1
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Li K, Green JEF, Tronnolone H, Tam AKY, Black AJ, Gardner JM, Sundstrom JF, Jiranek V, Binder BJ. An off-lattice discrete model to characterise filamentous yeast colony morphology. PLoS Comput Biol 2024; 20:e1012605. [PMID: 39570980 PMCID: PMC11620580 DOI: 10.1371/journal.pcbi.1012605] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2024] [Revised: 12/05/2024] [Accepted: 11/03/2024] [Indexed: 12/07/2024] Open
Abstract
We combine an off-lattice agent-based mathematical model and experimentation to explore filamentous growth of a yeast colony. Under environmental stress, Saccharomyces cerevisiae yeast cells can transition from a bipolar (sated) to unipolar (pseudohyphal) budding mechanism, where cells elongate and bud end-to-end. This budding asymmetry yields spatially non-uniform growth, where filaments extend away from the colony centre, foraging for food. We use approximate Bayesian computation to quantify how individual cell budding mechanisms give rise to spatial patterns observed in experiments. We apply this method of parameter inference to experimental images of colonies of two strains of S. cerevisiae, in low and high nutrient environments. The colony size at the transition from sated to pseudohyphal growth, and a forking mechanism for pseudohyphal cell proliferation are the key features driving colony morphology. Simulations run with the most likely inferred parameters produce colony morphologies that closely resemble experimental results.
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Affiliation(s)
- Kai Li
- School of Computer and Mathematical Sciences, University of Adelaide, Adelaide SA, Australia
| | - J. Edward F. Green
- School of Computer and Mathematical Sciences, University of Adelaide, Adelaide SA, Australia
| | - Hayden Tronnolone
- College of Science and Engineering, Flinders University, Adelaide SA, Australia
| | | | - Andrew J. Black
- School of Computer and Mathematical Sciences, University of Adelaide, Adelaide SA, Australia
| | - Jennifer M. Gardner
- Discipline of Wine Science, Waite Campus, University of Adelaide, Urrbrae SA, Australia
| | - Joanna F. Sundstrom
- Discipline of Wine Science, Waite Campus, University of Adelaide, Urrbrae SA, Australia
| | - Vladimir Jiranek
- Discipline of Wine Science, Waite Campus, University of Adelaide, Urrbrae SA, Australia
- School of Biological Sciences, The University of Southampton, Southampton, United Kingdom
| | - Benjamin J. Binder
- School of Computer and Mathematical Sciences, University of Adelaide, Adelaide SA, Australia
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2
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Arjmandi H, Kanebratt KP, Vilén L, Gennemark P, Noel A. 3D cell aggregates amplify diffusion signals. PLoS One 2024; 19:e0310109. [PMID: 39264935 DOI: 10.1371/journal.pone.0310109] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2023] [Accepted: 08/23/2024] [Indexed: 09/14/2024] Open
Abstract
Biophysical models can predict the behavior of cell cultures including 3D cell aggregates (3DCAs), thereby reducing the need for costly and time-consuming experiments. Specifically, mass transfer models enable studying the transport of nutrients, oxygen, signaling molecules, and drugs in 3DCA. These models require the defining of boundary conditions (BC) between the 3DCA and surrounding medium. However, accurately modeling the BC that relates the inner and outer boundary concentrations at the border between the 3DCA and the medium remains a challenge that this paper addresses using both theoretical and experimental methods. The provided biophysical analysis indicates that the concentration of molecules inside boundary is higher than that at the outer boundary, revealing an amplification factor that is confirmed by a particle-based simulator (PBS). Due to the amplification factor, the PBS confirms that when a 3DCA with a low concentration of target molecules is introduced to a culture medium with a higher concentration, the molecule concentration in the medium rapidly decreases. The theoretical model and PBS simulations were used to design a pilot experiment with liver spheroids as the 3DCA and glucose as the target molecule. Experimental results agree with the proposed theory and derived properties.
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Affiliation(s)
- Hamidreza Arjmandi
- Department of Cancer and Genomic Sciences, College of Medicine and Health, University of Birmingham, Birmingham, United Kingdom
| | - Kajsa P Kanebratt
- Drug Metabolism and Pharmacokinetics, Research and Early Development, Cardiovascular, Renal and Metabolism (CVRM), AstraZeneca, Gothenburg, Sweden
| | - Liisa Vilén
- Drug Metabolism and Pharmacokinetics, Research and Early Development, Cardiovascular, Renal and Metabolism (CVRM), AstraZeneca, Gothenburg, Sweden
| | - Peter Gennemark
- Drug Metabolism and Pharmacokinetics, Research and Early Development, Cardiovascular, Renal and Metabolism (CVRM), AstraZeneca, Gothenburg, Sweden
- Department of Biomedical Engineering, Linköping University, Linköping, Sweden
| | - Adam Noel
- School of Engineering, University of Warwick, Coventry, United Kingdom
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3
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Ma C, Gurkan-Cavusoglu E. A comprehensive review of computational cell cycle models in guiding cancer treatment strategies. NPJ Syst Biol Appl 2024; 10:71. [PMID: 38969664 PMCID: PMC11226463 DOI: 10.1038/s41540-024-00397-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2024] [Accepted: 06/24/2024] [Indexed: 07/07/2024] Open
Abstract
This article reviews the current knowledge and recent advancements in computational modeling of the cell cycle. It offers a comparative analysis of various modeling paradigms, highlighting their unique strengths, limitations, and applications. Specifically, the article compares deterministic and stochastic models, single-cell versus population models, and mechanistic versus abstract models. This detailed analysis helps determine the most suitable modeling framework for various research needs. Additionally, the discussion extends to the utilization of these computational models to illuminate cell cycle dynamics, with a particular focus on cell cycle viability, crosstalk with signaling pathways, tumor microenvironment, DNA replication, and repair mechanisms, underscoring their critical roles in tumor progression and the optimization of cancer therapies. By applying these models to crucial aspects of cancer therapy planning for better outcomes, including drug efficacy quantification, drug discovery, drug resistance analysis, and dose optimization, the review highlights the significant potential of computational insights in enhancing the precision and effectiveness of cancer treatments. This emphasis on the intricate relationship between computational modeling and therapeutic strategy development underscores the pivotal role of advanced modeling techniques in navigating the complexities of cell cycle dynamics and their implications for cancer therapy.
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Affiliation(s)
- Chenhui Ma
- Department of Electrical, Computer and Systems Engineering, Case Western Reserve University, Cleveland, OH, USA.
| | - Evren Gurkan-Cavusoglu
- Department of Electrical, Computer and Systems Engineering, Case Western Reserve University, Cleveland, OH, USA
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4
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Karras F, Kunz M. Patient-derived melanoma models. Pathol Res Pract 2024; 259:155231. [PMID: 38508996 DOI: 10.1016/j.prp.2024.155231] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 11/30/2023] [Revised: 02/15/2024] [Accepted: 02/26/2024] [Indexed: 03/22/2024]
Abstract
Melanoma is a very aggressive, rapidly metastasizing tumor that has been studied intensively in the past regarding the underlying genetic and molecular mechanisms. More recently developed treatment modalities have improved response rates and overall survival of patients. However, the majority of patients suffer from secondary treatment resistance, which requires in depth analyses of the underlying mechanisms. Here, melanoma models based on patients-derived material may play an important role. Consequently, a plethora of different experimental techniques have been developed in the past years. Among these are 3D and 4D culture techniques, organotypic skin reconstructs, melanoma-on-chip models and patient-derived xenografts, Every technique has its own strengths but also weaknesses regarding throughput, reproducibility, and reflection of the human situation. Here, we provide a comprehensive overview of currently used techniques and discuss their use in different experimental settings.
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Affiliation(s)
- Franziska Karras
- Institute of Pathology, Otto-von-Guericke University Magdeburg, Leipziger Str. 44, Magdeburg 39120, Germany.
| | - Manfred Kunz
- Department of Dermatology, Venereology and Allergology, University Medical Center Leipzig, Philipp-Rosenthal-Str. 23, Leipzig 04103, Germany
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5
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Falcó C, Cohen DJ, Carrillo JA, Baker RE. Quantifying cell cycle regulation by tissue crowding. Biophys J 2024:S0006-3495(24)00317-5. [PMID: 38715360 DOI: 10.1016/j.bpj.2024.05.003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2024] [Revised: 04/24/2024] [Accepted: 05/02/2024] [Indexed: 05/25/2024] Open
Abstract
The spatiotemporal coordination and regulation of cell proliferation is fundamental in many aspects of development and tissue maintenance. Cells have the ability to adapt their division rates in response to mechanical constraints, yet we do not fully understand how cell proliferation regulation impacts cell migration phenomena. Here, we present a minimal continuum model of cell migration with cell cycle dynamics, which includes density-dependent effects and hence can account for cell proliferation regulation. By combining minimal mathematical modeling, Bayesian inference, and recent experimental data, we quantify the impact of tissue crowding across different cell cycle stages in epithelial tissue expansion experiments. Our model suggests that cells sense local density and adapt cell cycle progression in response, during G1 and the combined S/G2/M phases, providing an explicit relationship between each cell-cycle-stage duration and local tissue density, which is consistent with several experimental observations. Finally, we compare our mathematical model's predictions to different experiments studying cell cycle regulation and present a quantitative analysis on the impact of density-dependent regulation on cell migration patterns. Our work presents a systematic approach for investigating and analyzing cell cycle data, providing mechanistic insights into how individual cells regulate proliferation, based on population-based experimental measurements.
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Affiliation(s)
- Carles Falcó
- Mathematical Institute, University of Oxford, Oxford, United Kingdom.
| | - Daniel J Cohen
- Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey; Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey
| | - José A Carrillo
- Mathematical Institute, University of Oxford, Oxford, United Kingdom
| | - Ruth E Baker
- Mathematical Institute, University of Oxford, Oxford, United Kingdom
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6
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Lacy MS, Jenner AL. Impact of Resistance on Therapeutic Design: A Moran Model of Cancer Growth. Bull Math Biol 2024; 86:43. [PMID: 38502371 PMCID: PMC10950993 DOI: 10.1007/s11538-024-01272-6] [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: 09/04/2023] [Accepted: 02/19/2024] [Indexed: 03/21/2024]
Abstract
Resistance of cancers to treatments, such as chemotherapy, largely arise due to cell mutations. These mutations allow cells to resist apoptosis and inevitably lead to recurrence and often progression to more aggressive cancer forms. Sustained-low dose therapies are being considered as an alternative over maximum tolerated dose treatments, whereby a smaller drug dosage is given over a longer period of time. However, understanding the impact that the presence of treatment-resistant clones may have on these new treatment modalities is crucial to validating them as a therapeutic avenue. In this study, a Moran process is used to capture stochastic mutations arising in cancer cells, inferring treatment resistance. The model is used to predict the probability of cancer recurrence given varying treatment modalities. The simulations predict that sustained-low dose therapies would be virtually ineffective for a cancer with a non-negligible probability of developing a sub-clone with resistance tendencies. Furthermore, calibrating the model to in vivo measurements for breast cancer treatment with Herceptin, the model suggests that standard treatment regimens are ineffective in this mouse model. Using a simple Moran model, it is possible to explore the likelihood of treatment success given a non-negligible probability of treatment resistant mutations and suggest more robust therapeutic schedules.
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Affiliation(s)
- Mason S Lacy
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, QLD, Australia
| | - Adrianne L Jenner
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, QLD, Australia.
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7
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Wang X, Jenner AL, Salomone R, Warne DJ, Drovandi C. Calibration of agent based models for monophasic and biphasic tumour growth using approximate Bayesian computation. J Math Biol 2024; 88:28. [PMID: 38358410 PMCID: PMC10869399 DOI: 10.1007/s00285-024-02045-4] [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: 06/28/2023] [Revised: 10/25/2023] [Accepted: 12/27/2023] [Indexed: 02/16/2024]
Abstract
Agent-based models (ABMs) are readily used to capture the stochasticity in tumour evolution; however, these models are often challenging to validate with experimental measurements due to model complexity. The Voronoi cell-based model (VCBM) is an off-lattice agent-based model that captures individual cell shapes using a Voronoi tessellation and mimics the evolution of cancer cell proliferation and movement. Evidence suggests tumours can exhibit biphasic growth in vivo. To account for this phenomena, we extend the VCBM to capture the existence of two distinct growth phases. Prior work primarily focused on point estimation for the parameters without consideration of estimating uncertainty. In this paper, approximate Bayesian computation is employed to calibrate the model to in vivo measurements of breast, ovarian and pancreatic cancer. Our approach involves estimating the distribution of parameters that govern cancer cell proliferation and recovering outputs that match the experimental data. Our results show that the VCBM, and its biphasic extension, provides insight into tumour growth and quantifies uncertainty in the switching time between the two phases of the biphasic growth model. We find this approach enables precise estimates for the time taken for a daughter cell to become a mature cell. This allows us to propose future refinements to the model to improve accuracy, whilst also making conclusions about the differences in cancer cell characteristics.
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Affiliation(s)
- Xiaoyu Wang
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, QLD, Australia.
- Centre for Data Science, Queensland University of Technology, Brisbane, QLD, Australia.
| | - Adrianne L Jenner
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, QLD, Australia
- Centre for Data Science, Queensland University of Technology, Brisbane, QLD, Australia
| | - Robert Salomone
- Centre for Data Science, Queensland University of Technology, Brisbane, QLD, Australia
- School of Computer Science, Queensland University of Technology, Brisbane, QLD, Australia
| | - David J Warne
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, QLD, Australia
- Centre for Data Science, Queensland University of Technology, Brisbane, QLD, Australia
| | - Christopher Drovandi
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, QLD, Australia
- Centre for Data Science, Queensland University of Technology, Brisbane, QLD, Australia
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8
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Spoerri L, Beaumont KA, Anfosso A, Murphy RJ, Browning AP, Gunasingh G, Haass NK. Real-Time Cell Cycle Imaging in a 3D Cell Culture Model of Melanoma, Quantitative Analysis, Optical Clearing, and Mathematical Modeling. Methods Mol Biol 2024; 2764:291-310. [PMID: 38393602 DOI: 10.1007/978-1-0716-3674-9_19] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/25/2024]
Abstract
Aberrant cell cycle progression is a hallmark of solid tumors. Therefore, cell cycle analysis is an invaluable technique to study cancer cell biology. However, cell cycle progression has been most commonly assessed by methods that are limited to temporal snapshots or that lack spatial information. In this chapter, we describe a technique that allows spatiotemporal real-time tracking of cell cycle progression of individual cells in a multicellular context. The power of this system lies in the use of 3D melanoma spheroids generated from melanoma cells engineered with the fluorescent ubiquitination-based cell cycle indicator (FUCCI). This technique, combined with mathematical modeling, allows us to gain further and more detailed insight into several relevant aspects of solid cancer cell biology, such as tumor growth, proliferation, invasion, and drug sensitivity.
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Affiliation(s)
- Loredana Spoerri
- Frazer Institute, The University of Queensland, Brisbane, QLD, Australia
| | - Kimberley A Beaumont
- The Centenary Institute, Sydney, NSW, Australia
- Uniquest, The University of Queensland, Brisbane, QLD, Australia
| | | | - Ryan J Murphy
- Mathematical Sciences, Queensland University of Technology, Brisbane, QLD, Australia
| | - Alexander P Browning
- Mathematical Sciences, Queensland University of Technology, Brisbane, QLD, Australia
| | - Gency Gunasingh
- Frazer Institute, The University of Queensland, Brisbane, QLD, Australia
| | - Nikolas K Haass
- Frazer Institute, The University of Queensland, Brisbane, QLD, Australia.
- The Centenary Institute, Sydney, NSW, Australia.
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9
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Murphy RJ, Gunasingh G, Haass NK, Simpson MJ. Formation and Growth of Co-Culture Tumour Spheroids: New Compartment-Based Mathematical Models and Experiments. Bull Math Biol 2023; 86:8. [PMID: 38091169 DOI: 10.1007/s11538-023-01229-1] [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: 03/15/2023] [Accepted: 10/23/2023] [Indexed: 12/18/2023]
Abstract
Co-culture tumour spheroid experiments are routinely performed to investigate cancer progression and test anti-cancer therapies. Therefore, methods to quantitatively characterise and interpret co-culture spheroid growth are of great interest. However, co-culture spheroid growth is complex. Multiple biological processes occur on overlapping timescales and different cell types within the spheroid may have different characteristics, such as differing proliferation rates or responses to nutrient availability. At present there is no standard, widely-accepted mathematical model of such complex spatio-temporal growth processes. Typical approaches to analyse these experiments focus on the late-time temporal evolution of spheroid size and overlook early-time spheroid formation, spheroid structure and geometry. Here, using a range of ordinary differential equation-based mathematical models and parameter estimation, we interpret new co-culture experimental data. We provide new biological insights about spheroid formation, growth, and structure. As part of this analysis we connect Greenspan's seminal mathematical model to co-culture data for the first time. Furthermore, we generalise a class of compartment-based spheroid mathematical models that have previously been restricted to one population so they can be applied to multiple populations. As special cases of the general model, we explore multiple natural two population extensions to Greenspan's seminal model and reveal biological mechanisms that can describe the internal dynamics of growing co-culture spheroids and those that cannot. This mathematical and statistical modelling-based framework is well-suited to analyse spheroids grown with multiple different cell types and the new class of mathematical models provide opportunities for further mathematical and biological insights.
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Affiliation(s)
- Ryan J Murphy
- Mathematical Sciences, Queensland University of Technology, Brisbane, Australia.
| | - Gency Gunasingh
- Frazer Institute, The University of Queensland, Brisbane, Australia
| | - Nikolas K Haass
- Frazer Institute, The University of Queensland, Brisbane, Australia
| | - Matthew J Simpson
- Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
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10
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Bon JJ, Bretherton A, Buchhorn K, Cramb S, Drovandi C, Hassan C, Jenner AL, Mayfield HJ, McGree JM, Mengersen K, Price A, Salomone R, Santos-Fernandez E, Vercelloni J, Wang X. Being Bayesian in the 2020s: opportunities and challenges in the practice of modern applied Bayesian statistics. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2023; 381:20220156. [PMID: 36970822 PMCID: PMC10041356 DOI: 10.1098/rsta.2022.0156] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/22/2022] [Accepted: 01/06/2023] [Indexed: 06/18/2023]
Abstract
Building on a strong foundation of philosophy, theory, methods and computation over the past three decades, Bayesian approaches are now an integral part of the toolkit for most statisticians and data scientists. Whether they are dedicated Bayesians or opportunistic users, applied professionals can now reap many of the benefits afforded by the Bayesian paradigm. In this paper, we touch on six modern opportunities and challenges in applied Bayesian statistics: intelligent data collection, new data sources, federated analysis, inference for implicit models, model transfer and purposeful software products. This article is part of the theme issue 'Bayesian inference: challenges, perspectives, and prospects'.
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Affiliation(s)
- Joshua J. Bon
- Centre for Data Science, Queensland University of Technology, Brisbane, Queensland, Australia
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia
| | - Adam Bretherton
- Centre for Data Science, Queensland University of Technology, Brisbane, Queensland, Australia
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia
| | - Katie Buchhorn
- Centre for Data Science, Queensland University of Technology, Brisbane, Queensland, Australia
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia
| | - Susanna Cramb
- Centre for Data Science, Queensland University of Technology, Brisbane, Queensland, Australia
- School of Public Health and Social Work, Queensland University of Technology, Brisbane, Queensland, Australia
| | - Christopher Drovandi
- Centre for Data Science, Queensland University of Technology, Brisbane, Queensland, Australia
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia
| | - Conor Hassan
- Centre for Data Science, Queensland University of Technology, Brisbane, Queensland, Australia
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia
| | - Adrianne L. Jenner
- Centre for Data Science, Queensland University of Technology, Brisbane, Queensland, Australia
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia
| | - Helen J. Mayfield
- Centre for Data Science, Queensland University of Technology, Brisbane, Queensland, Australia
- School of Public Health, The University of Queensland, Saint Lucia, Queensland, Australia
| | - James M. McGree
- Centre for Data Science, Queensland University of Technology, Brisbane, Queensland, Australia
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia
| | - Kerrie Mengersen
- Centre for Data Science, Queensland University of Technology, Brisbane, Queensland, Australia
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia
| | - Aiden Price
- Centre for Data Science, Queensland University of Technology, Brisbane, Queensland, Australia
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia
| | - Robert Salomone
- Centre for Data Science, Queensland University of Technology, Brisbane, Queensland, Australia
- School of Computer Science, Queensland University of Technology, Brisbane, Queensland, Australia
| | - Edgar Santos-Fernandez
- Centre for Data Science, Queensland University of Technology, Brisbane, Queensland, Australia
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia
| | - Julie Vercelloni
- Centre for Data Science, Queensland University of Technology, Brisbane, Queensland, Australia
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia
| | - Xiaoyu Wang
- Centre for Data Science, Queensland University of Technology, Brisbane, Queensland, Australia
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia
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11
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Bull JA, Byrne HM. Quantification of spatial and phenotypic heterogeneity in an agent-based model of tumour-macrophage interactions. PLoS Comput Biol 2023; 19:e1010994. [PMID: 36972297 PMCID: PMC10079237 DOI: 10.1371/journal.pcbi.1010994] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/14/2022] [Revised: 04/06/2023] [Accepted: 03/04/2023] [Indexed: 03/29/2023] Open
Abstract
We introduce a new spatial statistic, the weighted pair correlation function (wPCF). The wPCF extends the existing pair correlation function (PCF) and cross-PCF to describe spatial relationships between points marked with combinations of discrete and continuous labels. We validate its use through application to a new agent-based model (ABM) which simulates interactions between macrophages and tumour cells. These interactions are influenced by the spatial positions of the cells and by macrophage phenotype, a continuous variable that ranges from anti-tumour to pro-tumour. By varying model parameters that regulate macrophage phenotype, we show that the ABM exhibits behaviours which resemble the 'three Es of cancer immunoediting': Equilibrium, Escape, and Elimination. We use the wPCF to analyse synthetic images generated by the ABM. We show that the wPCF generates a 'human readable' statistical summary of where macrophages with different phenotypes are located relative to both blood vessels and tumour cells. We also define a distinct 'PCF signature' that characterises each of the three Es of immunoediting, by combining wPCF measurements with the cross-PCF describing interactions between vessels and tumour cells. By applying dimension reduction techniques to this signature, we identify its key features and train a support vector machine classifier to distinguish between simulation outputs based on their PCF signature. This proof-of-concept study shows how multiple spatial statistics can be combined to analyse the complex spatial features that the ABM generates, and to partition them into interpretable groups. The intricate spatial features produced by the ABM are similar to those generated by state-of-the-art multiplex imaging techniques which distinguish the spatial distribution and intensity of multiple biomarkers in biological tissue regions. Applying methods such as the wPCF to multiplex imaging data would exploit the continuous variation in biomarker intensities and generate more detailed characterisation of the spatial and phenotypic heterogeneity in tissue samples.
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Affiliation(s)
- Joshua A. Bull
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, United Kingdom
| | - Helen M. Byrne
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, United Kingdom
- Ludwig Institute for Cancer Research, Nuffield Department of Medicine, University of Oxford, Oxford, United Kingdom
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12
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Jenner AL, Kelly W, Dallaston M, Araujo R, Parfitt I, Steinitz D, Pooladvand P, Kim PS, Wade SJ, Vine KL. Examining the efficacy of localised gemcitabine therapy for the treatment of pancreatic cancer using a hybrid agent-based model. PLoS Comput Biol 2023; 19:e1010104. [PMID: 36649330 PMCID: PMC9891514 DOI: 10.1371/journal.pcbi.1010104] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2022] [Revised: 02/01/2023] [Accepted: 12/21/2022] [Indexed: 01/18/2023] Open
Abstract
The prognosis for pancreatic ductal adenocarcinoma (PDAC) patients has not significantly improved in the past 3 decades, highlighting the need for more effective treatment approaches. Poor patient outcomes and lack of response to therapy can be attributed, in part, to a lack of uptake of perfusion of systemically administered chemotherapeutic drugs into the tumour. Wet-spun alginate fibres loaded with the chemotherapeutic agent gemcitabine have been developed as a potential tool for overcoming the barriers in delivery of systemically administrated drugs to the PDAC tumour microenvironment by delivering high concentrations of drug to the tumour directly over an extended period. While exciting, the practicality, safety, and effectiveness of these devices in a clinical setting requires further investigation. Furthermore, an in-depth assessment of the drug-release rate from these devices needs to be undertaken to determine whether an optimal release profile exists. Using a hybrid computational model (agent-based model and partial differential equation system), we developed a simulation of pancreatic tumour growth and response to treatment with gemcitabine loaded alginate fibres. The model was calibrated using in vitro and in vivo data and simulated using a finite volume method discretisation. We then used the model to compare different intratumoural implantation protocols and gemcitabine-release rates. In our model, the primary driver of pancreatic tumour growth was the rate of tumour cell division. We were able to demonstrate that intratumoural placement of gemcitabine loaded fibres was more effective than peritumoural placement. Additionally, we quantified the efficacy of different release profiles from the implanted fibres that have not yet been tested experimentally. Altogether, the model developed here is a tool that can be used to investigate other drug delivery devices to improve the arsenal of treatments available for PDAC and other difficult-to-treat cancers in the future.
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Affiliation(s)
- Adrianne L. Jenner
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia
- * E-mail:
| | - Wayne Kelly
- School of Computer Science, Queensland University of Technology, Brisbane, Queensland, Australia
| | - Michael Dallaston
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia
| | - Robyn Araujo
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia
| | - Isobelle Parfitt
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia
| | - Dominic Steinitz
- Tweag Software Innovation Lab, London, United Kingdom
- Kingston University, Kingston, United Kingdom
| | - Pantea Pooladvand
- School of Mathematics and Statistics, University of Sydney, Sydney, New South Wales, Australia
| | - Peter S. Kim
- School of Mathematics and Statistics, University of Sydney, Sydney, New South Wales, Australia
| | - Samantha J. Wade
- Illawarra Health and Medical Research Institute, Wollongong, New South Wales, Australia
- School of Chemistry and Molecular Bioscience, University of Wollongong, Wollongong, New South Wales, Australia
| | - Kara L. Vine
- Illawarra Health and Medical Research Institute, Wollongong, New South Wales, Australia
- School of Chemistry and Molecular Bioscience, University of Wollongong, Wollongong, New South Wales, Australia
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13
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Murphy RJ, Gunasingh G, Haass NK, Simpson MJ. Growth and adaptation mechanisms of tumour spheroids with time-dependent oxygen availability. PLoS Comput Biol 2023; 19:e1010833. [PMID: 36634128 PMCID: PMC9876349 DOI: 10.1371/journal.pcbi.1010833] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2022] [Revised: 01/25/2023] [Accepted: 12/21/2022] [Indexed: 01/13/2023] Open
Abstract
Tumours are subject to external environmental variability. However, in vitro tumour spheroid experiments, used to understand cancer progression and develop cancer therapies, have been routinely performed for the past fifty years in constant external environments. Furthermore, spheroids are typically grown in ambient atmospheric oxygen (normoxia), whereas most in vivo tumours exist in hypoxic environments. Therefore, there are clear discrepancies between in vitro and in vivo conditions. We explore these discrepancies by combining tools from experimental biology, mathematical modelling, and statistical uncertainty quantification. Focusing on oxygen variability to develop our framework, we reveal key biological mechanisms governing tumour spheroid growth. Growing spheroids in time-dependent conditions, we identify and quantify novel biological adaptation mechanisms, including unexpected necrotic core removal, and transient reversal of the tumour spheroid growth phases.
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Affiliation(s)
- Ryan J. Murphy
- Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia
- * E-mail:
| | - Gency Gunasingh
- Frazer Institute, The University of Queensland, Brisbane, Queensland, Australia
| | - Nikolas K. Haass
- Frazer Institute, The University of Queensland, Brisbane, Queensland, Australia
| | - Matthew J. Simpson
- Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia
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Browning AP, Simpson MJ. Geometric analysis enables biological insight from complex non-identifiable models using simple surrogates. PLoS Comput Biol 2023; 19:e1010844. [PMID: 36662831 PMCID: PMC9891533 DOI: 10.1371/journal.pcbi.1010844] [Citation(s) in RCA: 7] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/07/2022] [Revised: 02/01/2023] [Accepted: 12/26/2022] [Indexed: 01/22/2023] Open
Abstract
An enduring challenge in computational biology is to balance data quality and quantity with model complexity. Tools such as identifiability analysis and information criterion have been developed to harmonise this juxtaposition, yet cannot always resolve the mismatch between available data and the granularity required in mathematical models to answer important biological questions. Often, it is only simple phenomenological models, such as the logistic and Gompertz growth models, that are identifiable from standard experimental measurements. To draw insights from complex, non-identifiable models that incorporate key biological mechanisms of interest, we study the geometry of a map in parameter space from the complex model to a simple, identifiable, surrogate model. By studying how non-identifiable parameters in the complex model quantitatively relate to identifiable parameters in surrogate, we introduce and exploit a layer of interpretation between the set of non-identifiable parameters and the goodness-of-fit metric or likelihood studied in typical identifiability analysis. We demonstrate our approach by analysing a hierarchy of mathematical models for multicellular tumour spheroid growth experiments. Typical data from tumour spheroid experiments are limited and noisy, and corresponding mathematical models are very often made arbitrarily complex. Our geometric approach is able to predict non-identifiabilities, classify non-identifiable parameter spaces into identifiable parameter combinations that relate to features in the data characterised by parameters in a surrogate model, and overall provide additional biological insight from complex non-identifiable models.
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Affiliation(s)
- Alexander P. Browning
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
- QUT Centre for Data Science, Queensland University of Technology, Brisbane, Australia
- Mathematical Institute, University of Oxford, Oxford, United Kingdom
| | - Matthew J. Simpson
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
- QUT Centre for Data Science, Queensland University of Technology, Brisbane, Australia
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