellular and tissue scale. The multiscale nature of cancer requires mathematical modeling approaches that can handle multiple intracellular and extracellular factors acting on different time and space scales. Hybrid models provide a way to integrate both discrete and continuous variables that are used to represent individual cells and concentration or density fields, respectively. Each discrete cell can also be equipped with submodels that drive cell behavior in response to microenvironmental cues. Moreover, the individual cells can interact with one another to form and act as an integrated tissue. Hybrid models form part of a larger class of individual-based models that can naturally connect with tumor cell biology and allow for the integration of multiple interacting variables both intrinsically and extrinsically and are therefore perfectly suited to a systems biology approach to tumor growth. WIREs Syst Biol Med 2011 3 115–125 DOI: 10.1002/wsbm.102For further resources related to this article, please visit the WIREs website
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Cancer is a complex, multiscale process, in which genetic mutations occurring at a subcellular level manifest themselves as functional and morphological changes at the cellular and tissue scale. The importance of interactions between... more
Cancer is a complex, multiscale process, in which genetic mutations occurring at a subcellular level manifest themselves as functional and morphological changes at the cellular and tissue scale. The importance of interactions between tumour cells and their microenvironment is currently of great interest in experimental as well as computational modelling. Both the immediate microenvironment (e.g. cell–cell signalling or cell–matrix interactions) and the extended microenvironment (e.g. nutrient supply or a host tissue structure) are thought to play crucial roles in both tumour progression and suppression. In this paper we focus on tumour invasion, as defined by the emergence of a fingering morphology, which has previously been shown to be dependent upon harsh microenvironmental conditions. Using three different modelling approaches at two different spatial scales we examine the impact of nutrient availability as a driving force for invasion. Specifically we investigate how cell metabolism (the intrinsic rate of nutrient consumption and cell resistance to starvation) influences the growing tumour. We also discuss how dynamical changes in genetic makeup and morphological characteristics, of the tumour population, are driven by extreme changes in nutrient supply during tumour development. The simulation results indicate that aggressive phenotypes produce tumour fingering in poor nutrient, but not rich, microenvironments. The implication of these results is that an invasive outcome appears to be co-dependent upon the evolutionary dynamics of the tumour population driven by the microenvironment.
Research Interests: Genetics, Mathematical Biology, Cell Adhesion, Apoptosis, Extracellular Matrix, and 15 moreBiological Sciences, Humans, Mathematical Sciences, Cell Signalling, Spatial Scale, Biological evolution, Mathematical, Evolutionary Dynamics, Mathematical Concepts, Neoplasm Invasiveness, Nutrient Availability, Computer Modelling, Cell Proliferation, Oxygen Consumption, and Driving force
Research Interests: Chemical Engineering, Applied Mathematics, Biomedical Engineering, Mathematical Modelling, Humans, and 16 moreComputer Simulation, Endothelial Cells, Reaction-Diffusion Systems, Mathematical, Endothelial cell, Neoplasms, Stromal Cells, Growth rate, Interactive application, Tumor Growth, Antineoplastic Agents, Quantitative Method, Blood Vessel, Vascular Endothelial Growth Factor, Spatial Model, and spatial context
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This study investigates the mechanism of action behind the long-term responses (12-16 months) of two BRAF WT melanoma patients to the AKT inhibitor MK-2206 in combination with paclitaxel and carboplatin. Although single agent MK-2206... more
This study investigates the mechanism of action behind the long-term responses (12-16 months) of two BRAF WT melanoma patients to the AKT inhibitor MK-2206 in combination with paclitaxel and carboplatin. Although single agent MK-2206 inhibited phospho-AKT signaling, it did not impact in vitro melanoma growth or survival. The combination of MK-2206 with paclitaxel and carboplatin was cytotoxic in long-term colony formation and 3D spheroid assays, and induced autophagy. Autophagy was initially protective with autophagy inhibitors and deletion of ATG5 found to enhance cytotoxicity. Although prolonged autophagy induction (>6 days) led to caspase-dependent apoptosis, drug resistant clones still emerged. Autophagy inhibition enhanced the cell death response through reactive oxygen species and could be reversed by anti-oxidants. We demonstrate for the first time that AKT inhibition in combination with chemotherapy may have clinical activity in BRAF WT melanoma and show that an autophagy inhibitor may prevent resistance to these drugs.This article is protected by copyright. All rights reserved.
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When searching for hosts, parasitoids are observed to aggregate in response to chemical signalling cues emitted by plants during host feeding. In this paper we model aggregative parasitoid behaviour in a multi-species host-parasitoid... more
When searching for hosts, parasitoids are observed to aggregate in response to chemical signalling cues emitted by plants during host feeding. In this paper we model aggregative parasitoid behaviour in a multi-species host-parasitoid community using a system of reaction-diffusion-chemotaxis equations. The stability properties of the steady-states of the model system are studied using linear stability analysis which highlights the possibility of interesting dynamical behaviour when the chemotactic response is above a certain threshold. We observe quasi-chaotic dynamic heterogeneous spatio-temporal patterns, quasi-stationary heterogeneous patterns and a destabilisation of the steady-states of the system. The generation of heterogeneous spatio-temporal patterns and destabilisation of the steady state are due to parasitoid chemotactic response to hosts. The dynamical behaviour of our system has both mathematical and ecological implications and the concepts of chemotaxis-driven instability and coexistence and ecological change are discussed.
Research Interests: Algorithms, Mathematical Biology, Ecology, Population Dynamics, Mathematical biology (Mathematics), and 21 moreHymenoptera, Biological Sciences, Butterflies, Computer Simulation, Mathematical Sciences, Diffusion, Animals, Reaction-Diffusion Systems, Chaotic Dynamics, Host-parasite interactions, Population Density, Chemotaxis, Feeding Behavior, Mathematical, Steady state, Ecosystem, Brassica, Model System, Larva, Dynamic behaviour of materials, and Linear Stability Analysis
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Research Interests: Electron Microscopy, Fluorescence Microscopy, Biophysical Chemistry, Extracellular Matrix, Biological Sciences, and 11 moreHumans, Computer Simulation, Basement Membrane, Collagen, Computer Model, Physical sciences, Gelatin, Live cell Imaging, CHEMICAL SCIENCES, Experimental Validation, and Cellular automaton
The extracellular matrix profoundly affects cellular response to soluble motogens. In view of this critical aspect of matrix functionality, we have developed a novel assay to quantify chemo-regulated cell migration within biologically... more
The extracellular matrix profoundly affects cellular response to soluble motogens. In view of this critical aspect of matrix functionality, we have developed a novel assay to quantify chemo-regulated cell migration within biologically relevant 3-dimensional matrices. In this “sandwich” assay, target cells are plated at the interface between an upper and lower matrix compartment, either in the presence of an isotropic (uniform) or anisotropic (gradient) spatial distribution of test motogen. Cell migration in response to the different conditions is ascertained by quantifying their subsequent disposition within the upper and lower matrix compartments. The objective of this study has been to compare the motogenic activities of platelet-derived growth factor (PDGF-AB) and transforming growth factor-beta isoforms (TGF-β1, -β2 and -β3) in the sandwich assay and the commonly employed transmembrane assay. As previously reported, dermal fibroblasts exhibited a motogenic response to isotropic and anisotropic distributions of all tested cytokines in the transmembrane assay. In contrast, only PDGF-AB and TGF-β3 were active in the sandwich assay, each eliciting directionally unbiased (symmetrical) migration into the upper and lower type I collagen matrices in response to an isotropic cytokine distribution and a directionally biased response to an anisotropic distribution. TGF-β1 and -β2 were completely devoid of motogenic activity. These results are consistent with the reported differential bioactivities of PDGF and TGF-β3 compared to TGF-β1 and -β2 in animal models of wound healing and suggest that the sandwich assay provides a means of obtaining physiologically relevant data regarding chemo-regulated cell migration.
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Research Interests: Mathematics, Biomedical Engineering, Mathematical Biology, Microcirculation, Drug delivery, and 18 moreExtracellular Matrix, Signal Transduction, Biological Sciences, Cellular mechanotransduction, Humans, Computer Simulation, Endothelial Cells, Mathematical Sciences, Computer Model, Animals, Mathematical Model, Theoretical Models, Endothelial cell, Blood Flow, Neoplasms, Network Flow, Blood Vessel, and Drug treatment
Research Interests: Kinetics, Population Dynamics, Theoretical biology, Temporal dynamics, Biological Sciences, and 11 moreSpatial Heterogeneity, Mathematical Sciences, Animals, Host-parasite interactions, Steady state, Mathematical Model, Theoretical, Ecosystem, Population dynamic, Ordinary Differential Equation, and Hopf Bifurcation
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Research Interests: Genetics, Morphogenesis, Apoptosis, Extracellular Matrix, Biological Sciences, and 16 moreCell line, Humans, Computer Simulation, Mutation, Mathematical Sciences, Computer Model, Case Study, Female, Epithelium, Mammary gland, Very high throughput, Three Dimensional, Simulation Study, Cell Proliferation, In Silico, and parameter space
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In this article, we present a new multiscale mathematical model for solid tumour growth which couples an improved model of tumour invasion with a model of tumour-induced angiogenesis. We perform nonlinear simulations of the ulti-scale... more
In this article, we present a new multiscale mathematical model for solid tumour growth which couples an improved model of tumour invasion with a model of tumour-induced angiogenesis. We perform nonlinear simulations of the ulti-scale model that demonstrate the importance of the coupling between the development and remodeling of the vascular network, the blood flow through the network and the tumour progression. Consistent with clinical observations, the hydrostatic stress generated by tumour cell proliferation shuts down large portions of the vascular network dramatically affecting the flow, the subsequent network remodeling, the delivery of nutrients to the tumour and the subsequent tumour progression. In addition, extracellular matrix degradation by tumour cells is seen to have a dramatic affect on both the development of the vascular network and the growth response of the tumour. In particular, the newly developing vessels tend to encapsulate, rather than penetrate, the tumour and are thus less effective in delivering nutrients.
Research Interests: Mathematical Biology, Nonlinear dynamics, Multiscale Modelling, Extracellular Matrix, Biological Sciences, and 13 moreHumans, Capillaries, Mathematical Sciences, Animals, Mathematical, Mathematical Model, Mathematical Concepts, Neoplasm Invasiveness, Blood Flow, Neoplasms, Cell Proliferation, Blood Flow Velocity, and Biomechanical Phenomena
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Research Interests: Theoretical biology, Extracellular Matrix, Cancer treatment, Biological Sciences, Humans, and 11 moreMathematical Sciences, Phenotype, Evolutionary Dynamics, Mathematical Model, Neoplasm Invasiveness, Neoplasms, Individual Based Modelling, Individual Based Model, Cellular automaton, Cell Motility, and Feed Forward Neural Network
Normal hollow epithelial acini are 3-dimensional culture structures that resemble the architecture and functions of normal breast glands and lobules. This experimental model enables in vitro investigations of genotypic and molecular... more
Normal hollow epithelial acini are 3-dimensional culture structures that resemble the architecture and functions of normal breast glands and lobules. This experimental model enables in vitro investigations of genotypic and molecular abnormalities associated with epithelial cancers. However, the way in which the acinar structure is formed is not yet completely understood. Gaining more information about consecutive stages of acini development—starting from a single cell that gives rise to a cluster of randomly oriented cells, followed by cell differentiation that leads to a layer of polarised cells enclosing the hollow lumen—will provide insight into the transformations of eukaryotic cells that are necessary for their successful arrangement into an epithelium. In this paper, we introduce a two-dimensional single-cell-based model representing the cross section of a typical acinus. Using this model, we investigate mechanisms that lead to the unpolarised cell growth, cell polarisation, stabilisation of the acinar structure and maintenance of the hollow lumen and discuss the sufficient conditions for each stage of acinar formation. In the follow-up paper (Rejniak and Anderson, A computational study of the development of epithelial acini. II. Necessary conditions for structure and lumen stability), we investigate what morphological changes are observable in the growing acini when some assumptions of this model are relaxed.