1
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Baldwin SA, Haugh JM. Semi-autonomous wound invasion via matrix-deposited, haptotactic cues. J Theor Biol 2023; 568:111506. [PMID: 37094713 PMCID: PMC10393182 DOI: 10.1016/j.jtbi.2023.111506] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/20/2022] [Revised: 04/18/2023] [Accepted: 04/19/2023] [Indexed: 04/26/2023]
Abstract
Proper wound healing relies on invasion of fibroblasts via directed migration. While the related experimental and mathematical modeling literature has mainly focused on cell migration directed by soluble cues (chemotaxis), there is ample evidence that fibroblast migration is also directed by insoluble, matrix-bound cues (haptotaxis). Furthermore, numerous studies indicate that fibronectin (FN), a haptotactic ligand for fibroblasts, is present and dynamic in the provisional matrix throughout the proliferative phase of wound healing. In the present work, we show the plausibility of a hypothesis that fibroblasts themselves form and maintain haptotactic gradients in a semi-autonomous fashion. As a precursor to this, we examine the positive control scenario where FN is pre-deposited in the wound matrix, and fibroblasts maintain haptotaxis by removing FN at an appropriate rate. After developing conceptual and quantitative understanding of this scenario, we consider two cases in which fibroblasts activate the latent form of a matrix-loaded cytokine, TGFβ, which upregulates the fibroblasts' own secretion of FN. In the first of these, the latent cytokine is pre-patterned and released by the fibroblasts. In the second, fibroblasts in the wound produce the latent TGFβ, with the presence of the wound providing the only instruction. In all cases, wound invasion is more effective than a negative control model with haptotaxis disabled; however, there is a trade-off between the degree of fibroblast autonomy and the rate of invasion.
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Affiliation(s)
- Scott A Baldwin
- Department of Chemical and Biomolecular Engineering, North Carolina State University, Campus Box 7905, Raleigh, NC 27695, USA
| | - Jason M Haugh
- Department of Chemical and Biomolecular Engineering, North Carolina State University, Campus Box 7905, Raleigh, NC 27695, USA.
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2
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Lewinsohn MA, Bedford T, Müller NF, Feder AF. State-dependent evolutionary models reveal modes of solid tumour growth. Nat Ecol Evol 2023; 7:581-596. [PMID: 36894662 PMCID: PMC10089931 DOI: 10.1038/s41559-023-02000-4] [Citation(s) in RCA: 16] [Impact Index Per Article: 16.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2022] [Accepted: 01/26/2023] [Indexed: 03/11/2023]
Abstract
Spatial properties of tumour growth have profound implications for cancer progression, therapeutic resistance and metastasis. Yet, how spatial position governs tumour cell division remains difficult to evaluate in clinical tumours. Here, we demonstrate that faster division on the tumour periphery leaves characteristic genetic patterns, which become evident when a phylogenetic tree is reconstructed from spatially sampled cells. Namely, rapidly dividing peripheral lineages branch more extensively and acquire more mutations than slower-dividing centre lineages. We develop a Bayesian state-dependent evolutionary phylodynamic model (SDevo) that quantifies these patterns to infer the differential division rates between peripheral and central cells. We demonstrate that this approach accurately infers spatially varying birth rates of simulated tumours across a range of growth conditions and sampling strategies. We then show that SDevo outperforms state-of-the-art, non-cancer multi-state phylodynamic methods that ignore differential sequence evolution. Finally, we apply SDevo to single-time-point, multi-region sequencing data from clinical hepatocellular carcinomas and find evidence of a three- to six-times-higher division rate on the tumour edge. With the increasing availability of high-resolution, multi-region sequencing, we anticipate that SDevo will be useful in interrogating spatial growth restrictions and could be extended to model non-spatial factors that influence tumour progression.
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Affiliation(s)
- Maya A Lewinsohn
- Department of Genome Sciences, University of Washington, Seattle, WA, USA.
- Vaccine and Infectious Disease Division, Fred Hutchinson Cancer Center, Seattle, WA, USA.
| | - Trevor Bedford
- Department of Genome Sciences, University of Washington, Seattle, WA, USA
- Vaccine and Infectious Disease Division, Fred Hutchinson Cancer Center, Seattle, WA, USA
- Howard Hughes Medical Institute, Seattle, WA, USA
| | - Nicola F Müller
- Vaccine and Infectious Disease Division, Fred Hutchinson Cancer Center, Seattle, WA, USA.
| | - Alison F Feder
- Department of Genome Sciences, University of Washington, Seattle, WA, USA.
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3
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Kaykanat SI, Uguz AK. The role of acoustofluidics and microbubble dynamics for therapeutic applications and drug delivery. BIOMICROFLUIDICS 2023; 17:021502. [PMID: 37153864 PMCID: PMC10162024 DOI: 10.1063/5.0130769] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/14/2022] [Accepted: 03/18/2023] [Indexed: 05/10/2023]
Abstract
Targeted drug delivery is proposed to reduce the toxic effects of conventional therapeutic methods. For that purpose, nanoparticles are loaded with drugs called nanocarriers and directed toward a specific site. However, biological barriers challenge the nanocarriers to convey the drug to the target site effectively. Different targeting strategies and nanoparticle designs are used to overcome these barriers. Ultrasound is a new, safe, and non-invasive drug targeting method, especially when combined with microbubbles. Microbubbles oscillate under the effect of the ultrasound, which increases the permeability of endothelium, hence, the drug uptake to the target site. Consequently, this new technique reduces the dose of the drug and avoids its side effects. This review aims to describe the biological barriers and the targeting types with the critical features of acoustically driven microbubbles focusing on biomedical applications. The theoretical part covers the historical developments in microbubble models for different conditions: microbubbles in an incompressible and compressible medium and bubbles encapsulated by a shell. The current state and the possible future directions are discussed.
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Affiliation(s)
- S. I. Kaykanat
- Department of Chemical Engineering, Boğaziçi University, 34342 Bebek, Istanbul, Türkiye
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4
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Gonçalves IG, Garcia-Aznar JM. Extracellular matrix density regulates the formation of tumour spheroids through cell migration. PLoS Comput Biol 2021; 17:e1008764. [PMID: 33635856 PMCID: PMC7968691 DOI: 10.1371/journal.pcbi.1008764] [Citation(s) in RCA: 19] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/06/2020] [Revised: 03/17/2021] [Accepted: 02/02/2021] [Indexed: 11/18/2022] Open
Abstract
In this work, we show how the mechanical properties of the cellular microenvironment modulate the growth of tumour spheroids. Based on the composition of the extracellular matrix, its stiffness and architecture can significantly vary, subsequently influencing cell movement and tumour growth. However, it is still unclear exactly how both of these processes are regulated by the matrix composition. Here, we present a centre-based computational model that describes how collagen density, which modulates the steric hindrance properties of the matrix, governs individual cell migration and, consequently, leads to the formation of multicellular clusters of varying size. The model was calibrated using previously published experimental data, replicating a set of experiments in which cells were seeded in collagen matrices of different collagen densities, hence producing distinct mechanical properties. At an initial stage, we tracked individual cell trajectories and speeds. Subsequently, the formation of multicellular clusters was also analysed by quantifying their size. Overall, the results showed that our model could accurately replicate what was previously seen experimentally. Specifically, we showed that cells seeded in matrices with low collagen density tended to migrate more. Accordingly, cells strayed away from their original cluster and thus promoted the formation of small structures. In contrast, we also showed that high collagen densities hindered cell migration and produced multicellular clusters with increased volume. In conclusion, this model not only establishes a relation between matrix density and individual cell migration but also showcases how migration, or its inhibition, modulates tumour growth.
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Affiliation(s)
- Inês G. Gonçalves
- Multiscale in Mechanical and Biological Engineering, Aragon Institute of Engineering Research, Mechanical Engineering Department, University of Zaragoza, Zaragoza, Spain
| | - Jose Manuel Garcia-Aznar
- Multiscale in Mechanical and Biological Engineering, Aragon Institute of Engineering Research, Mechanical Engineering Department, University of Zaragoza, Zaragoza, Spain
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5
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Cortesi M, Liverani C, Mercatali L, Ibrahim T, Giordano E. An in-silico study of cancer cell survival and spatial distribution within a 3D microenvironment. Sci Rep 2020; 10:12976. [PMID: 32737377 PMCID: PMC7395763 DOI: 10.1038/s41598-020-69862-7] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/24/2020] [Accepted: 07/21/2020] [Indexed: 12/11/2022] Open
Abstract
3D cell cultures are in-vitro models representing a significant improvement with respect to traditional monolayers. Their diffusion and applicability, however, are hampered by the complexity of 3D systems, that add new physical variables for experimental analyses. In order to account for these additional features and improve the study of 3D cultures, we here present SALSA (ScAffoLd SimulAtor), a general purpose computational tool that can simulate the behavior of a population of cells cultured in a 3D scaffold. This software allows for the complete customization of both the polymeric template structure and the cell population behavior and characteristics. In the following the technical description of SALSA will be presented, together with its validation and an example of how it could be used to optimize the experimental analysis of two breast cancer cell lines cultured in collagen scaffolds. This work contributes to the growing field of integrated in-silico/in-vitro analysis of biological systems, which have great potential for the study of complex cell population behaviours and could lead to improve and facilitate the effectiveness and diffusion of 3D cell culture models.
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Affiliation(s)
- Marilisa Cortesi
- Department of Electrical, Electronic and Information Engineering "G. Marconi", University of Bologna, Cesena, FC, Italy.
| | - Chiara Liverani
- Osteoncology and Rare Tumors Center, Istituto Scientifico Romagnolo Per Lo Studio E La Cura Dei Tumori (IRST) IRCCS, Meldola, FC, Italy
| | - Laura Mercatali
- Osteoncology and Rare Tumors Center, Istituto Scientifico Romagnolo Per Lo Studio E La Cura Dei Tumori (IRST) IRCCS, Meldola, FC, Italy
| | - Toni Ibrahim
- Osteoncology and Rare Tumors Center, Istituto Scientifico Romagnolo Per Lo Studio E La Cura Dei Tumori (IRST) IRCCS, Meldola, FC, Italy
| | - Emanuele Giordano
- Department of Electrical, Electronic and Information Engineering "G. Marconi", University of Bologna, Cesena, FC, Italy.,Advanced Research Center On Electronic Systems (ARCES), University of Bologna, Bologna, BO, Italy.,BioEngLab, Health Science and Technology, Interdepartmental Center for Industrial Research (HST-CIRI), University of Bologna, Ozzano Emilia, BO, Italy
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6
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Abstract
Tumor immunology is undergoing a renaissance due to the recent profound clinical successes of tumor immunotherapy. These advances have coincided with an exponential growth in the development of -omics technologies. Armed with these technologies and their associated computational and modeling toolsets, systems biologists have turned their attention to tumor immunology in an effort to understand the precise nature and consequences of interactions between tumors and the immune system. Such interactions are inherently multivariate, spanning multiple time and size scales, cell types, and organ systems, rendering systems biology approaches particularly amenable to their interrogation. While in its infancy, the field of 'Cancer Systems Immunology' has already influenced our understanding of tumor immunology and immunotherapy. As the field matures, studies will move beyond descriptive characterizations toward functional investigations of the emergent behavior that govern tumor-immune responses. Thus, Cancer Systems Immunology holds incredible promise to advance our ability to fight this disease.
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Affiliation(s)
| | - Edgar G Engleman
- Department of Pathology, Stanford University School of MedicineStanfordUnited States
- Division of Immunology and Rheumatology, Department of Medicine, Stanford University School of MedicineStanfordUnited States
- Stanford Cancer Institute, Stanford UniversityStanfordUnited States
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7
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Letort G, Montagud A, Stoll G, Heiland R, Barillot E, Macklin P, Zinovyev A, Calzone L. PhysiBoSS: a multi-scale agent-based modelling framework integrating physical dimension and cell signalling. Bioinformatics 2020; 35:1188-1196. [PMID: 30169736 PMCID: PMC6449758 DOI: 10.1093/bioinformatics/bty766] [Citation(s) in RCA: 55] [Impact Index Per Article: 13.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2018] [Revised: 07/28/2018] [Accepted: 08/30/2018] [Indexed: 01/22/2023] Open
Abstract
MOTIVATION Due to the complexity and heterogeneity of multicellular biological systems, mathematical models that take into account cell signalling, cell population behaviour and the extracellular environment are particularly helpful. We present PhysiBoSS, an open source software which combines intracellular signalling using Boolean modelling (MaBoSS) and multicellular behaviour using agent-based modelling (PhysiCell). RESULTS PhysiBoSS provides a flexible and computationally efficient framework to explore the effect of environmental and genetic alterations of individual cells at the population level, bridging the critical gap from single-cell genotype to single-cell phenotype and emergent multicellular behaviour. PhysiBoSS thus becomes very useful when studying heterogeneous population response to treatment, mutation effects, different modes of invasion or isomorphic morphogenesis events. To concretely illustrate a potential use of PhysiBoSS, we studied heterogeneous cell fate decisions in response to TNF treatment. We explored the effect of different treatments and the behaviour of several resistant mutants. We highlighted the importance of spatial information on the population dynamics by considering the effect of competition for resources like oxygen. AVAILABILITY AND IMPLEMENTATION PhysiBoSS is freely available on GitHub (https://github.com/sysbio-curie/PhysiBoSS), with a Docker image (https://hub.docker.com/r/gletort/physiboss/). It is distributed as open source under the BSD 3-clause license. SUPPLEMENTARY INFORMATION Supplementary data are available at Bioinformatics online.
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Affiliation(s)
- Gaelle Letort
- Institut Curie, PSL Research University, Paris, France.,INSERM, U900, Paris, France.,CBIO-Centre for Computational Biology, MINES ParisTech, PSL Research University, Paris, France
| | - Arnau Montagud
- Institut Curie, PSL Research University, Paris, France.,INSERM, U900, Paris, France.,CBIO-Centre for Computational Biology, MINES ParisTech, PSL Research University, Paris, France
| | - Gautier Stoll
- Université Paris Descartes/Paris V, Sorbonne Paris Cité, Paris, France.,Gustave Roussy Cancer Campus, Villejuif, France.,INSERM, U1138, Paris, France.,Equipe 11 Labellisée par la Ligue Nationale Contre le Cancer, Centre de Recherche des Cordeliers, Paris, France
| | - Randy Heiland
- Intelligent Systems Engineering, Indiana University, Bloomington, IN, USA
| | - Emmanuel Barillot
- Institut Curie, PSL Research University, Paris, France.,INSERM, U900, Paris, France.,CBIO-Centre for Computational Biology, MINES ParisTech, PSL Research University, Paris, France
| | - Paul Macklin
- Intelligent Systems Engineering, Indiana University, Bloomington, IN, USA
| | - Andrei Zinovyev
- Institut Curie, PSL Research University, Paris, France.,INSERM, U900, Paris, France.,CBIO-Centre for Computational Biology, MINES ParisTech, PSL Research University, Paris, France
| | - Laurence Calzone
- Institut Curie, PSL Research University, Paris, France.,INSERM, U900, Paris, France.,CBIO-Centre for Computational Biology, MINES ParisTech, PSL Research University, Paris, France
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8
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Cassani S, Olson SD. A Hybrid Model of Cartilage Regeneration Capturing the Interactions Between Cellular Dynamics and Porosity. Bull Math Biol 2020; 82:18. [PMID: 31970523 DOI: 10.1007/s11538-020-00695-1] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/27/2019] [Accepted: 12/27/2019] [Indexed: 12/31/2022]
Abstract
To accelerate the development of strategies for cartilage tissue engineering, models are necessary to investigate the interactions between cellular dynamics and the local microenvironment. We use a discrete framework to capture the individual behavior of cells, modeling experiments where cells are seeded in a porous scaffold or hydrogel and over the time course of a month, the scaffold slowly degrades while cells divide and synthesize extracellular matrix constituents. The movement of cells and the ability to proliferate is a function of the local porosity, defined as the volume fraction of fluid in the surrounding region. A phenomenological approach is used to capture a continuous profile for the degrading scaffold and accumulating matrix, which will then change the local porosity throughout the construct. We parameterize the model by first matching total cell counts in the construct to chondrocytes seeded in a polyglycolic acid scaffold (Freed et al. in Biotechnol Bioeng 43:597-604, 1994). We investigate the influence of initial scaffold porosity on the total cell count and spatial profiles of cell and ECM in the construct. Cell counts were higher at day 30 in scaffolds of lower initial porosity, and similar cell counts were obtained using different models of scaffold degradation and matrix accumulation (either uniform or cell-specific). Using this modeling framework, we study the interplay between a phenomenological representation of scaffold architecture and porosity as well as the potential continuous application of growth factors. We determine parameter regimes where large cellular aggregates occur, which can hinder matrix accumulation and cellular proliferation. The developed modeling framework can easily be extended and can be used to identify optimal scaffolds and culture conditions that lead to a desired distribution of extracellular matrix and cell counts throughout the construct.
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Affiliation(s)
- Simone Cassani
- Department of Mathematics, University at Buffalo, The State University of New York, 244 Mathematics Building, Buffalo, NY, 14260, USA
| | - Sarah D Olson
- Department of Mathematical Sciences, Worcester Polytechnic Institute, 100 Institute Rd, Worcester, MA, 01609, USA.
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9
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10
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Peter Cummings – a pillar in the field of statistical mechanics and molecular simulation. Mol Phys 2019. [DOI: 10.1080/00268976.2019.1684664] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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11
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Mathematical Models of Cancer Cell Plasticity. JOURNAL OF ONCOLOGY 2019; 2019:2403483. [PMID: 31814825 PMCID: PMC6877945 DOI: 10.1155/2019/2403483] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/02/2019] [Revised: 08/20/2019] [Accepted: 09/17/2019] [Indexed: 01/29/2023]
Abstract
Quantitative modelling is increasingly important in cancer research, helping to integrate myriad diverse experimental data into coherent pictures of the disease and able to discriminate between competing hypotheses or suggest specific experimental lines of enquiry and new approaches to therapy. Here, we review a diverse set of mathematical models of cancer cell plasticity (a process in which, through genetic and epigenetic changes, cancer cells survive in hostile environments and migrate to more favourable environments, respectively), tumour growth, and invasion. Quantitative models can help to elucidate the complex biological mechanisms of cancer cell plasticity. In this review, we discuss models of plasticity, tumour progression, and metastasis under three broadly conceived mathematical modelling techniques: discrete, continuum, and hybrid, each with advantages and disadvantages. An emerging theme from the predictions of many of these models is that cell escape from the tumour microenvironment (TME) is encouraged by a combination of physiological stress locally (e.g., hypoxia), external stresses (e.g., the presence of immune cells), and interactions with the extracellular matrix. We also discuss the value of mathematical modelling for understanding cancer more generally.
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12
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Chen H, Cai Y, Chen Q, Li Z. Multiscale modeling of solid stress and tumor cell invasion in response to dynamic mechanical microenvironment. Biomech Model Mechanobiol 2019; 19:577-590. [PMID: 31571083 DOI: 10.1007/s10237-019-01231-4] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2019] [Accepted: 09/23/2019] [Indexed: 12/16/2022]
Abstract
Mathematical models can provide a quantitatively sophisticated description of tumor cell (TC) behaviors under mechanical microenvironment and help us better understand the role of specific biophysical factors based on their influences on the TC behaviors. To this end, we propose an off-lattice cell-based multiscale mathematical model to describe the dynamic growth-induced solid stress during tumor progression and investigate the influence of the mechanical microenvironment on TC invasion. At the cellular level, cell-cell and cell-matrix interactive forces depend on the mechanical properties of the cells and the cancer-associated fibroblasts in the stroma, respectively. The constitutive relationship between the interactive forces and cell migrations obeys the Hooke's law and damping effects. At the tissue level, the integrated growth-induced forces caused by proliferating cells within the simulation region are balanced by the external forces applied by the surrounding host tissues. Then, the cell movements are calculated according to the Newton's second law of motion, and the morphology of TC invasion is updated. The simulation results reveal the continuous changes of the macroscopic mechanical forces due to the interactions among the structural components and the microscopic environmental factors. Moreover, the simulation results demonstrate the adverse effect of the stiffness of tumor tissue on tumor growth and invasion. A decrease in the stiffness of tumor and matrix can promote TCs to proliferate at a much faster rate and invade into the surrounding healthy tissue more easily, whereas an increase in the stiffness can lead to an aggressive morphology of tumor invasion. We envision that the proposed model can be served as a quantitative theoretical platform to study the underlying biophysical role of the mechanical microenvironmental factors during tumor invasion and metastasis.
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Affiliation(s)
- H Chen
- School of Biological Science and Medical Engineering, Southeast University, Nanjing, 210096, China.,School of Chemistry, Physics and Mechanical Engineering, Queensland University of Technology, Brisbane, QLD, 4001, Australia
| | - Y Cai
- School of Biological Science and Medical Engineering, Southeast University, Nanjing, 210096, China
| | - Q Chen
- School of Biological Science and Medical Engineering, Southeast University, Nanjing, 210096, China
| | - Z Li
- School of Biological Science and Medical Engineering, Southeast University, Nanjing, 210096, China. .,School of Chemistry, Physics and Mechanical Engineering, Queensland University of Technology, Brisbane, QLD, 4001, Australia.
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13
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Matsiaka OM, Baker RE, Simpson MJ. Continuum descriptions of spatial spreading for heterogeneous cell populations: Theory and experiment. J Theor Biol 2019; 482:109997. [PMID: 31491498 DOI: 10.1016/j.jtbi.2019.109997] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2019] [Revised: 08/16/2019] [Accepted: 09/03/2019] [Indexed: 11/19/2022]
Abstract
Variability in cell populations is frequently observed in both in vitro and in vivo settings. Intrinsic differences within populations of cells, such as differences in cell sizes or differences in rates of cell motility, can be present even within a population of cells from the same cell line. We refer to this variability as cell heterogeneity. Mathematical models of cell migration, for example, in the context of tumour growth and metastatic invasion, often account for both undirected (random) migration and directed migration that is mediated by cell-to-cell contacts and cell-to-cell adhesion. A key feature of standard models is that they often assume that the population is composed of identical cells with constant properties. This leads to relatively simple single-species homogeneous models that neglect the role of heterogeneity. In this work, we use a continuum modelling approach to explore the role of heterogeneity in spatial spreading of cell populations. We employ a three-species heterogeneous model of cell motility that explicitly incorporates different types of experimentally-motivated heterogeneity in cell sizes: (i) monotonically decreasing; (ii) uniform; (iii) non-monotonic; and (iv) monotonically increasing distributions of cell size. Comparing the density profiles generated by the three-species heterogeneous model with density profiles predicted by a more standard single-species homogeneous model reveals that when we are dealing with monotonically decreasing and uniform distributions a simple and computationally efficient single-species homogeneous model can be remarkably accurate in describing the evolution of a heterogeneous cell population. In contrast, we find that the simpler single-species homogeneous model performs relatively poorly when applied to non-monotonic and monotonically increasing distributions of cell sizes. Additional results for heterogeneity in parameters describing both undirected and directed cell migration are also considered, and we find that similar results apply.
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Affiliation(s)
- Oleksii M Matsiaka
- School of Mathematical Sciences, Queensland University of Technology (QUT) Brisbane, Queensland, Australia
| | - Ruth E Baker
- Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Woodstock Road, Oxford, United Kingdom
| | - Matthew J Simpson
- School of Mathematical Sciences, Queensland University of Technology (QUT) Brisbane, Queensland, Australia.
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14
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Piretto E, Delitala M, Kim PS, Frascoli F. Effects of mutations and immunogenicity on outcomes of anti-cancer therapies for secondary lesions. Math Biosci 2019; 315:108238. [PMID: 31401294 DOI: 10.1016/j.mbs.2019.108238] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/06/2019] [Revised: 08/02/2019] [Accepted: 08/03/2019] [Indexed: 12/30/2022]
Abstract
Cancer development is driven by mutations and selective forces, including the action of the immune system and interspecific competition. When administered to patients, anti-cancer therapies affect the development and dynamics of tumours, possibly with various degrees of resistance due to immunoediting and microenvironment. Tumours are able to express a variety of competing phenotypes with different attributes and thus respond differently to various anti-cancer therapies. In this paper, a mathematical framework incorporating a system of delay differential equations for the immune system activation cycle and an agent-based approach for tumour-immune interaction is presented. The focus is on those metastatic, secondary solid lesions that are still undetected and non-vascularised. By using available experimental data, we analyse the effects of combination therapies on these lesions and investigate the role of mutations on the rates of success of common treatments. Findings show that mutations, growth properties and immunoediting influence therapies' outcomes in nonlinear and complex ways, affecting cancer lesion morphologies, phenotypical compositions and overall proliferation patterns. Cascade effects on final outcomes for secondary lesions are also investigated, showing that actions on primary lesions could sometimes result in unexpected clearances of secondary tumours. This outcome is strongly dependent on the clonal composition of the primary and secondary masses and is shown to allow, in some cases, the control of the disease for years.
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Affiliation(s)
- Elena Piretto
- Department of Mathematical Sciences, Politecnico di Torino, Turin, Italy; Department of Mathematics, Universitá di Torino, Turin, Italy; Department of Mathematics, Faculty of Science, Engineering and Technology, Swinburne University of Technology, Hawthorn, Victoria, Australia
| | - Marcello Delitala
- Department of Mathematical Sciences, Politecnico di Torino, Turin, Italy
| | - Peter S Kim
- School of Mathematics and Statistics, University of Sydney, Sydney, New South Wales, Australia
| | - Federico Frascoli
- Department of Mathematics, Faculty of Science, Engineering and Technology, Swinburne University of Technology, Hawthorn, Victoria, Australia.
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15
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Oraiopoulou ME, Tampakaki M, Tzamali E, Tamiolakis T, Makatounakis V, Vakis AF, Zacharakis G, Sakkalis V, Papamatheakis J. A 3D tumor spheroid model for the T98G Glioblastoma cell line phenotypic characterization. Tissue Cell 2019; 59:39-43. [PMID: 31383287 DOI: 10.1016/j.tice.2019.05.007] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/21/2018] [Revised: 05/23/2019] [Accepted: 05/23/2019] [Indexed: 01/25/2023]
Abstract
Major Glioblastoma's hallmarks include proliferation, invasion and heterogeneity. Biological 3D tumor spheroid models can serve as intermediate systems between traditional 2D cell culture and complex in vivo models. Tumor spheroids have been shown to more accurately reproduce the spatial organization and microenvironmental factors of in vivo micro-tumors, such as relevant gradients of nutrients and other molecular agents, while they maintain cell-to-cell and cell-to-matrix interactions. In vitro 3D assays are useful to monitor these properties. Here, we test the suitability of the well-known T98 G Glioblastoma cell line in such a 3D assay. The doubling time and death rate parameters of T98 G are estimated, as well as their spheroidal growth-expansion curves with and without the presence of basement membrane substrate. The T98 G invasive profile is characterized by collective morphology and proliferation-associated invasion. We show that the T98 G secondary GB cell line exhibits both invasive and proliferative capabilities in 3D and thus, can serve as control cell line for the 3D in vitro study of primary GB cell cultures.
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Affiliation(s)
- Mariam-Eleni Oraiopoulou
- School of Medicine, University of Crete, Heraklion, Crete, Greece; Institute of Computer Science, Foundation for Research and Technology-Hellas, Heraklion, Crete, Greece
| | - Maria Tampakaki
- School of Medicine, University of Crete, Heraklion, Crete, Greece; Institute of Computer Science, Foundation for Research and Technology-Hellas, Heraklion, Crete, Greece
| | - Eleftheria Tzamali
- Institute of Computer Science, Foundation for Research and Technology-Hellas, Heraklion, Crete, Greece
| | - Theodoros Tamiolakis
- School of Medicine, University of Crete, Heraklion, Crete, Greece; Institute of Computer Science, Foundation for Research and Technology-Hellas, Heraklion, Crete, Greece
| | - Venediktos Makatounakis
- Institute of Molecular Biology and Biotechnology, Foundation for Research and Technology-Hellas, Heraklion, Crete, Greece
| | - Antonios F Vakis
- School of Medicine, University of Crete, Heraklion, Crete, Greece; Neurosurgery Clinic, University General Hospital of Heraklion, Heraklion, Greece
| | - Giannis Zacharakis
- Institute of Electronic Structure and Laser, Foundation for Research and Technology-Hellas, Heraklion, Crete, Greece
| | - Vangelis Sakkalis
- Institute of Computer Science, Foundation for Research and Technology-Hellas, Heraklion, Crete, Greece
| | - Joseph Papamatheakis
- Institute of Molecular Biology and Biotechnology, Foundation for Research and Technology-Hellas, Heraklion, Crete, Greece; Department of Biology, University of Crete, Heraklion, Crete, Greece.
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16
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Oraiopoulou ME, Tzamali E, Tzedakis G, Liapis E, Zacharakis G, Vakis A, Papamatheakis J, Sakkalis V. Integrating in vitro experiments with in silico approaches for Glioblastoma invasion: the role of cell-to-cell adhesion heterogeneity. Sci Rep 2018; 8:16200. [PMID: 30385804 PMCID: PMC6212459 DOI: 10.1038/s41598-018-34521-5] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2018] [Accepted: 10/01/2018] [Indexed: 01/08/2023] Open
Abstract
Glioblastoma cells adopt migration strategies to invade into the brain parenchyma ranging from individual to collective mechanisms, whose role and dynamics are not yet fully understood. In this work, we explore Glioblastoma heterogeneity and recapitulate its invasive patterns both in vitro, by utilizing primary cells along with the U87MG cell line, and in silico, by adopting discrete, individual cell-based mathematics. Glioblastoma cells are cultured three-dimensionally in an ECM-like substrate. The primary Glioblastoma spheroids adopt a novel cohesive pattern, mimicking perivascular invasion in the brain, while the U87MG adopt a typical, starburst invasive pattern under the same experimental setup. Mathematically, we focus on the role of the intrinsic heterogeneity with respect to cell-to-cell adhesion. Our proposed mathematical approach mimics the invasive morphologies observed in vitro and predicts the dynamics of tumour expansion. The role of the proliferation and migration is also explored showing that their effect on tumour morphology is different per cell type. The proposed model suggests that allowing cell-to-cell adhesive heterogeneity within the tumour population is sufficient for variable invasive morphologies to emerge which remain originally undetectable by conventional imaging, indicating that exploration in pathological samples is needed to improve our understanding and reveal potential patient-specific therapeutic targets.
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Affiliation(s)
- M-E Oraiopoulou
- Department of Medicine, University of Crete, Heraklion, Crete, Greece
- Computational Bio-Medicine Laboratory, Institute of Computer Science, Foundation for Research and Technology-Hellas, Heraklion, Crete, Greece
| | - E Tzamali
- Computational Bio-Medicine Laboratory, Institute of Computer Science, Foundation for Research and Technology-Hellas, Heraklion, Crete, Greece
| | - G Tzedakis
- Computational Bio-Medicine Laboratory, Institute of Computer Science, Foundation for Research and Technology-Hellas, Heraklion, Crete, Greece
| | - E Liapis
- Institute of Electronic Structure and Laser, Foundation for Research and Technology-Hellas, Heraklion, Crete, Greece
- Helmholtz Zentrum München, German Research Center for Environmental Health (GmbH), Neuherberg, Germany
| | - G Zacharakis
- Institute of Electronic Structure and Laser, Foundation for Research and Technology-Hellas, Heraklion, Crete, Greece
| | - A Vakis
- Department of Medicine, University of Crete, Heraklion, Crete, Greece
- Neurosurgery Clinic, University General Hospital of Heraklion, Crete, Greece
| | - J Papamatheakis
- Gene Expression Laboratory, Institute of Molecular Biology and Biotechnology, Foundation for Research and Technology-Hellas, Heraklion, Crete, Greece
- Department of Biology, University of Crete, Heraklion, Crete, Greece
| | - V Sakkalis
- Computational Bio-Medicine Laboratory, Institute of Computer Science, Foundation for Research and Technology-Hellas, Heraklion, Crete, Greece.
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17
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Al-Saedi HM, Archer AJ, Ward J. Dynamical density-functional-theory-based modeling of tissue dynamics: Application to tumor growth. Phys Rev E 2018; 98:022407. [PMID: 30253518 DOI: 10.1103/physreve.98.022407] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2018] [Indexed: 06/08/2023]
Abstract
We present a theoretical framework based on an extension of dynamical density-functional theory (DDFT) for describing the structure and dynamics of cells in living tissues and tumors. DDFT is a microscopic statistical mechanical theory for the time evolution of the density distribution of interacting many-particle systems. The theory accounts for cell-pair interactions, different cell types, phenotypes, and cell birth and death processes (including cell division), to provide a biophysically consistent description of processes bridging across the scales, including describing the tissue structure down to the level of the individual cells. Analysis of the model is presented for single-species and two-species cases, the latter aimed at describing competition between tumor and healthy cells. In suitable parameter regimes, model results are consistent with biological observations. Of particular note, divergent tumor growth behavior, mirroring metastatic and benign growth characteristics, are shown to be dependent on the cell-pair-interaction parameters.
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Affiliation(s)
- Hayder M Al-Saedi
- Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, United Kingdom
- Department of Mathematical Sciences, Baghdad University, Baghdad, Iraq
| | - Andrew J Archer
- Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, United Kingdom
| | - John Ward
- Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, United Kingdom
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18
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Glioma growth modeling based on the effect of vital nutrients and metabolic products. Med Biol Eng Comput 2018. [PMID: 29516334 DOI: 10.1007/s11517-018-1809-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
Abstract
Glioma brain tumors exhibit considerably aggressive behavior leading to high mortality rates. Mathematical modeling of tumor growth aims to explore the interactions between glioma cells and tissue microenvironment, which affect tumor evolution. Leveraging this concept, we present a three-dimensional model of glioma spatio-temporal evolution based on existing continuum approaches, yet incorporating novel factors of the phenomenon. The proposed model involves the interactions between different tumor cell phenotypes and their microenvironment, investigating how tumor growth is affected by complex biological exchanges. It focuses on the separate and combined effect of vital nutrients and cellular wastes on tumor expansion, leading to the formation of cell populations with different metabolic, proliferative, and diffusive profiles. Several simulations were performed on a virtual and a real glioma, using combinations of proliferation and diffusion rates for different evolution times. The model results were validated on a glioma model available in the literature and a real case of tumor progression. The experimental observations indicate that our model estimates quite satisfactorily the expansion of each region and the overall tumor growth. Based on the individual results, the proposed model may provide an important research tool for patient-specific simulation of different tumor evolution scenarios and reliable estimation of glioma evolution. Graphical Abstract Outline of the mathematical model functionality and application to glioma growth with indicative results.
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19
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Soleimani S, Shamsi M, Ghazani MA, Modarres HP, Valente KP, Saghafian M, Ashani MM, Akbari M, Sanati-Nezhad A. Translational models of tumor angiogenesis: A nexus of in silico and in vitro models. Biotechnol Adv 2018; 36:880-893. [PMID: 29378235 DOI: 10.1016/j.biotechadv.2018.01.013] [Citation(s) in RCA: 30] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2017] [Revised: 01/10/2018] [Accepted: 01/20/2018] [Indexed: 12/13/2022]
Abstract
Emerging evidence shows that endothelial cells are not only the building blocks of vascular networks that enable oxygen and nutrient delivery throughout a tissue but also serve as a rich resource of angiocrine factors. Endothelial cells play key roles in determining cancer progression and response to anti-cancer drugs. Furthermore, the endothelium-specific deposition of extracellular matrix is a key modulator of the availability of angiocrine factors to both stromal and cancer cells. Considering tumor vascular network as a decisive factor in cancer pathogenesis and treatment response, these networks need to be an inseparable component of cancer models. Both computational and in vitro experimental models have been extensively developed to model tumor-endothelium interactions. While informative, they have been developed in different communities and do not yet represent a comprehensive platform. In this review, we overview the necessity of incorporating vascular networks for both in vitro and in silico cancer models and discuss recent progresses and challenges of in vitro experimental microfluidic cancer vasculature-on-chip systems and their in silico counterparts. We further highlight how these two approaches can merge together with the aim of presenting a predictive combinatorial platform for studying cancer pathogenesis and testing the efficacy of single or multi-drug therapeutics for cancer treatment.
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Affiliation(s)
- Shirin Soleimani
- BioMEMS and Bioinspired Microfluidic Laboratory, Department of Mechanical and Manufacturing Engineering, University of Calgary, Calgary, AB T2N 1N4, Canada; Center for BioEngineering Research and Education, University of Calgary, Calgary, AB T2N 1N4, Canada
| | - Milad Shamsi
- BioMEMS and Bioinspired Microfluidic Laboratory, Department of Mechanical and Manufacturing Engineering, University of Calgary, Calgary, AB T2N 1N4, Canada; Center for BioEngineering Research and Education, University of Calgary, Calgary, AB T2N 1N4, Canada; Department of Mechanical Engineering, Isfahan University of Technology, Isfahan 8415683111, Iran
| | - Mehran Akbarpour Ghazani
- Department of Mechanical Engineering, Isfahan University of Technology, Isfahan 8415683111, Iran
| | - Hassan Pezeshgi Modarres
- BioMEMS and Bioinspired Microfluidic Laboratory, Department of Mechanical and Manufacturing Engineering, University of Calgary, Calgary, AB T2N 1N4, Canada
| | - Karolina Papera Valente
- Laboratory for Innovations in MicroEngineering (LiME), Department of Mechanical Engineering, University of Victoria, Victoria, BC V8P 5C2, Canada
| | - Mohsen Saghafian
- Department of Mechanical Engineering, Isfahan University of Technology, Isfahan 8415683111, Iran
| | - Mehdi Mohammadi Ashani
- BioMEMS and Bioinspired Microfluidic Laboratory, Department of Mechanical and Manufacturing Engineering, University of Calgary, Calgary, AB T2N 1N4, Canada
| | - Mohsen Akbari
- Laboratory for Innovations in MicroEngineering (LiME), Department of Mechanical Engineering, University of Victoria, Victoria, BC V8P 5C2, Canada; Division of Medical Sciences, University of Victoria, Victoria, BC V8P 5C2, Canada
| | - Amir Sanati-Nezhad
- BioMEMS and Bioinspired Microfluidic Laboratory, Department of Mechanical and Manufacturing Engineering, University of Calgary, Calgary, AB T2N 1N4, Canada; Center for BioEngineering Research and Education, University of Calgary, Calgary, AB T2N 1N4, Canada.
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20
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Klank RL, Rosenfeld SS, Odde DJ. A Brownian dynamics tumor progression simulator with application to glioblastoma. CONVERGENT SCIENCE PHYSICAL ONCOLOGY 2018; 4:015001. [PMID: 30627438 PMCID: PMC6322960 DOI: 10.1088/2057-1739/aa9e6e] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023]
Abstract
Tumor progression modeling offers the potential to predict tumor-spreading behavior to improve prognostic accuracy and guide therapy development. Common simulation methods include continuous reaction-diffusion (RD) approaches that capture mean spatio-temporal tumor spreading behavior and discrete agent-based (AB) approaches which capture individual cell events such as proliferation or migration. The brain cancer glioblastoma (GBM) is especially appropriate for such proliferation-migration modeling approaches because tumor cells seldom metastasize outside of the central nervous system and cells are both highly proliferative and migratory. In glioblastoma research, current RD estimates of proliferation and migration parameters are derived from computed tomography or magnetic resonance images. However, these estimates of glioblastoma cell migration rates, modeled as a diffusion coefficient, are approximately 1-2 orders of magnitude larger than single-cell measurements in animal models of this disease. To identify possible sources for this discrepancy, we evaluated the fundamental RD simulation assumptions that cells are point-like structures that can overlap. To give cells physical size (~10 μm), we used a Brownian dynamics approach that simulates individual single-cell diffusive migration, growth, and proliferation activity via a gridless, off-lattice, AB method where cells can be prohibited from overlapping each other. We found that for realistic single-cell parameter growth and migration rates, a non-overlapping model gives rise to a jammed configuration in the center of the tumor and a biased outward diffusion of cells in the tumor periphery, creating a quasi-ballistic advancing tumor front. The simulations demonstrate that a fast-progressing tumor can result from minimally diffusive cells, but at a rate that is still dependent on single-cell diffusive migration rates. Thus, modeling with the assumption of physically-grounded volume conservation can account for the apparent discrepancy between estimated and measured diffusion of GBM cells and provide a new theoretical framework that naturally links single-cell growth and migration dynamics to tumor-level progression.
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Affiliation(s)
- Rebecca L Klank
- Department of Biomedical Engineering, University of Minnesota, Minneapolis, MN, United States of America
| | - Steven S Rosenfeld
- Burkhardt Brain Tumor Center, Department of Cancer Biology, Cleveland Clinic, Cleveland, OH, United States of America
| | - David J Odde
- Department of Biomedical Engineering, University of Minnesota, Minneapolis, MN, United States of America
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21
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Smith CA, Yates CA. Spatially extended hybrid methods: a review. J R Soc Interface 2018; 15:20170931. [PMID: 29491179 PMCID: PMC5832735 DOI: 10.1098/rsif.2017.0931] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2017] [Accepted: 02/08/2018] [Indexed: 12/13/2022] Open
Abstract
Many biological and physical systems exhibit behaviour at multiple spatial, temporal or population scales. Multiscale processes provide challenges when they are to be simulated using numerical techniques. While coarser methods such as partial differential equations are typically fast to simulate, they lack the individual-level detail that may be required in regions of low concentration or small spatial scale. However, to simulate at such an individual level throughout a domain and in regions where concentrations are high can be computationally expensive. Spatially coupled hybrid methods provide a bridge, allowing for multiple representations of the same species in one spatial domain by partitioning space into distinct modelling subdomains. Over the past 20 years, such hybrid methods have risen to prominence, leading to what is now a very active research area across multiple disciplines including chemistry, physics and mathematics. There are three main motivations for undertaking this review. Firstly, we have collated a large number of spatially extended hybrid methods and presented them in a single coherent document, while comparing and contrasting them, so that anyone who requires a multiscale hybrid method will be able to find the most appropriate one for their need. Secondly, we have provided canonical examples with algorithms and accompanying code, serving to demonstrate how these types of methods work in practice. Finally, we have presented papers that employ these methods on real biological and physical problems, demonstrating their utility. We also consider some open research questions in the area of hybrid method development and the future directions for the field.
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Affiliation(s)
- Cameron A Smith
- Centre for Mathematical Biology, Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, UK
| | - Christian A Yates
- Centre for Mathematical Biology, Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, UK
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22
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Discrete and Continuum Approximations for Collective Cell Migration in a Scratch Assay with Cell Size Dynamics. Bull Math Biol 2018; 80:738-757. [DOI: 10.1007/s11538-018-0398-2] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/09/2017] [Accepted: 01/19/2018] [Indexed: 10/18/2022]
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23
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Nargis NN, Aldredge RC, Guy RD. The influence of soluble fragments of extracellular matrix (ECM) on tumor growth and morphology. Math Biosci 2017; 296:1-16. [PMID: 29208360 DOI: 10.1016/j.mbs.2017.11.014] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2016] [Revised: 11/22/2017] [Accepted: 11/30/2017] [Indexed: 01/27/2023]
Abstract
A major challenge in matrix-metalloproteinase (MMP) target validation and MMP-inhibitor-drug development for anti-cancer clinical trials is to better understand their complex roles (often competing with each other) in tumor progression. While there is extensive research on the growth-promoting effects of MMPs, the growth-inhibiting effects of MMPs has not been investigated thoroughly. So we develop a continuum model of tumor growth and invasion including chemotaxis and haptotaxis in order to examine the complex interaction between the tumor and its host microenvironment and to explore the inhibiting influence of the gradients of soluble fragments of extracellular matrix (ECM) density on tumor growth and morphology. Previously, it was shown both computationally (in one spatial dimension) and experimentally that the chemotactic pull due to soluble ECM gradients is anti-invasive, contrary to the traditional view of the role of chemotaxis in malignant invasion [1]. With two-dimensional numerical simulation and using a level set based tumor-host interface capturing method, we examine the effects of chemotaxis on the progression and morphology of a tumor growing in nutrient-rich and nutrient-poor microenvironments which was not investigated before. In particular we examine how the geometry of the growing tumor is affected when placed in different environments. We also investigate the effects of varying ECM degradation rate, the production rate of matrix degrading enzymes (MDE), and the conversion of ECM into soluble ECM. We find that chemotaxis due to ECM-fragment gradients strongly influences tumor growth and morphology, and that the instabilities caused by tumor cell proliferation and haptotactic movements can be prevented if chemotaxis is sufficiently strong. The influence of chemotaxis and the above factors on tumor growth and morphology are found to be more prominent in nutrient-poor environments than in nutrient-rich environments. So we extend our investigations of these antinvasive chemotactic influences by examining the effects of cell-cell and cell-ECM adhesion and low proliferation rate for tumors growing in low-nutrient environments. We find that as the extent of chemotaxis increases, the effects of adhesion on tumor growth and shape become negligible. Under conditions of low cell mitosis, chemotaxis may cause the tumor to shrink, as the extent of chemotaxis increases. Both stable and unstable tumor shrinkage are predicted by our model. Unexpectedly, in some cases chemotaxis may contribute toward developing instability where haptotaxis alone induces stable growth.
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Affiliation(s)
- Nurun N Nargis
- Department of Mechanical and Aerospace Engineering, University of California, Davis, CA 95616, USA
| | - Ralph C Aldredge
- Department of Mechanical and Aerospace Engineering, University of California, Davis, CA 95616, USA.
| | - Robert D Guy
- Department of Mathematics, University of California, Davis, CA 95616, USA
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24
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Frascoli F, Flood E, Kim PS. A model of the effects of cancer cell motility and cellular adhesion properties on tumour-immune dynamics. MATHEMATICAL MEDICINE AND BIOLOGY-A JOURNAL OF THE IMA 2017; 34:215-240. [PMID: 27094601 DOI: 10.1093/imammb/dqw004] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2015] [Accepted: 01/18/2016] [Indexed: 02/07/2023]
Abstract
We present a three-dimensional model simulating the dynamics of an anti-cancer T-cell response against a small, avascular, early-stage tumour. Interactions at the tumour site are accounted for using an agent-based model (ABM), while immune cell dynamics in the lymph node are modelled as a system of delay differential equations (DDEs). We combine these separate approaches into a two-compartment hybrid ABM-DDE system to capture the T-cell response against the tumour. In the ABM at the tumour site, movement of tumour cells is modelled using effective physical forces with a specific focus on cell-to-cell adhesion properties and varying levels of tumour cell motility, thus taking into account the ability of cancer cells to spread and form clusters. We consider the effectiveness of the immune response over a range of parameters pertaining to tumour cell motility, cell-to-cell adhesion strength and growth rate. We also investigate the dependence of outcomes on the distribution of tumour cells. Low tumour cell motility is generally a good indicator for successful tumour eradication before relapse, while high motility leads, almost invariably, to relapse and tumour escape. In general, the effect of cell-to-cell adhesion on prognosis is dependent on the level of tumour cell motility, with an often unpredictable cross influence between adhesion and motility, which can lead to counterintuitive effects. In terms of overall tumour shape and structure, the spatial distribution of cancer cells in clusters of various sizes has shown to be strongly related to the likelihood of extinction.
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Affiliation(s)
- Federico Frascoli
- Faculty of Science, Engineering and Technology, Department of Mathematics, Swinburne University of Technology, Melbourne, Victoria, Australia
| | - Emelie Flood
- School of Applied Sciences, RMIT University, Melbourne, Victoria, Australia
| | - Peter S Kim
- School of Mathematics and Statistics, University of Sydney, New South Wales, Australia
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25
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Matsiaka OM, Penington CJ, Baker RE, Simpson MJ. Continuum approximations for lattice-free multi-species models of collective cell migration. J Theor Biol 2017; 422:1-11. [PMID: 28400108 DOI: 10.1016/j.jtbi.2017.04.009] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/05/2016] [Revised: 03/22/2017] [Accepted: 04/07/2017] [Indexed: 11/25/2022]
Abstract
Cell migration within tissues involves the interaction of many cells from distinct subpopulations. In this work, we present a discrete model of collective cell migration where the motion of individual cells is driven by random forces, short range repulsion forces to mimic crowding, and longer range attraction forces to mimic adhesion. This discrete model can be used to simulate a population of cells that is composed of K ≥ 1 distinct subpopulations. To analyse the discrete model we formulate a hierarchy of moment equations that describe the spatial evolution of the density of agents, pairs of agents, triplets of agents, and so forth. To solve the hierarchy of moment equations we introduce two forms of closure: (i) the mean field approximation, which effectively assumes that the distributions of individual agents are independent; and (ii) a moment dynamics description that is based on the Kirkwood superposition approximation. The moment dynamics description provides an approximate way of incorporating spatial patterns, such as agent clustering, into the continuum description. Comparing the performance of the two continuum descriptions confirms that both perform well when adhesive forces are sufficiently weak. In contrast, the moment dynamics description outperforms the mean field model when adhesive forces are sufficiently large. This is a first attempt to provide an accurate continuum description of a lattice-free, multi-species model of collective cell migration.
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Affiliation(s)
- Oleksii M Matsiaka
- School of Mathematical Sciences, Queensland University of Technology (QUT) Brisbane, Queensland, Australia
| | - Catherine J Penington
- School of Mathematical Sciences, Queensland University of Technology (QUT) Brisbane, Queensland, Australia
| | - Ruth E Baker
- Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Woodstock Road, Oxford, United Kingdom
| | - Matthew J Simpson
- School of Mathematical Sciences, Queensland University of Technology (QUT) Brisbane, Queensland, Australia.
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26
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Matsushita K. Cell-alignment patterns in the collective migration of cells with polarized adhesion. Phys Rev E 2017; 95:032415. [PMID: 28415314 DOI: 10.1103/physreve.95.032415] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/07/2016] [Indexed: 06/07/2023]
Abstract
Dictyostelium discoideum (Dd) utilizes inhomogeneities in the distribution of cell-cell adhesion molecules on cell membranes for collective cell migration. A simple example of an inhomogeneity is a front-side (leading-edge) polarization in the distribution at the early streaming stage. Experiments have shown that the polarized cell-cell adhesion induces side-by-side contact between cells [Beug et al., Nature (London) 274, 445 (1978)NATUAS0028-083610.1038/274445a0]. This result is counterintuitive, as one would expect cells to align front to front in contact with each other on the basis of front-side polarization. In this work, we theoretically examine whether front-side polarization induces side-by-side contact in collective cell migration. We construct a model for expressing cells with this polarization based on the two-dimensional cellular Potts model. By a numerical simulation with this model, we find cell-cell alignment wherein cells form lateral arrays with side-by-side contacts as observed in the experiments.
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27
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Ahmadzadeh H, Webster MR, Behera R, Jimenez Valencia AM, Wirtz D, Weeraratna AT, Shenoy VB. Modeling the two-way feedback between contractility and matrix realignment reveals a nonlinear mode of cancer cell invasion. Proc Natl Acad Sci U S A 2017; 114:E1617-E1626. [PMID: 28196892 PMCID: PMC5338523 DOI: 10.1073/pnas.1617037114] [Citation(s) in RCA: 109] [Impact Index Per Article: 15.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022] Open
Abstract
Cancer cell invasion from primary tumors is mediated by a complex interplay between cellular adhesions, actomyosin-driven contractility, and the physical characteristics of the extracellular matrix (ECM). Here, we incorporate a mechanochemical free-energy-based approach to elucidate how the two-way feedback loop between cell contractility (induced by the activity of chemomechanical interactions such as Ca2+ and Rho signaling pathways) and matrix fiber realignment and strain stiffening enables the cells to polarize and develop contractile forces to break free from the tumor spheroids and invade into the ECM. Interestingly, through this computational model, we are able to identify a critical stiffness that is required by the matrix to break intercellular adhesions and initiate cell invasion. Also, by considering the kinetics of the cell movement, our model predicts a biphasic invasiveness with respect to the stiffness of the matrix. These predictions are validated by analyzing the invasion of melanoma cells in collagen matrices of varying concentration. Our model also predicts a positive correlation between the elongated morphology of the invading cells and the alignment of fibers in the matrix, suggesting that cell polarization is directly proportional to the stiffness and alignment of the matrix. In contrast, cells in nonfibrous matrices are found to be rounded and not polarized, underscoring the key role played by the nonlinear mechanics of fibrous matrices. Importantly, our model shows that mechanical principles mediated by the contractility of the cells and the nonlinearity of the ECM behavior play a crucial role in determining the phenotype of the cell invasion.
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Affiliation(s)
- Hossein Ahmadzadeh
- Department of Materials Science and Engineering, School of Engineering and Applied Science, University of Pennsylvania, Philadelphia, PA 19104
| | - Marie R Webster
- Tumor Microenvironment and Metastasis Program, The Wistar Institute, Philadelphia, PA 19104
| | - Reeti Behera
- Tumor Microenvironment and Metastasis Program, The Wistar Institute, Philadelphia, PA 19104
| | - Angela M Jimenez Valencia
- Department of Chemical and Biomolecular Engineering, The Johns Hopkins University, Baltimore, MD 21218
- Physical Sciences-Oncology Center, The Johns Hopkins University, Baltimore, MD 21218
- Institute for NanoBioTechnology, The Johns Hopkins University, Baltimore, MD 21218
| | - Denis Wirtz
- Department of Chemical and Biomolecular Engineering, The Johns Hopkins University, Baltimore, MD 21218
- Physical Sciences-Oncology Center, The Johns Hopkins University, Baltimore, MD 21218
- Institute for NanoBioTechnology, The Johns Hopkins University, Baltimore, MD 21218
- Department of Oncology, The Johns Hopkins School of Medicine, Baltimore, MD 21218
- Department of Pathology, The Johns Hopkins School of Medicine, Baltimore, MD 21218
| | - Ashani T Weeraratna
- Tumor Microenvironment and Metastasis Program, The Wistar Institute, Philadelphia, PA 19104
| | - Vivek B Shenoy
- Department of Materials Science and Engineering, School of Engineering and Applied Science, University of Pennsylvania, Philadelphia, PA 19104;
- Department of Bioengineering, School of Engineering and Applied Science, University of Pennsylvania, Philadelphia, PA 19104
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28
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Sundstrom A, Bar-Sagi D, Mishra B. Simulating Heterogeneous Tumor Cell Populations. PLoS One 2016; 11:e0168984. [PMID: 28030620 PMCID: PMC5193460 DOI: 10.1371/journal.pone.0168984] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/07/2015] [Accepted: 12/09/2016] [Indexed: 12/12/2022] Open
Abstract
Certain tumor phenomena, like metabolic heterogeneity and local stable regions of chronic hypoxia, signify a tumor's resistance to therapy. Although recent research has shed light on the intracellular mechanisms of cancer metabolic reprogramming, little is known about how tumors become metabolically heterogeneous or chronically hypoxic, namely the initial conditions and spatiotemporal dynamics that drive these cell population conditions. To study these aspects, we developed a minimal, spatially-resolved simulation framework for modeling tissue-scale mixed populations of cells based on diffusible particles the cells consume and release, the concentrations of which determine their behavior in arbitrarily complex ways, and on stochastic reproduction. We simulate cell populations that self-sort to facilitate metabolic symbiosis, that grow according to tumor-stroma signaling patterns, and that give rise to stable local regions of chronic hypoxia near blood vessels. We raise two novel questions in the context of these results: (1) How will two metabolically symbiotic cell subpopulations self-sort in the presence of glucose, oxygen, and lactate gradients? We observe a robust pattern of alternating striations. (2) What is the proper time scale to observe stable local regions of chronic hypoxia? We observe the stability is a function of the balance of three factors related to O2-diffusion rate, local vessel release rate, and viable and hypoxic tumor cell consumption rate. We anticipate our simulation framework will help researchers design better experiments and generate novel hypotheses to better understand dynamic, emergent whole-tumor behavior.
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Affiliation(s)
- Andrew Sundstrom
- Department of Pharmacology and Systems Therapeutics, Icahn School of Medicine at Mount Sinai, New York, NY, United States of America
- Department of Computer Science, Courant Institute of Mathematical Sciences, New York, NY, United States of America
| | - Dafna Bar-Sagi
- Department of Biochemistry and Molecular Pharmacology, NYU School of Medicine, New York, NY, United States of America
| | - Bud Mishra
- Department of Computer Science, Courant Institute of Mathematical Sciences, New York, NY, United States of America
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29
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Dallavalle M, Lugli F, Rapino S, Zerbetto F. "Active" drops as phantom models for living cells: a mesoscopic particle-based approach. SOFT MATTER 2016; 12:3538-3544. [PMID: 26890581 DOI: 10.1039/c5sm02686e] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Drops and biological cells share some morphological features and visco-elastic properties. The modelling of drops by mesoscopic non-atomistic models has been carried out to a high degree of success in recent years. We extend such treatment and discuss a simple, drop-like model to describe the interactions of the outer layer of cells with the surfaces of materials. Cells are treated as active mechanical objects that are able to generate adhesion forces. They appear with their true size and are made of "parcels of fluids" or beads. The beads are described by (very) few quantities/parameters related to fundamental chemical forces such as hydrophilicity and lipophilicity that represent an average of the properties of a patch of material or an area of the cell(s) surface. The investigation of adhesion dynamics, motion of individual cells, and the collective behavior of clusters of cells on materials is possible. In the simulations, the drops become active soft matter objects and different from regular droplets they do not fuse when in contact, their trajectories are not Brownian, and they can be forced "to secrete" molecules, to name some of the properties targeted by the modeling. The behavior that emerges from the simulations allows ascribing some cell properties to their mechanics, which are related to their biological features.
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Affiliation(s)
- Marco Dallavalle
- Dipartimento di Chimica "G. Ciamician", Università di Bologna, V. F. Selmi 2, 40126, Bologna, Italia.
| | - Francesca Lugli
- Dipartimento di Chimica "G. Ciamician", Università di Bologna, V. F. Selmi 2, 40126, Bologna, Italia.
| | - Stefania Rapino
- Dipartimento di Chimica "G. Ciamician", Università di Bologna, V. F. Selmi 2, 40126, Bologna, Italia.
| | - Francesco Zerbetto
- Dipartimento di Chimica "G. Ciamician", Università di Bologna, V. F. Selmi 2, 40126, Bologna, Italia.
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Kennedy RC, Ropella GE, Hunt CA. A cell-centered, agent-based framework that enables flexible environment granularities. Theor Biol Med Model 2016; 13:4. [PMID: 26839017 PMCID: PMC4736144 DOI: 10.1186/s12976-016-0030-9] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2015] [Accepted: 01/20/2016] [Indexed: 11/25/2022] Open
Abstract
BACKGROUND Mechanistic explanations of cell-level phenomena typically adopt an observer perspective. Explanations developed from a cell's perspective may offer new insights. Agent-based models lend themselves to model from an individual perspective, and existing agent-based models generally utilize a regular lattice-based environment. A framework which utilizes a cell's perspective in an off-lattice environment could improve the overall understanding of biological phenomena. RESULTS We present an agent-based, discrete event framework, with a demonstrative focus on biomimetic agents. The framework was first developed in 2-dimensions and then extended, with a subset of behaviors, to 3-dimensions. The framework is expected to facilitate studies of more complex biological phenomena through exploitation of a dynamic Delaunay and Voronoi off-lattice environment. We used the framework to model biological cells and to specifically demonstrate basic biological cell behaviors in two- and three-dimensional space. Potential use cases are highlighted, suggesting the utility of the framework in various scenarios. CONCLUSIONS The framework presented in this manuscript expands on existing cell- and agent-centered methods by offering a new perspective in an off-lattice environment. As the demand for biomimetic models grows, the demand for new methods, such as the presented Delaunay and Voronoi framework, is expected to increase.
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Affiliation(s)
- Ryan C Kennedy
- Department of Bioengineering and Therapeutic Sciences, University of California, San Francisco, CA, USA
| | | | - C Anthony Hunt
- Department of Bioengineering and Therapeutic Sciences, University of California, San Francisco, CA, USA.
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Tzedakis G, Tzamali E, Marias K, Sakkalis V. The Importance of Neighborhood Scheme Selection in Agent-based Tumor Growth Modeling. Cancer Inform 2015; 14:67-81. [PMID: 26396490 PMCID: PMC4562677 DOI: 10.4137/cin.s19343] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2015] [Revised: 05/20/2015] [Accepted: 05/21/2015] [Indexed: 11/05/2022] Open
Abstract
Modeling tumor growth has proven a very challenging problem, mainly due to the fact that tumors are highly complex systems that involve dynamic interactions spanning multiple scales both in time and space. The desire to describe interactions in various scales has given rise to modeling approaches that use both continuous and discrete variables, known as hybrid approaches. This work refers to a hybrid model on a 2D square lattice focusing on cell movement dynamics as they play an important role in tumor morphology, invasion and metastasis and are considered as indicators for the stage of malignancy used for early prognosis and effective treatment. Considering various distributions of the microenvironment, we explore how Neumann vs. Moore neighborhood schemes affects tumor growth and morphology. The results indicate that the importance of neighborhood selection is critical under specific conditions that include i) increased hapto/chemo-tactic coefficient, ii) a rugged microenvironment and iii) ECM degradation.
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Affiliation(s)
- Georgios Tzedakis
- Computational BioMedicine Laboratory, Institute of Computer Science, Foundation for Research and Technology-Hellas, Heraklion, Greece
| | - Eleftheria Tzamali
- Computational BioMedicine Laboratory, Institute of Computer Science, Foundation for Research and Technology-Hellas, Heraklion, Greece
| | - Kostas Marias
- Computational BioMedicine Laboratory, Institute of Computer Science, Foundation for Research and Technology-Hellas, Heraklion, Greece
| | - Vangelis Sakkalis
- Computational BioMedicine Laboratory, Institute of Computer Science, Foundation for Research and Technology-Hellas, Heraklion, Greece
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Middleton AM, Fleck C, Grima R. A continuum approximation to an off-lattice individual-cell based model of cell migration and adhesion. J Theor Biol 2014; 359:220-32. [PMID: 24972155 DOI: 10.1016/j.jtbi.2014.06.011] [Citation(s) in RCA: 52] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2013] [Revised: 06/05/2014] [Accepted: 06/10/2014] [Indexed: 11/24/2022]
Abstract
Cell-cell adhesion plays a key role in the collective migration of cells and in determining correlations in the relative cell positions and velocities. Recently, it was demonstrated that off-lattice individual cell based models (IBMs) can accurately capture the correlations observed experimentally in a migrating cell population. However, IBMs are often computationally expensive and difficult to analyse mathematically. Traditional continuum-based models, in contrast, are amenable to mathematical analysis and are computationally less demanding, but typically correspond to a mean-field approximation of cell migration and so ignore cell-cell correlations. In this work, we address this problem by using an off-lattice IBM to derive a continuum approximation which does take into account correlations. We furthermore show that a mean-field approximation of the off-lattice IBM leads to a single partial integro-differential equation of the same form as proposed by Sherratt and co-workers to model cell adhesion. The latter is found to be only effective at approximating the ensemble averaged cell number density when mechanical interactions between cells are weak. In contrast, the predictions of our novel continuum model for the time-evolution of the ensemble cell number density distribution and of the density-density correlation function are in close agreement with those obtained from the IBM for a wide range of mechanical interaction strengths. In particular, we observe 'front-like' propagation of cells in simulations using both our IBM and our continuum model, but not in the continuum model simulations obtained using the mean-field approximation.
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Affiliation(s)
- Alistair M Middleton
- University of Heidelberg, Im Neuenheimer Feld 267, 69120 Heidelberg, Germany; Center for Biological Systems Analysis, University of Freiburg, Habsburgerstr. 49, 79104 Freiburg, Germany
| | - Christian Fleck
- Laboratory for Systems and Synthetic Biology, Dreijenplein 10, 6703HB Wageningen, The Netherlands
| | - Ramon Grima
- SynthSys and School of Biological Sciences, University of Edinburgh, EH9 3JR Edinburgh, UK.
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Bloom AB, Zaman MH. Influence of the microenvironment on cell fate determination and migration. Physiol Genomics 2014; 46:309-14. [PMID: 24619520 DOI: 10.1152/physiolgenomics.00170.2013] [Citation(s) in RCA: 46] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023] Open
Abstract
Several critical cell functions are influenced not only by internal cellular machinery but also by external mechanical and biochemical cues from the surrounding microenvironment. Slight changes to the microenvironment can result in dramatic changes to the cell's phenotype; for example, a change in the nutrients or pH of a tumor microenvironment can result in increased tumor metastasis. While cellular fate and the regulators of cell fate have been studied in detail for several decades now, our understanding of the extracellular regulators remains qualitative and far from comprehensive. In this review, we discuss the microenvironment influence on cell fate in terms of adhesion, migration, and differentiation and focus on both developments in experimental and computation tools to analyze cellular fate.
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Affiliation(s)
- Alexander B Bloom
- Department of Molecular Biology, Cell Biology, and Biochemistry, Boston University, Boston, Massachusetts; and
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35
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Gallaher J, Anderson ARA. Evolution of intratumoral phenotypic heterogeneity: the role of trait inheritance. Interface Focus 2014; 3:20130016. [PMID: 24511380 DOI: 10.1098/rsfs.2013.0016] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Abstract
A tumour is a heterogeneous population of cells that competes for limited resources. In the clinic, we typically probe the tumour by biopsy, and then characterize it by the dominant genetic clone. But genotypes are only the first link in the chain of hierarchical events that leads to a specific cell phenotype. The relationship between genotype and phenotype is not simple, and the so-called genotype to phenotype map is poorly understood. Many genotypes can produce the same phenotype, so genetic heterogeneity may not translate directly to phenotypic heterogeneity. We therefore choose to focus on the functional endpoint, the phenotype as defined by a collection of cellular traits (e.g. proliferative and migratory ability). Here, we will examine how phenotypic heterogeneity evolves in space and time and how the way in which phenotypes are inherited will drive this evolution. A tumour can be thought of as an ecosystem, which critically means that we cannot just consider it as a collection of mutated cells but more as a complex system of many interacting cellular and microenvironmental elements. At its simplest, a growing tumour with increased proliferation capacity must compete for space as a limited resource. Hypercellularity leads to a contact-inhibited core with a competitive proliferating rim. Evolution and selection occurs, and an individual cell's capacity to survive and propagate is determined by its combination of traits and interaction with the environment. With heterogeneity in phenotypes, the clone that will dominate is not always obvious as there are both local interactions and global pressures. Several combinations of phenotypes can coexist, changing the fitness of the whole. To understand some aspects of heterogeneity in a growing tumour, we build an off-lattice agent-based model consisting of individual cells with assigned trait values for proliferation and migration rates. We represent heterogeneity in these traits with frequency distributions and combinations of traits with density maps. How the distributions change over time is dependent on how traits are passed on to progeny cells, which is our main enquiry. We bypass the translation of genetics to behaviour by focusing on the functional end result of inheritance of the phenotype combined with the environmental influence of limited space.
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Affiliation(s)
- Jill Gallaher
- Department of Mathematical Oncology, H. Lee Moffitt Cancer Center, Tampa, FL 33612 , USA
| | - Alexander R A Anderson
- Department of Mathematical Oncology, H. Lee Moffitt Cancer Center, Tampa, FL 33612 , USA
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Werfel J, Krause S, Bischof AG, Mannix RJ, Tobin H, Bar-Yam Y, Bellin RM, Ingber DE. How changes in extracellular matrix mechanics and gene expression variability might combine to drive cancer progression. PLoS One 2013; 8:e76122. [PMID: 24098430 PMCID: PMC3789713 DOI: 10.1371/journal.pone.0076122] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2013] [Accepted: 08/20/2013] [Indexed: 01/16/2023] Open
Abstract
Changes in extracellular matrix (ECM) structure or mechanics can actively drive cancer progression; however, the underlying mechanism remains unknown. Here we explore whether this process could be mediated by changes in cell shape that lead to increases in genetic noise, given that both factors have been independently shown to alter gene expression and induce cell fate switching. We do this using a computer simulation model that explores the impact of physical changes in the tissue microenvironment under conditions in which physical deformation of cells increases gene expression variability among genetically identical cells. The model reveals that cancerous tissue growth can be driven by physical changes in the microenvironment: when increases in cell shape variability due to growth-dependent increases in cell packing density enhance gene expression variation, heterogeneous autonomous growth and further structural disorganization can result, thereby driving cancer progression via positive feedback. The model parameters that led to this prediction are consistent with experimental measurements of mammary tissues that spontaneously undergo cancer progression in transgenic C3(1)-SV40Tag female mice, which exhibit enhanced stiffness of mammary ducts, as well as progressive increases in variability of cell-cell relations and associated cell shape changes. These results demonstrate the potential for physical changes in the tissue microenvironment (e.g., altered ECM mechanics) to induce a cancerous phenotype or accelerate cancer progression in a clonal population through local changes in cell geometry and increased phenotypic variability, even in the absence of gene mutation.
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Affiliation(s)
- Justin Werfel
- Wyss Institute for Biologically Inspired Engineering, Harvard University, Boston, Massachusetts, United States of America
| | - Silva Krause
- Vascular Biology Program and Department of Surgery, Boston Children’s Hospital and Harvard Medical School, Boston, Massachusetts, United States of America
| | - Ashley G. Bischof
- Vascular Biology Program and Department of Surgery, Boston Children’s Hospital and Harvard Medical School, Boston, Massachusetts, United States of America
- Graduate Program in Biophysics, Harvard University, Cambridge, Massachusetts, United States of America
| | - Robert J. Mannix
- Vascular Biology Program and Department of Surgery, Boston Children’s Hospital and Harvard Medical School, Boston, Massachusetts, United States of America
| | - Heather Tobin
- Vascular Biology Program and Department of Surgery, Boston Children’s Hospital and Harvard Medical School, Boston, Massachusetts, United States of America
| | - Yaneer Bar-Yam
- New England Complex Systems Institute, Cambridge, Massachusetts, United States of America
| | - Robert M. Bellin
- Department of Biology, College of the Holy Cross, Worcester, Massachusetts, United States of America
| | - Donald E. Ingber
- Wyss Institute for Biologically Inspired Engineering, Harvard University, Boston, Massachusetts, United States of America
- Vascular Biology Program and Department of Surgery, Boston Children’s Hospital and Harvard Medical School, Boston, Massachusetts, United States of America
- Harvard School of Engineering and Applied Sciences, Cambridge, Massachusetts, United States of America
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Kurbatova P, Eymard N, Volpert V. Hybrid model of erythropoiesis. Acta Biotheor 2013; 61:305-15. [PMID: 23904072 DOI: 10.1007/s10441-013-9188-2] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2012] [Accepted: 07/19/2013] [Indexed: 10/26/2022]
Abstract
A hybrid model of cell dynamics is presented. It is illustrated by model examples and applied to study erythropoiesis (red blood cell production). In this approach, cells are considered as discrete objects while intra-cellular proteins and extra-cellular biochemical substances are described with continuous models. Spatial organization of erythropoiesis occurring in specific structures of the bone marrow, called erythroblastic island, is investigated.
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38
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Papadogiorgaki M, Koliou P, Kotsiakis X, Zervakis ME. Mathematical modelling of spatio-temporal glioma evolution. Theor Biol Med Model 2013; 10:47. [PMID: 23880133 PMCID: PMC3734056 DOI: 10.1186/1742-4682-10-47] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/04/2013] [Accepted: 07/16/2013] [Indexed: 11/10/2022] Open
Abstract
Background Gliomas are the most common types of brain cancer, well known for their aggressive proliferation and the invasive behavior leading to a high mortality rate. Several mathematical models have been developed for identifying the interactions between glioma cells and tissue microenvironment, which play an important role in the mechanism of the tumor formation and progression. Methods Building and expanding on existing approaches, this paper develops a continuous three-dimensional model of avascular glioma spatio-temporal evolution. The proposed spherical model incorporates the interactions between the populations of four different glioma cell phenotypes (proliferative, hypoxic, hypoglychemic and necrotic) and their tissue microenvironment, in order to investigate how they affect tumor growth and invasion in an isotropic and homogeneous medium. The model includes two key variables involved in the proliferation and invasion processes of cancer cells; i.e. the extracellular matrix and the matrix-degradative enzymes concentrations inside the tumor and its surroundings. Additionally, the proposed model focuses on innovative features, such as the separate and independent impact of two vital nutrients, namely oxygen and glucose, in tumor growth, leading to the formation of cell populations with different metabolic profiles. The model implementation takes under consideration the variations of particular factors, such as the local cell proliferation rate, the variable conversion rates of cells from one category to another and the nutrient-dependent thresholds of conversion. All model variables (cell densities, ingredients concentrations) are continuous and described by reaction-diffusion equations. Results Several simulations were performed using combinations of growth and invasion rates, for different evolution times. The model results were evaluated by medical experts and validated on experimental glioma models available in the literature, revealing high agreement between simulated and experimental results. Conclusions Based on the experimental validation, as well as the evaluation by clinical experts, the proposed model may provide an essential tool for the patient-specific simulation of different tumor evolution scenarios and reliable prognosis of glioma spatio-temporal progression.
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Affiliation(s)
- Maria Papadogiorgaki
- Digital Image and Signal Processing Laboratory, Electronic and Computer Engineering Department, Technical University of Crete, Polytechnioupolis, Kounopidiana Campus, Chania, Crete, Greece.
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Frascoli F, Hughes BD, Zaman MH, Landman KA. A computational model for collective cellular motion in three dimensions: general framework and case study for cell pair dynamics. PLoS One 2013; 8:e59249. [PMID: 23527148 PMCID: PMC3602115 DOI: 10.1371/journal.pone.0059249] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2012] [Accepted: 02/13/2013] [Indexed: 11/19/2022] Open
Abstract
Cell migration in healthy and diseased systems is a combination of single and collective cell motion. While single cell motion has received considerable attention, our understanding of collective cell motion remains elusive. A new computational framework for the migration of groups of cells in three dimensions is presented, which focuses on the forces acting at the microscopic scale and the interactions between cells and their extracellular matrix (ECM) environment. Cell-cell adhesion, resistance due to the ECM and the factors regulating the propulsion of each cell through the matrix are considered. In particular, our approach emphasizes the role of receptors that mediate cell-cell and cell-matrix interactions, and examines how variation in their properties induces changes in cellular motion. As an important case study, we analyze two interacting cells. Our results show that the dynamics of cell pairs depends on the magnitude and the stochastic nature of the forces. Stronger intercellular stability is generally promoted by surface receptors that move. We also demonstrate that matrix resistance, cellular stiffness and intensity of adhesion contribute to migration behaviors in different ways, with memory effects present that can alter pair motility. If adhesion weakens with time, our findings show that cell pair break-up depends strongly on the way cells interact with the matrix. Finally, the motility for cells in a larger cluster (size 50 cells) is examined to illustrate the full capabilities of the model and to stress the role of cellular pairs in complex cellular structures. Overall, our framework shows how properties of cells and their environment influence the stability and motility of cellular assemblies. This is an important step in the advancement of the understanding of collective motility, and can contribute to knowledge of complex biological processes involving migration, aggregation and detachment of cells in healthy and diseased systems.
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Affiliation(s)
- Federico Frascoli
- Department of Mathematics and Statistics, University of Melbourne, Victoria, Australia.
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40
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Polacheck WJ, Zervantonakis IK, Kamm RD. Tumor cell migration in complex microenvironments. Cell Mol Life Sci 2012; 70:1335-56. [PMID: 22926411 DOI: 10.1007/s00018-012-1115-1] [Citation(s) in RCA: 152] [Impact Index Per Article: 12.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/29/2012] [Revised: 06/21/2012] [Accepted: 07/31/2012] [Indexed: 12/18/2022]
Abstract
Tumor cell migration is essential for invasion and dissemination from primary solid tumors and for the establishment of lethal secondary metastases at distant organs. In vivo and in vitro models enabled identification of different factors in the tumor microenvironment that regulate tumor progression and metastasis. However, the mechanisms by which tumor cells integrate these chemical and mechanical signals from multiple sources to navigate the complex microenvironment remain poorly understood. In this review, we discuss the factors that influence tumor cell migration with a focus on the migration of transformed carcinoma cells. We provide an overview of the experimental and computational methods that allow the investigation of tumor cell migration, and we highlight the benefits and shortcomings of the various assays. We emphasize that the chemical and mechanical stimulus paradigms are not independent and that crosstalk between them motivates the development of new assays capable of applying multiple, simultaneous stimuli and imaging the cellular migratory response in real-time. These next-generation assays will more closely mimic the in vivo microenvironment to provide new insights into tumor progression, inform techniques to control tumor cell migration, and render cancer more treatable.
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Affiliation(s)
- William J Polacheck
- Department of Mechanical Engineering, MIT, 77 Massachusetts Ave. Room NE47-315, Cambridge, MA 02139, USA.
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A novel method for simulating the extracellular matrix in models of tumour growth. COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE 2012; 2012:109019. [PMID: 22919426 PMCID: PMC3420324 DOI: 10.1155/2012/109019] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/17/2012] [Revised: 06/01/2012] [Accepted: 06/11/2012] [Indexed: 02/06/2023]
Abstract
A novel hybrid continuum-discrete model to simulate tumour growth on a cellular scale is proposed. The lattice-based spatiotemporal model consists of reaction-diffusion equations that describe interactions between cancer cells and their microenvironment. The fundamental ingredients that are typically considered are the nutrient concentration, the extracellular matrix (ECM), and matrix degrading enzymes (MDEs). The in vivo processes are very complex and occur on different levels. This in turn leads to huge computational costs. The main contribution of the present work is therefore to describe the processes on the basis of simplified mathematical approaches, which, at the same time, depict realistic results to understand the biological processes. In this work, we discuss if we have to simulate the MDE or if the degraded matrix can be estimated directly with respect to the cancer cell distribution. Additionally, we compare the results for modelling tumour growth using the common and our simplified approach, thereby demonstrating the advantages of the proposed method. Therefore, we introduce variations of the positioning of the nutrient delivering blood vessels and use different initializations of the ECM. We conclude that the novel method, which does not explicitly model the matrix degrading
enzymes, provides means for a straightforward and fast implementation for modelling tumour growth.
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42
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Narang V, Wong SY, Leong SR, Harish B, Abastado JP, Gouaillard A. Selection of Mesenchymal-Like Metastatic Cells in Primary Tumors - An in silico Investigation. Front Immunol 2012; 3:88. [PMID: 22566967 PMCID: PMC3342023 DOI: 10.3389/fimmu.2012.00088] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2012] [Accepted: 04/05/2012] [Indexed: 01/08/2023] Open
Abstract
In order to metastasize, cancer cells must undergo phenotypic transition from an anchorage-dependent form to a motile form via a process referred to as epithelial to mesenchymal transition. It is currently unclear whether metastatic cells emerge late during tumor progression by successive accumulation of mutations, or whether they derive from distinct cell populations already present during the early stages of tumorigenesis. Similarly, the selective pressures that drive metastasis are poorly understood. Selection of cancer cells with increased proliferative capacity and enhanced survival characteristics may explain how some transformations promote a metastatic phenotype. However, it is difficult to explain how cancer cells that disseminate can emerge due to such selective pressure, since these cells usually remain dormant for prolonged periods of time. In the current study, we have used in silico modeling and simulation to investigate the hypothesis that mesenchymal-like cancer cells evolve during the early stages of primary tumor development, and that these cells exhibit survival and proliferative advantages within the tumor microenvironment. In an agent-based tumor microenvironment model, cancer cell agents with distinct sets of attributes governing nutrient consumption, proliferation, apoptosis, random motility, and cell adhesion were allowed to compete for space and nutrients. These simulation data indicated that mesenchymal-like cancer cells displaying high motility and low adhesion proliferate more rapidly and display a survival advantage over epithelial-like cancer cells. Furthermore, the presence of mesenchymal-like cells within the primary tumor influences the macroscopic properties, emergent morphology, and growth rate of tumors.
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Affiliation(s)
- Vipin Narang
- Agency for Science, Technology and Research, Singapore Immunology Network Singapore
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43
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Fischer S, Kurbatova P, Bessonov N, Gandrillon O, Volpert V, Crauste F. Modeling erythroblastic islands: Using a hybrid model to assess the function of central macrophage. J Theor Biol 2012; 298:92-106. [DOI: 10.1016/j.jtbi.2012.01.002] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2011] [Revised: 11/10/2011] [Accepted: 01/03/2012] [Indexed: 11/30/2022]
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Szabó A, Varga K, Garay T, Hegedus B, Czirók A. Invasion from a cell aggregate--the roles of active cell motion and mechanical equilibrium. Phys Biol 2012; 9:016010. [PMID: 22313673 DOI: 10.1088/1478-3975/9/1/016010] [Citation(s) in RCA: 42] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
Cell invasion from an aggregate into a surrounding extracellular matrix (ECM) is an important process during development disease, e.g., vascular network assembly or tumor progression. To describe the behavior emerging from autonomous cell motility, cell-cell adhesion and contact guidance by ECM filaments, we propose a suitably modified cellular Potts model. We consider an active cell motility process in which internal polarity is governed by a positive feedback from cell displacements, a mechanism that can result in highly persistent motion when constrained by an oriented ECM structure. The model allows us to explore the interplay between haptotaxis, matrix degradation and active cell movement. We show that for certain conditions the cells are able to both invade the ECM and follow the ECM tracks. Furthermore, we argue that enforcing mechanical equilibrium within a bulk cell mass is of key importance in multicellular simulations.
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Affiliation(s)
- A Szabó
- Department of Biological Physics, Eotvos University, Budapest, Hungary
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45
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Murray PJ, Edwards CM, Tindall MJ, Maini PK. Classifying general nonlinear force laws in cell-based models via the continuum limit. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:021921. [PMID: 22463258 DOI: 10.1103/physreve.85.021921] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/06/2011] [Indexed: 05/31/2023]
Abstract
Although discrete cell-based frameworks are now commonly used to simulate a whole range of biological phenomena, it is typically not obvious how the numerous different types of model are related to one another, nor which one is most appropriate in a given context. Here we demonstrate how individual cell movement on the discrete scale modeled using nonlinear force laws can be described by nonlinear diffusion coefficients on the continuum scale. A general relationship between nonlinear force laws and their respective diffusion coefficients is derived in one spatial dimension and, subsequently, a range of particular examples is considered. For each case excellent agreement is observed between numerical solutions of the discrete and corresponding continuum models. Three case studies are considered in which we demonstrate how the derived nonlinear diffusion coefficients can be used to (a) relate different discrete models of cell behavior; (b) derive discrete, intercell force laws from previously posed diffusion coefficients, and (c) describe aggregative behavior in discrete simulations.
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Affiliation(s)
- Philip J Murray
- Centre for Mathematical Biology, Mathematical Institute, 24-29 St Giles', Oxford OX1 3LB, United Kingdom
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Wang CC, Jamal L, Janes KA. Normal morphogenesis of epithelial tissues and progression of epithelial tumors. WILEY INTERDISCIPLINARY REVIEWS. SYSTEMS BIOLOGY AND MEDICINE 2012; 4:51-78. [PMID: 21898857 PMCID: PMC3242861 DOI: 10.1002/wsbm.159] [Citation(s) in RCA: 38] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Abstract
Epithelial cells organize into various tissue architectures that largely maintain their structure throughout the life of an organism. For decades, the morphogenesis of epithelial tissues has fascinated scientists at the interface of cell, developmental, and molecular biology. Systems biology offers ways to combine knowledge from these disciplines by building integrative models that are quantitative and predictive. Can such models be useful for gaining a deeper understanding of epithelial morphogenesis? Here, we take inventory of some recurring themes in epithelial morphogenesis that systems approaches could strive to capture. Predictive understanding of morphogenesis at the systems level would prove especially valuable for diseases such as cancer, where epithelial tissue architecture is profoundly disrupted.
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Affiliation(s)
- Chun-Chao Wang
- Department of Biomedical Engineering, University of Virginia, Charlottesville, VA, USA
| | - Leen Jamal
- Department of Biomedical Engineering, University of Virginia, Charlottesville, VA, USA
| | - Kevin A. Janes
- Department of Biomedical Engineering, University of Virginia, Charlottesville, VA, USA
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Buenzli PR, Jeon J, Pivonka P, Smith DW, Cummings PT. Investigation of bone resorption within a cortical basic multicellular unit using a lattice-based computational model. Bone 2012; 50:378-89. [PMID: 22100414 PMCID: PMC5603083 DOI: 10.1016/j.bone.2011.10.021] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 05/19/2011] [Revised: 10/17/2011] [Accepted: 10/21/2011] [Indexed: 11/20/2022]
Abstract
In this paper we develop a lattice-based computational model focused on bone resorption by osteoclasts in a single cortical basic multicellular unit (BMU). Our model takes into account the interaction of osteoclasts with the bone matrix, the interaction of osteoclasts with each other, the generation of osteoclasts from a growing blood vessel, and the renewal of osteoclast nuclei by cell fusion. All these features are shown to strongly influence the geometrical properties of the developing resorption cavity including its size, shape and progression rate, and are also shown to influence the distribution, resorption pattern and trajectories of individual osteoclasts within the BMU. We demonstrate that for certain parameter combinations, resorption cavity shapes can be recovered from the computational model that closely resemble resorption cavity shapes observed from microCT imaging of human cortical bone.
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Affiliation(s)
- Pascal R Buenzli
- Faculty of Engineering, Computing and Mathematics, The University of Western Australia, WA 6009, Australia.
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Tindall MJ, Dyson L, Smallbone K, Maini PK. Modelling acidosis and the cell cycle in multicellular tumour spheroids. J Theor Biol 2011; 298:107-15. [PMID: 22155133 DOI: 10.1016/j.jtbi.2011.11.009] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/03/2011] [Revised: 10/12/2011] [Accepted: 11/09/2011] [Indexed: 11/18/2022]
Abstract
A partial differential equation model is developed to understand the effect that nutrient and acidosis have on the distribution of proliferating and quiescent cells and dead cell material (necrotic and apoptotic) within a multicellular tumour spheroid. The rates of cell quiescence and necrosis depend upon the local nutrient and acid concentrations and quiescent cells are assumed to consume less nutrient and produce less acid than proliferating cells. Analysis of the differences in nutrient consumption and acid production by quiescent and proliferating cells shows low nutrient levels do not necessarily lead to increased acid concentration via anaerobic metabolism. Rather, it is the balance between proliferating and quiescent cells within the tumour which is important; decreased nutrient levels lead to more quiescent cells, which produce less acid than proliferating cells. We examine this effect via a sensitivity analysis which also includes a quantification of the effect that nutrient and acid concentrations have on the rates of cell quiescence and necrosis.
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Affiliation(s)
- Marcus J Tindall
- School of Biological Sciences, University of Reading, Whiteknights, Reading RG6 6BX, UK.
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d'Onofrio A. Spatiotemporal effects of a possible chemorepulsion of tumor cells by immune system effectors. J Theor Biol 2011; 296:41-8. [PMID: 22119911 DOI: 10.1016/j.jtbi.2011.11.013] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2011] [Revised: 10/18/2011] [Accepted: 11/11/2011] [Indexed: 11/27/2022]
Abstract
Tumor-immune system interplay is a landmark of tumor development, and chemotactic attraction of immune system cells towards a tumor is a landmark of immune control. Since tumor cells are capable of chemotactic and chemorepulsive motion, based on a number of analogies between the behavior of tumor cells and that of bacteria, and on the production of potentially chemorepulsive semaphorins by immune systems effectors, we propose here the possibility of chemorepulsion of tumor cells, elicited by chemicals produced by immune system effectors such as macrophages and cytotoxic T lymphocytes. To study the effects of this hypothesized phenomenon within the framework of the interplay of neoplasias with the innate and adaptive immune system, we appropriately extend two well-known models: the tumor-macrophage models by Owen and Sherratt [Owen and Sherratt, J. Theor. Biol., 1998] and the Matzavinos-Chaplain model of tumor-CTL interaction [Matzavinos, Chaplain and Kuznetsov, Math. Med. Biol., 2004]. Our simulations suggest that this mechanism might allow a faster expansion of tumors, and in the concluding remarks we envisage a new possible route of immunoevasion.
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Affiliation(s)
- Alberto d'Onofrio
- Department of Experimental Oncology, European Institute of Oncology, Via Ripamonti 435, Milano I-20141, Italy.
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Rejniak KA, Anderson ARA. Hybrid models of tumor growth. WILEY INTERDISCIPLINARY REVIEWS-SYSTEMS BIOLOGY AND MEDICINE 2011; 3:115-25. [PMID: 21064037 DOI: 10.1002/wsbm.102] [Citation(s) in RCA: 159] [Impact Index Per Article: 12.2] [Reference Citation Analysis] [Abstract] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Abstract
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.
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Affiliation(s)
- Katarzyna A Rejniak
- Integrated Mathematical Oncology Department, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL, USA.
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