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García-Astrain C, Henriksen-Lacey M, Lenzi E, Renero-Lecuna C, Langer J, Piñeiro P, Molina-Martínez B, Plou J, Jimenez de Aberasturi D, Liz-Marzán LM. A Scaffold-Assisted 3D Cancer Cell Model for Surface-Enhanced Raman Scattering-Based Real-Time Sensing and Imaging. ACS NANO 2024; 18:11257-11269. [PMID: 38632933 PMCID: PMC11064228 DOI: 10.1021/acsnano.4c00543] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/12/2024] [Revised: 04/02/2024] [Accepted: 04/09/2024] [Indexed: 04/19/2024]
Abstract
Despite recent advances in the development of scaffold-based three-dimensional (3D) cell models, challenges persist in imaging and monitoring cell behavior within these complex structures due to their heterogeneous cell distribution and geometries. Incorporating sensors into 3D scaffolds provides a potential solution for real-time, in situ sensing and imaging of biological processes such as cell growth and disease development. We introduce a 3D printed hydrogel-based scaffold capable of supporting both surface-enhanced Raman scattering (SERS) biosensing and imaging of 3D breast cancer cell models. The scaffold incorporates plasmonic nanoparticles and SERS tags, for sensing and imaging, respectively. We demonstrate the scaffold's adaptability and modularity in supporting breast cancer spheroids, thereby enabling spatial and temporal monitoring of tumor evolution.
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Affiliation(s)
- Clara García-Astrain
- CIC
biomaGUNE, Basque Research and Technology Alliance (BRTA), 20014 Donostia-San
Sebastián, Spain
- Centro
de Investigación Biomédica en Red, Bioingeniería,
Biomateriales y Nanomedicina (CIBER-BBN), 20014 Donostia-San Sebastián, Spain
| | - Malou Henriksen-Lacey
- CIC
biomaGUNE, Basque Research and Technology Alliance (BRTA), 20014 Donostia-San
Sebastián, Spain
- Centro
de Investigación Biomédica en Red, Bioingeniería,
Biomateriales y Nanomedicina (CIBER-BBN), 20014 Donostia-San Sebastián, Spain
| | - Elisa Lenzi
- CIC
biomaGUNE, Basque Research and Technology Alliance (BRTA), 20014 Donostia-San
Sebastián, Spain
| | - Carlos Renero-Lecuna
- CIC
biomaGUNE, Basque Research and Technology Alliance (BRTA), 20014 Donostia-San
Sebastián, Spain
- Cinbio,
University of Vigo, 36310 Vigo, Spain
| | - Judith Langer
- CIC
biomaGUNE, Basque Research and Technology Alliance (BRTA), 20014 Donostia-San
Sebastián, Spain
| | - Paula Piñeiro
- CIC
biomaGUNE, Basque Research and Technology Alliance (BRTA), 20014 Donostia-San
Sebastián, Spain
- Department
of Applied Chemistry, University of the
Basque Country (UPV-EHU), 20018 Donostia-San Sebastián, Spain
| | - Beatriz Molina-Martínez
- CIC
biomaGUNE, Basque Research and Technology Alliance (BRTA), 20014 Donostia-San
Sebastián, Spain
| | - Javier Plou
- CIC
biomaGUNE, Basque Research and Technology Alliance (BRTA), 20014 Donostia-San
Sebastián, Spain
| | - Dorleta Jimenez de Aberasturi
- CIC
biomaGUNE, Basque Research and Technology Alliance (BRTA), 20014 Donostia-San
Sebastián, Spain
- Centro
de Investigación Biomédica en Red, Bioingeniería,
Biomateriales y Nanomedicina (CIBER-BBN), 20014 Donostia-San Sebastián, Spain
- Ikerbasque,
Basque Foundation for Science, 48009 Bilbao, Spain
| | - Luis M. Liz-Marzán
- CIC
biomaGUNE, Basque Research and Technology Alliance (BRTA), 20014 Donostia-San
Sebastián, Spain
- Centro
de Investigación Biomédica en Red, Bioingeniería,
Biomateriales y Nanomedicina (CIBER-BBN), 20014 Donostia-San Sebastián, Spain
- Cinbio,
University of Vigo, 36310 Vigo, Spain
- Ikerbasque,
Basque Foundation for Science, 48009 Bilbao, Spain
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2
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Ciavolella G, Ferrand N, Sabbah M, Perthame B, Natalini R. A Model for Membrane Degradation Using a Gelatin Invadopodia Assay. Bull Math Biol 2024; 86:30. [PMID: 38347328 DOI: 10.1007/s11538-024-01260-w] [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: 07/11/2023] [Accepted: 01/15/2024] [Indexed: 02/15/2024]
Abstract
One of the most crucial and lethal characteristics of solid tumors is represented by the increased ability of cancer cells to migrate and invade other organs during the so-called metastatic spread. This is allowed thanks to the production of matrix metalloproteinases (MMPs), enzymes capable of degrading a type of collagen abundant in the basal membrane separating the epithelial tissue from the connective one. In this work, we employ a synergistic experimental and mathematical modelling approach to explore the invasion process of tumor cells. A mathematical model composed of reaction-diffusion equations describing the evolution of the tumor cells density on a gelatin substrate, MMPs enzymes concentration and the degradation of the gelatin is proposed. This is completed with a calibration strategy. We perform a sensitivity analysis and explore a parameter estimation technique both on synthetic and experimental data in order to find the optimal parameters that describe the in vitro experiments. A comparison between numerical and experimental solutions ends the work.
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Affiliation(s)
- Giorgia Ciavolella
- Inria Centre de l'Université de Bordeaux, Institut de Mathématiques de Bordeaux, CNRS UMR 5251, 351 cours de la Libération, 33405, Talence Cedex, France.
| | - Nathalie Ferrand
- Sorbonne Université Cancer Biology and Therapeutics, INSERM, CNRS, Institut Universitaire de Cancérologie, Saint- Antoine Research Center (CRSA), 75012, Paris, France
| | - Michéle Sabbah
- Sorbonne Université Cancer Biology and Therapeutics, INSERM, CNRS, Institut Universitaire de Cancérologie, Saint- Antoine Research Center (CRSA), 75012, Paris, France
| | - Benoît Perthame
- Sorbonne Université, Inria, Université de Paris, Laboratoire Jacques-Louis Lions, UMR7598, 4 place Jussieu, 75005, Paris, France
| | - Roberto Natalini
- Istituto per le Applicazioni del Calcolo 'M.Picone', Rome, Italy
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Villa C, Gerisch A, Chaplain MAJ. A novel nonlocal partial differential equation model of endothelial progenitor cell cluster formation during the early stages of vasculogenesis. J Theor Biol 2022; 534:110963. [PMID: 34838584 DOI: 10.1016/j.jtbi.2021.110963] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2021] [Revised: 11/03/2021] [Accepted: 11/12/2021] [Indexed: 11/18/2022]
Abstract
The formation of new vascular networks is essential for tissue development and regeneration, in addition to playing a key role in pathological settings such as ischemia and tumour development. Experimental findings in the past two decades have led to the identification of a new mechanism of neovascularisation, known as cluster-based vasculogenesis, during which endothelial progenitor cells (EPCs) mobilised from the bone marrow are capable of bridging distant vascular beds in a variety of hypoxic settings in vivo. This process is characterised by the formation of EPC clusters during its early stages and, while much progress has been made in identifying various mechanisms underlying cluster formation, we are still far from a comprehensive description of such spatio-temporal dynamics. In order to achieve this, we propose a novel mathematical model of the early stages of cluster-based vasculogenesis, comprising of a system of nonlocal partial differential equations including key mechanisms such as endogenous chemotaxis, matrix degradation, cell proliferation and cell-to-cell adhesion. We conduct a linear stability analysis on the system and solve the equations numerically. We then conduct a parametric analysis of the numerical solutions of the one-dimensional problem to investigate the role of underlying dynamics on the speed of cluster formation and the size of clusters, measured via appropriate metrics for the cluster width and compactness. We verify the key results of the parametric analysis with simulations of the two-dimensional problem. Our results, which qualitatively compare with data from in vitro experiments, elucidate the complementary role played by endogenous chemotaxis and matrix degradation in the formation of clusters, suggesting chemotaxis is responsible for the cluster topology while matrix degradation is responsible for the speed of cluster formation. Our results also indicate that the nonlocal cell-to-cell adhesion term in our model, even though it initially causes cells to aggregate, is not sufficient to ensure clusters are stable over long time periods. Consequently, new modelling strategies for cell-to-cell adhesion are required to stabilise in silico clusters. We end the paper with a thorough discussion of promising, fruitful future modelling and experimental research perspectives.
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Affiliation(s)
- Chiara Villa
- School of Mathematics and Statistics, University of St Andrews, St Andrews KY16 9SS, UK.
| | - Alf Gerisch
- Fachbereich Mathematik, Technische Universität Darmstadt, Dolivostr. 15, 64293 Darmstadt, Germany
| | - Mark A J Chaplain
- School of Mathematics and Statistics, University of St Andrews, St Andrews KY16 9SS, UK
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Aldurayhim A, Elsonbaty A, Elsadany AA. Dynamics of diffusive modified Previte-Hoffman food web model. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2020; 17:4225-4256. [PMID: 32987577 DOI: 10.3934/mbe.2020234] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
This paper formulates and analyzes a modified Previte-Hoffman food web with mixed functional responses. We investigate the existence, uniqueness, positivity and boundedness of the proposed model's solutions. The asymptotic local and global stability of the steady states are discussed. Analytical study of the proposed model reveals that it can undergo supercritical Hopf bifurcation. Furthermore, analysis of Turing instability in spatiotemporal version of the model is carried out where regions of pattern creation in parameters space are obtained. Using detailed numerical simulations for the diffusive and non-diffusive cases, the theoretical findings are verified for distinct sets of parameters.
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Affiliation(s)
- A Aldurayhim
- Mathematics Department, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj, Saudi Arabia
| | - A Elsonbaty
- Mathematics Department, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj, Saudi Arabia
- Department of Engineering Mathematics and Physics, Faculty of Engineering, Mansoura University, Mansoura 35516, Egypt
| | - A A Elsadany
- Mathematics Department, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj, Saudi Arabia
- Department of Basic Science, Faculty of Computers and Informatics, Suez Canal University, Ismailia 41522, Egypt
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Bubba F, Lorenzi T, Macfarlane FR. From a discrete model of chemotaxis with volume-filling to a generalized Patlak-Keller-Segel model. Proc Math Phys Eng Sci 2020; 476:20190871. [PMID: 32523414 DOI: 10.1098/rspa.2019.0871] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/02/2020] [Accepted: 04/02/2020] [Indexed: 12/26/2022] Open
Abstract
We present a discrete model of chemotaxis whereby cells responding to a chemoattractant are seen as individual agents whose movement is described through a set of rules that result in a biased random walk. In order to take into account possible alterations in cellular motility observed at high cell densities (i.e. volume-filling), we let the probabilities of cell movement be modulated by a decaying function of the cell density. We formally show that a general form of the celebrated Patlak-Keller-Segel (PKS) model of chemotaxis can be formally derived as the appropriate continuum limit of this discrete model. The family of steady-state solutions of such a generalized PKS model are characterized and the conditions for the emergence of spatial patterns are studied via linear stability analysis. Moreover, we carry out a systematic quantitative comparison between numerical simulations of the discrete model and numerical solutions of the corresponding PKS model, both in one and in two spatial dimensions. The results obtained indicate that there is excellent quantitative agreement between the spatial patterns produced by the two models. Finally, we numerically show that the outcomes of the two models faithfully replicate those of the classical PKS model in a suitable asymptotic regime.
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Affiliation(s)
- Federica Bubba
- Sorbonne Universités, Universités Paris-Diderot, Laboratoire Jacques-Louis Lions, 75005 Paris, France
| | - Tommaso Lorenzi
- School of Mathematics and Statistics, University of St Andrews, St Andrews KY16 9SS, UK.,Department of Mathematical Sciences 'G. L. Lagrange', Dipartimento di Eccellenza 2018-2022, Politecnico di Torino, 10129 Torino, Italy
| | - Fiona R Macfarlane
- School of Mathematics and Statistics, University of St Andrews, St Andrews KY16 9SS, UK
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Agosti A, Marchesi S, Scita G, Ciarletta P. Modelling cancer cell budding in-vitro as a self-organised, non-equilibrium growth process. J Theor Biol 2020; 492:110203. [DOI: 10.1016/j.jtbi.2020.110203] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/20/2019] [Revised: 02/09/2020] [Accepted: 02/12/2020] [Indexed: 10/25/2022]
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7
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Adenis L, Gontran E, Deroulers C, Grammaticos B, Juchaux M, Seksek O, Badoual M. Experimental and modeling study of the formation of cell aggregates with differential substrate adhesion. PLoS One 2020; 15:e0222371. [PMID: 32023245 PMCID: PMC7001941 DOI: 10.1371/journal.pone.0222371] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2019] [Accepted: 12/05/2019] [Indexed: 12/20/2022] Open
Abstract
The study of cell aggregation in vitro has a tremendous importance these days. In cancer biology, aggregates and spheroids serve as model systems and are considered as pseudo-tumors that are more realistic than 2D cell cultures. Recently, in the context of brain tumors (gliomas), we developed a new poly(ethylene glycol) (PEG)-based hydrogel, with adhesive properties that can be controlled by the addition of poly(L-lysine) (PLL), and a stiffness close to the brain’s. This substrate allows the motion of individual cells and the formation of cell aggregates (within one day), and we showed that on a non-adhesive substrate (PEG without PLL is inert for cells), the aggregates are bigger and less numerous than on an adhesive substrate (with PLL). In this article, we present new experimental results on the follow-up of the formation of aggregates on our hydrogels, from the early stages (individual cells) to the late stages (aggregate compaction), in order to compare, for two cell lines (F98 and U87), the aggregation process on the adhesive and non-adhesive substrates. We first show that a spaceless model of perikinetic aggregation can reproduce the experimental evolution of the number of aggregates, but not of the mean area of the aggregates. We thus develop a minimal off-lattice agent-based model, with a few simple rules reproducing the main processes that are at stack during aggregation. Our spatial model can reproduce very well the experimental temporal evolution of both the number of aggregates and their mean area, on adhesive and non-adhesive soft gels and for the two different cell lines. From the fit of the experimental data, we were able to infer the quantitative values of the speed of motion of each cell line, its rate of proliferation in aggregates and its ability to organize in 3D. We also found qualitative differences between the two cell lines regarding the ability of aggregates to compact. These parameters could be inferred for any cell line, and correlated with clinical properties such as aggressiveness and invasiveness.
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Affiliation(s)
- Léo Adenis
- CNRS UMR 8165, Laboratoire IMNC, Univ Paris-Sud, Univ Paris Diderot, 91405 Orsay, France
| | - Emilie Gontran
- ICPH Interactions Cellulaires et Physiopathologie Hépatique, UMR S 1174 INSERM, Univ Paris-Sud, 91405 Orsay, France
| | - Christophe Deroulers
- Univ Paris Diderot, Laboratoire IMNC, UMR 8165 CNRS, Univ Paris-Sud, 91405 Orsay, France
| | - Basile Grammaticos
- CNRS UMR 8165, Laboratoire IMNC, Univ Paris-Sud, Univ Paris Diderot, 91405 Orsay, France
| | - Marjorie Juchaux
- CNRS UMR 8165, Laboratoire IMNC, Univ Paris-Sud, Univ Paris Diderot, 91405 Orsay, France
| | - Olivier Seksek
- CNRS UMR 8165, Laboratoire IMNC, Univ Paris-Sud, Univ Paris Diderot, 91405 Orsay, France
| | - Mathilde Badoual
- Univ Paris Diderot, Laboratoire IMNC, UMR 8165 CNRS, Univ Paris-Sud, 91405 Orsay, France
- * E-mail:
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