1
|
Chiang H, Chung CA. Simulation of Soluble and Bound VEGF-stimulated in vitro Capillary-like Network Formation on Deformed Substrate. PLoS Comput Biol 2024; 20:e1012281. [PMID: 39038038 PMCID: PMC11262697 DOI: 10.1371/journal.pcbi.1012281] [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: 12/08/2023] [Accepted: 06/26/2024] [Indexed: 07/24/2024] Open
Abstract
Capillary plexus cultivation is crucial in tissue engineering and regenerative medicine. Theoretical simulations have been conducted to supplement the expensive experimental works. However, the mechanisms connecting mechanical and chemical stimuli remained undefined, and the functions of the different VEGF forms in the culture environment were still unclear. In this paper, we developed a hybrid model for simulating short-term in vitro capillary incubations. We used the Cellular Potts model to predict individual cell migration, morphology change, and continuum mechanics to quantify biogel deformation and VEGF transport dynamics. By bridging the mechanical regulation and chemical stimulation in the model, the results showed good agreement between the predicted network topology and experiments, in which elongated cells connected, forming the network cords and round cells gathered, creating cobblestone-like aggregates. The results revealed that the capillary-like networks could develop in high integrity only when the mechanical and chemical couplings worked adequately, with the cell morphology and haptotaxis driven by the soluble and bound forms of VEGF, respectively, functioning simultaneously.
Collapse
Affiliation(s)
- Hsun Chiang
- Department of Mechanical Engineering, National Central University, Taoyuan, Taiwan
| | - Chih-Ang Chung
- Department of Mechanical Engineering, National Central University, Taoyuan, Taiwan
| |
Collapse
|
2
|
Al-Badri G, Phillips JB, Shipley RJ, Ovenden NC. Formation of vascular-like structures using a chemotaxis-driven multiphase model. Math Biosci 2024; 372:109183. [PMID: 38554855 DOI: 10.1016/j.mbs.2024.109183] [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: 11/28/2023] [Revised: 03/18/2024] [Accepted: 03/21/2024] [Indexed: 04/02/2024]
Abstract
We propose a continuum model for pattern formation, based on the multiphase model framework, to explore in vitro cell patterning within an extracellular matrix (ECM). We demonstrate that, within this framework, chemotaxis-driven cell migration can lead to the formation of cell clusters and vascular-like structures in 1D and 2D respectively. The influence on pattern formation of additional mechanisms commonly included in multiphase tissue models, including cell-matrix traction, contact inhibition, and cell-cell aggregation, are also investigated. Using sensitivity analysis, the relative impact of each model parameter on the simulation outcomes is assessed to identify the key parameters involved. Chemoattractant-matrix binding is further included, motivated by previous experimental studies, and found to reduce the spatial scale of patterning to within a biologically plausible range for capillary structures. Key findings from the in-depth parameter analysis of the 1D models, both with and without chemoattractant-matrix binding, are demonstrated to translate well to the 2D model, obtaining vascular-like cell patterning for multiple parameter regimes. Overall, we demonstrate a biologically-motivated multiphase model capable of generating long-term pattern formation on a biologically plausible spatial scale both in 1D and 2D, with applications for modelling in vitro vascular network formation.
Collapse
Affiliation(s)
- Georgina Al-Badri
- Department of Mathematics, University College London, London, UK; Centre for Nerve Engineering, University College London, London, UK.
| | - James B Phillips
- Centre for Nerve Engineering, University College London, London, UK; Department of Pharmacology, University College London, London, UK
| | - Rebecca J Shipley
- Centre for Nerve Engineering, University College London, London, UK; Department of Mechanical Engineering, University College London, London, UK
| | - Nicholas C Ovenden
- Department of Mathematics, University College London, London, UK; Centre for Nerve Engineering, University College London, London, UK
| |
Collapse
|
3
|
Crossley RM, Johnson S, Tsingos E, Bell Z, Berardi M, Botticelli M, Braat QJS, Metzcar J, Ruscone M, Yin Y, Shuttleworth R. Modeling the extracellular matrix in cell migration and morphogenesis: a guide for the curious biologist. Front Cell Dev Biol 2024; 12:1354132. [PMID: 38495620 PMCID: PMC10940354 DOI: 10.3389/fcell.2024.1354132] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2023] [Accepted: 02/12/2024] [Indexed: 03/19/2024] Open
Abstract
The extracellular matrix (ECM) is a highly complex structure through which biochemical and mechanical signals are transmitted. In processes of cell migration, the ECM also acts as a scaffold, providing structural support to cells as well as points of potential attachment. Although the ECM is a well-studied structure, its role in many biological processes remains difficult to investigate comprehensively due to its complexity and structural variation within an organism. In tandem with experiments, mathematical models are helpful in refining and testing hypotheses, generating predictions, and exploring conditions outside the scope of experiments. Such models can be combined and calibrated with in vivo and in vitro data to identify critical cell-ECM interactions that drive developmental and homeostatic processes, or the progression of diseases. In this review, we focus on mathematical and computational models of the ECM in processes such as cell migration including cancer metastasis, and in tissue structure and morphogenesis. By highlighting the predictive power of these models, we aim to help bridge the gap between experimental and computational approaches to studying the ECM and to provide guidance on selecting an appropriate model framework to complement corresponding experimental studies.
Collapse
Affiliation(s)
- Rebecca M. Crossley
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, United Kingdom
| | - Samuel Johnson
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, United Kingdom
| | - Erika Tsingos
- Computational Developmental Biology Group, Institute of Biodynamics and Biocomplexity, Utrecht University, Utrecht, Netherlands
| | - Zoe Bell
- Northern Institute for Cancer Research, Newcastle University, Newcastle upon Tyne, United Kingdom
| | - Massimiliano Berardi
- LaserLab, Department of Physics and Astronomy, Vrije Universiteit Amsterdam, Amsterdam, Netherlands
- Optics11 life, Amsterdam, Netherlands
| | | | - Quirine J. S. Braat
- Department of Applied Physics and Science Education, Eindhoven University of Technology, Eindhoven, Netherlands
| | - John Metzcar
- Department of Intelligent Systems Engineering, Indiana University, Bloomington, IN, United States
- Department of Informatics, Indiana University, Bloomington, IN, United States
| | | | - Yuan Yin
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, United Kingdom
| | | |
Collapse
|
4
|
Karperien AL, Jelinek HF. ImageJ in Computational Fractal-Based Neuroscience: Pattern Extraction and Translational Research. ADVANCES IN NEUROBIOLOGY 2024; 36:795-814. [PMID: 38468064 DOI: 10.1007/978-3-031-47606-8_40] [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: 03/13/2024]
Abstract
To explore questions asked in neuroscience, neuroscientists rely heavily on the tools available. One such toolset is ImageJ, open-source, free, biological digital image analysis software. Open-source software has matured alongside of fractal analysis in neuroscience, and today ImageJ is not a niche but a foundation relied on by a substantial number of neuroscientists for work in diverse fields including fractal analysis. This is largely owing to two features of open-source software leveraged in ImageJ and vital to vigorous neuroscience: customizability and collaboration. With those notions in mind, this chapter's aim is threefold: (1) it introduces ImageJ, (2) it outlines ways this software tool has influenced fractal analysis in neuroscience and shaped the questions researchers devote time to, and (3) it reviews a few examples of ways investigators have developed and used ImageJ for pattern extraction in fractal analysis. Throughout this chapter, the focus is on fostering a collaborative and creative mindset for translating knowledge of the fractal geometry of the brain into clinical reality.
Collapse
Affiliation(s)
| | - Herbert F Jelinek
- Department of Medical Sciences and Biotechnology Center, Khalifa University, Abu Dhabi, UAE
| |
Collapse
|
5
|
Alamoudi E, Schälte Y, Müller R, Starruß J, Bundgaard N, Graw F, Brusch L, Hasenauer J. FitMultiCell: simulating and parameterizing computational models of multi-scale and multi-cellular processes. Bioinformatics 2023; 39:btad674. [PMID: 37947308 PMCID: PMC10666203 DOI: 10.1093/bioinformatics/btad674] [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: 02/21/2023] [Revised: 10/25/2023] [Accepted: 11/07/2023] [Indexed: 11/12/2023] Open
Abstract
MOTIVATION Biological tissues are dynamic and highly organized. Multi-scale models are helpful tools to analyse and understand the processes determining tissue dynamics. These models usually depend on parameters that need to be inferred from experimental data to achieve a quantitative understanding, to predict the response to perturbations, and to evaluate competing hypotheses. However, even advanced inference approaches such as approximate Bayesian computation (ABC) are difficult to apply due to the computational complexity of the simulation of multi-scale models. Thus, there is a need for a scalable pipeline for modeling, simulating, and parameterizing multi-scale models of multi-cellular processes. RESULTS Here, we present FitMultiCell, a computationally efficient and user-friendly open-source pipeline that can handle the full workflow of modeling, simulating, and parameterizing for multi-scale models of multi-cellular processes. The pipeline is modular and integrates the modeling and simulation tool Morpheus and the statistical inference tool pyABC. The easy integration of high-performance infrastructure allows to scale to computationally expensive problems. The introduction of a novel standard for the formulation of parameter inference problems for multi-scale models additionally ensures reproducibility and reusability. By applying the pipeline to multiple biological problems, we demonstrate its broad applicability, which will benefit in particular image-based systems biology. AVAILABILITY AND IMPLEMENTATION FitMultiCell is available open-source at https://gitlab.com/fitmulticell/fit.
Collapse
Affiliation(s)
- Emad Alamoudi
- Life and Medical Sciences Institute, University of Bonn, Bonn 53113, Germany
| | - Yannik Schälte
- Life and Medical Sciences Institute, University of Bonn, Bonn 53113, Germany
- Institute of Computational Biology, Helmholtz Zentrum München—German Research Center for Environmental Health, Neuherberg 85764, Germany
- Center for Mathematics, Chair of Mathematical Modeling of Biological Systems, Technische Universität München, Garching 85748, Germany
| | - Robert Müller
- Center of Information Services and High Performance Computing (ZIH), Technische Universität Dresden, Dresden 01062, Germany
| | - Jörn Starruß
- Center of Information Services and High Performance Computing (ZIH), Technische Universität Dresden, Dresden 01062, Germany
| | - Nils Bundgaard
- BioQuant—Center for Quantitative Biology, Heidelberg University, Heidelberg 69120, Germany
| | - Frederik Graw
- BioQuant—Center for Quantitative Biology, Heidelberg University, Heidelberg 69120, Germany
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Heidelberg 69120, Germany
- Department of Medicine 5, Friedrich-Alexander-University Erlangen-Nürnberg, Erlangen 91054, Germany
| | - Lutz Brusch
- Center of Information Services and High Performance Computing (ZIH), Technische Universität Dresden, Dresden 01062, Germany
| | - Jan Hasenauer
- Life and Medical Sciences Institute, University of Bonn, Bonn 53113, Germany
- Institute of Computational Biology, Helmholtz Zentrum München—German Research Center for Environmental Health, Neuherberg 85764, Germany
- Center for Mathematics, Chair of Mathematical Modeling of Biological Systems, Technische Universität München, Garching 85748, Germany
| |
Collapse
|
6
|
Dallinga MG, Habani YI, Schimmel AWM, Dallinga-Thie GM, van Noorden CJF, Klaassen I, Schlingemann RO. The Role of Heparan Sulfate and Neuropilin 2 in VEGFA Signaling in Human Endothelial Tip Cells and Non-Tip Cells during Angiogenesis In Vitro. Cells 2021; 10:cells10040926. [PMID: 33923753 PMCID: PMC8073389 DOI: 10.3390/cells10040926] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/31/2020] [Revised: 04/01/2021] [Accepted: 04/13/2021] [Indexed: 12/17/2022] Open
Abstract
During angiogenesis, vascular endothelial growth factor A (VEGFA) regulates endothelial cell (EC) survival, tip cell formation, and stalk cell proliferation via VEGF receptor 2 (VEGFR2). VEGFR2 can interact with VEGFR2 co-receptors such as heparan sulfate proteoglycans (HSPGs) and neuropilin 2 (NRP2), but the exact roles of these co-receptors, or of sulfatase 2 (SULF2), an enzyme that removes sulfate groups from HSPGs and inhibits HSPG-mediated uptake of very low density lipoprotein (VLDL), in angiogenesis and tip cell biology are unknown. In the present study, we investigated whether the modulation of binding of VEGFA to VEGFR2 by knockdown of SULF2 or NRP2 affects sprouting angiogenesis, tip cell formation, proliferation of non-tip cells, and EC survival, or uptake of VLDL. To this end, we employed VEGFA splice variant 121, which lacks an HSPG binding domain, and VEGFA splice variant 165, which does have this domain, in in vitro models of angiogenic tip cells and vascular sprouting. We conclude that VEGFA165 and VEGFA121 have similar inducing effects on tip cells and sprouting in vitro, and that the binding of VEGFA165 to HSPGs in the extracellular matrix does not seem to play a role, as knockdown of SULF2 did not alter these effects. Co-binding of NRP2 appears to regulate VEGFA–VEGFR2-induced sprout initiation, but not tip cell formation. Finally, as the addition of VLDL increased sprout formation but not tip cell formation, and as VLDL uptake was limited to non-tip cells, our findings suggest that VLDL plays a role in sprout formation by providing biomass for stalk cell proliferation.
Collapse
Affiliation(s)
- Marchien G. Dallinga
- Ocular Angiogenesis Group, Departments of Ophthalmology and Medical Biology, Amsterdam Cardiovascular Sciences, Cancer Center Amsterdam, Amsterdam UMC, University of Amsterdam, Meibergdreef 15, 1105 AZ Amsterdam, The Netherlands; (M.G.D.); (Y.I.H.); (C.J.F.v.N.); (R.O.S.)
| | - Yasmin I. Habani
- Ocular Angiogenesis Group, Departments of Ophthalmology and Medical Biology, Amsterdam Cardiovascular Sciences, Cancer Center Amsterdam, Amsterdam UMC, University of Amsterdam, Meibergdreef 15, 1105 AZ Amsterdam, The Netherlands; (M.G.D.); (Y.I.H.); (C.J.F.v.N.); (R.O.S.)
| | - Alinda W. M. Schimmel
- Department of Experimental Vascular Medicine, Amsterdam UMC, University of Amsterdam, Meibergdreef 15, 1105 AZ Amsterdam, The Netherlands; (A.W.M.S.); (G.M.D.-T.)
| | - Geesje M. Dallinga-Thie
- Department of Experimental Vascular Medicine, Amsterdam UMC, University of Amsterdam, Meibergdreef 15, 1105 AZ Amsterdam, The Netherlands; (A.W.M.S.); (G.M.D.-T.)
| | - Cornelis J. F. van Noorden
- Ocular Angiogenesis Group, Departments of Ophthalmology and Medical Biology, Amsterdam Cardiovascular Sciences, Cancer Center Amsterdam, Amsterdam UMC, University of Amsterdam, Meibergdreef 15, 1105 AZ Amsterdam, The Netherlands; (M.G.D.); (Y.I.H.); (C.J.F.v.N.); (R.O.S.)
- Department of Genetic Toxicology and Cancer Biology, National Institute of Biology, Večna pot 111, 1000 Ljubljana, Slovenia
| | - Ingeborg Klaassen
- Ocular Angiogenesis Group, Departments of Ophthalmology and Medical Biology, Amsterdam Cardiovascular Sciences, Cancer Center Amsterdam, Amsterdam UMC, University of Amsterdam, Meibergdreef 15, 1105 AZ Amsterdam, The Netherlands; (M.G.D.); (Y.I.H.); (C.J.F.v.N.); (R.O.S.)
- Correspondence:
| | - Reinier O. Schlingemann
- Ocular Angiogenesis Group, Departments of Ophthalmology and Medical Biology, Amsterdam Cardiovascular Sciences, Cancer Center Amsterdam, Amsterdam UMC, University of Amsterdam, Meibergdreef 15, 1105 AZ Amsterdam, The Netherlands; (M.G.D.); (Y.I.H.); (C.J.F.v.N.); (R.O.S.)
- Department of Ophthalmology, University of Lausanne, Jules Gonin Eye Hospital, Fondation Asile des Aveugles, Avenue de France 15, 1004 Lausanne, Switzerland
| |
Collapse
|
7
|
Information Processing in the Brain as Optimal Entropy Transport: A Theoretical Approach. ENTROPY 2020; 22:e22111231. [PMID: 33287001 PMCID: PMC7712441 DOI: 10.3390/e22111231] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/09/2020] [Revised: 10/14/2020] [Accepted: 10/15/2020] [Indexed: 01/20/2023]
Abstract
We consider brain activity from an information theoretic perspective. We analyze the information processing in the brain, considering the optimality of Shannon entropy transport using the Monge–Kantorovich framework. It is proposed that some of these processes satisfy an optimal transport of informational entropy condition. This optimality condition allows us to derive an equation of the Monge–Ampère type for the information flow that accounts for the branching structure of neurons via the linearization of this equation. Based on this fact, we discuss a version of Murray’s law in this context.
Collapse
|
8
|
Yuan Y, Basu S, Lin MH, Shukla S, Sarkar D. Colloidal Gels for Guiding Endothelial Cell Organization via Microstructural Morphology. ACS APPLIED MATERIALS & INTERFACES 2019; 11:31709-31728. [PMID: 31403768 PMCID: PMC7219539 DOI: 10.1021/acsami.9b11293] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/07/2023]
Abstract
One of the fundamental challenges in vascular morphogenesis is to understand how the microstructural morphology of a 3D matrix can provide the spatial cues to organize the endothelial cells (ECs) into specific vascular structures. Colloidal gels can provide well-controlled distinct morphological matrices because these gels are formed by the aggregation of particles. By altering the aggregation mode, the spatial organization of the particles can be controlled to yield different microstructural morphology. To demonstrate this, colloidal aggregates and gels were developed by electrostatic interaction-mediated aggregation of cationic polyurethane (PU) colloidal particles by using low molecular weight electrolyte and polyelectrolyte to develop microstructurally different colloidal gels without altering their bulk elasticity. Compact dense colloidal aggregates with constricted voids were developed via electrolyte-mediated aggregation, whereas stranded branched networks with interconnected voids were formed via polyelectrolyte-mediated bridging interactions. Results show that the microstructure of aggregated colloids and gels can regulate EC organizations. Within endothelial matrices, ECs track the microstructure of particulate phase to interconnect with stranded colloidal network but cluster around compact colloidal aggregate. Similarly, in colloidal gels, ECs formed capillary-like structures by interconnecting along the stranded networks with enhanced cell-matrix interactions and increased cell extension but aggregated within the constricted voids of compact dense gel with enhanced cell-cell interaction. Both morphometric analysis and expression of EC markers corroborated the cell organizations in these gels. Using these colloidal gels, we demonstrated the role of 3D microstructural morphology as an important regulator for spatial guidance of ECs and simultaneously established the significance of colloidal gels as 3D matrix to regulate cellular morphogenesis.
Collapse
Affiliation(s)
- Yuan Yuan
- Department of Biomedical Engineering, University at Buffalo, The State University of New York, Buffalo, NY 14260, USA
| | - Sukanya Basu
- Department of Pharmacology and Therapeutics, Roswell Park Comprehensive Cancer Center, Buffalo, NY 14263, USA
| | - Meng Huisan Lin
- Department of Biomedical Engineering, University at Buffalo, The State University of New York, Buffalo, NY 14260, USA
| | - Shruti Shukla
- Department of Biomedical Engineering, University at Buffalo, The State University of New York, Buffalo, NY 14260, USA
| | - Debanjan Sarkar
- Department of Biomedical Engineering, University at Buffalo, The State University of New York, Buffalo, NY 14260, USA
- Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, NY 14260, USA
- Correspondence to: D. Sarkar. Biomedical Engineering, University at Buffalo, Ph: 716-645-8497, Fax: 716-645-2207,
| |
Collapse
|
9
|
Abstract
The complexity of morphogenesis poses a fundamental challenge to understanding the mechanisms governing the formation of biological patterns and structures. Over the past century, numerous processes have been identified as critically contributing to morphogenetic events, but the interplay between the various components and aspects of pattern formation have been much harder to grasp. The combination of traditional biology with mathematical and computational methods has had a profound effect on our current understanding of morphogenesis and led to significant insights and advancements in the field. In particular, the theoretical concepts of reaction–diffusion systems and positional information, proposed by Alan Turing and Lewis Wolpert, respectively, dramatically influenced our general view of morphogenesis, although typically in isolation from one another. In recent years, agent-based modeling has been emerging as a consolidation and implementation of the two theories within a single framework. Agent-based models (ABMs) are unique in their ability to integrate combinations of heterogeneous processes and investigate their respective dynamics, especially in the context of spatial phenomena. In this review, we highlight the benefits and technical challenges associated with ABMs as tools for examining morphogenetic events. These models display unparalleled flexibility for studying various morphogenetic phenomena at multiple levels and have the important advantage of informing future experimental work, including the targeted engineering of tissues and organs.
Collapse
|
10
|
Kühn C, Checa S. Computational Modeling to Quantify the Contributions of VEGFR1, VEGFR2, and Lateral Inhibition in Sprouting Angiogenesis. Front Physiol 2019; 10:288. [PMID: 30971939 PMCID: PMC6445957 DOI: 10.3389/fphys.2019.00288] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/27/2018] [Accepted: 03/05/2019] [Indexed: 12/25/2022] Open
Abstract
Sprouting angiogenesis is a necessary process in regeneration and development as well as in tumorigenesis. VEGF-A is the main pro-angiogenic chemoattractant and it can bind to the decoy receptor VEGFR1 or to VEGFR2 to induce sprouting. Active sprout cells express Dll4, which binds to Notch1 on neighboring cells, in turn inhibiting VEGFR2 expression. It is known that the balance between VEGFR2 and VEGFR1 determines tip selection and network architecture, however the quantitative interrelationship of the receptors and their interrelated balances, also with relation to Dll4-Notch1 signaling, remains yet largely unknown. Here, we present an agent-based computer model of sprouting angiogenesis, integrating VEGFR1 and VEGFR2 in a detailed model of cellular signaling. Our model reproduces experimental data on VEGFR1 knockout. We show that soluble VEGFR1 improves the efficiency of angiogenesis by directing sprouts away from existing cells over a wide range of parameters. Our analysis unravels the relevance of the stability of the active notch intracellular domain as a dominating hub in this regulatory network. Our analysis quantitatively dissects the regulatory interactions in sprouting angiogenesis. Because we use a detailed model of intracellular signaling, the results of our analysis are directly linked to biological entities. We provide our computational model and simulation engine for integration in complementary modeling approaches.
Collapse
Affiliation(s)
- Clemens Kühn
- Julius Wolff Institute, Charite - Universitätsmedizin Berlin, Berlin, Germany
| | - Sara Checa
- Julius Wolff Institute, Charite - Universitätsmedizin Berlin, Berlin, Germany.,Berlin-Brandenburg School for Regenerative Therapies, Charite - UIniversitätsmedizin Berlin, Berlin, Germany
| |
Collapse
|
11
|
Lakatos D, Somfai E, Méhes E, Czirók A. Soluble VEGFR1 signaling guides vascular patterns into dense branching morphologies. J Theor Biol 2018; 456:261-278. [PMID: 30086288 PMCID: PMC6292526 DOI: 10.1016/j.jtbi.2018.08.005] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2018] [Revised: 08/01/2018] [Accepted: 08/03/2018] [Indexed: 01/27/2023]
Abstract
Vascular patterning is a key process during development and disease. The diffusive decoy receptor sVEGFR1 (sFlt1) is a known regulator of endothelial cell behavior, yet the mechanism by which it controls vascular structure is little understood. We propose computational models to shed light on how vascular patterning is guided by self-organized gradients of the VEGF/sVEGFR1 factors. We demonstrate that a diffusive inhibitor can generate structures with a dense branching morphology in models where the activator elicits directed growth. Inadequate presence of the inhibitor leads to compact growth, while excessive production of the inhibitor blocks expansion and stabilizes existing structures. Model predictions were compared with time-resolved experimental data obtained from endothelial sprout kinetics in fibrin gels. In the presence of inhibitory antibodies against VEGFR1 vascular sprout density increases while the speed of sprout expansion remains unchanged. Thus, the rate of secretion and stability of extracellular sVEGFR1 can modulate vascular sprout density.
Collapse
Affiliation(s)
- Dóra Lakatos
- Department of Biological Physics, Eötvös Loránd University, Budapest, Hungary.
| | - Ellák Somfai
- Institute for Solid State Physics and Optics, Wigner Research Center for Physics, Hungarian Academy of Sciences, Budapest, Hungary
| | - Előd Méhes
- Department of Biological Physics, Eötvös Loránd University, Budapest, Hungary
| | - András Czirók
- Department of Biological Physics, Eötvös Loránd University, Budapest, Hungary; Department of Anatomy & Cell Biology, University of Kansas Medical Center, Kansas City, KS, USA.
| |
Collapse
|
12
|
Ramos JRD, Travasso R, Carvalho J. Capillary network formation from dispersed endothelial cells: Influence of cell traction, cell adhesion, and extracellular matrix rigidity. Phys Rev E 2018; 97:012408. [PMID: 29448490 DOI: 10.1103/physreve.97.012408] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/25/2017] [Indexed: 11/07/2022]
Abstract
The formation of a functional vascular network depends on biological, chemical, and physical processes being extremely well coordinated. Among them, the mechanical properties of the extracellular matrix and cell adhesion are fundamental to achieve a functional network of endothelial cells, able to fully cover a required domain. By the use of a Cellular Potts Model and Finite Element Method it is shown that there exists a range of values of endothelial traction forces, cell-cell adhesion, and matrix rigidities where the network can spontaneously be formed, and its properties are characterized. We obtain the analytical relation that the minimum traction force required for cell network formation must obey. This minimum value for the traction force is approximately independent on the considered cell number and cell-cell adhesion. We quantify how these two parameters influence the morphology of the resulting networks (size and number of meshes).
Collapse
Affiliation(s)
- João R D Ramos
- Centro de Física da Universidade de Coimbra, CFisUC, 3007-516 Coimbra, Portugal.,Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany
| | - Rui Travasso
- Centro de Física da Universidade de Coimbra, CFisUC, 3007-516 Coimbra, Portugal
| | - João Carvalho
- Centro de Física da Universidade de Coimbra, CFisUC, 3007-516 Coimbra, Portugal
| |
Collapse
|
13
|
Boas SEM, Carvalho J, van den Broek M, Weijers EM, Goumans MJ, Koolwijk P, Merks RMH. A local uPAR-plasmin-TGFβ1 positive feedback loop in a qualitative computational model of angiogenic sprouting explains the in vitro effect of fibrinogen variants. PLoS Comput Biol 2018; 14:e1006239. [PMID: 29979675 PMCID: PMC6072121 DOI: 10.1371/journal.pcbi.1006239] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2017] [Revised: 08/02/2018] [Accepted: 05/28/2018] [Indexed: 11/19/2022] Open
Abstract
In experimental assays of angiogenesis in three-dimensional fibrin matrices, a temporary scaffold formed during wound healing, the type and composition of fibrin impacts the level of sprouting. More sprouts form on high molecular weight (HMW) than on low molecular weight (LMW) fibrin. It is unclear what mechanisms regulate the number and the positions of the vascular-like structures in cell cultures. To address this question, we propose a mechanistic simulation model of endothelial cell migration and fibrin proteolysis by the plasmin system. The model is a hybrid, cell-based and continuum, computational model based on the cellular Potts model and sets of partial-differential equations. Based on the model results, we propose that a positive feedback mechanism between uPAR, plasmin and transforming growth factor β1 (TGFβ1) selects cells in the monolayer for matrix invasion. Invading cells releases TGFβ1 from the extracellular matrix through plasmin-mediated fibrin degradation. The activated TGFβ1 further stimulates fibrin degradation and keeps proteolysis active as the sprout invades the fibrin matrix. The binding capacity for TGFβ1 of LMW is reduced relative to that of HMW. This leads to reduced activation of proteolysis and, consequently, reduced cell ingrowth in LMW fibrin compared to HMW fibrin. Thus our model predicts that endothelial cells in LMW fibrin matrices compared to HMW matrices show reduced sprouting due to a lower bio-availability of TGFβ1. Therapies for a range of medical conditions, including cancer, wound healing and diabetic retinopathy can benefit from a better control over the growth of blood vessels. The chemical properties of fibrin, the material that forms scabs in wounds and can also occur in large concentrations in tumors, can regulate the degree of blood vessel growth (angiogenesis). Angiogenesis can be mimicked in cell cultures. These allow us to modulate the chemical properties of fibrin and study the effect on angiogenesis. Fibrin occurs in high molecular weight (HMW) and in low molecular weight (LMW) forms. Interestingly, there is more ingrowth of angiogenic-like structures into HMW than in LMW fibrin, but the mechanisms are poorly understood. To get more insight into these, we constructed a computational model. Using the model, we propose and analyse a hypothetical mechanism for sprouting that could explain the differences in endothelial cell sprouting in LMW and HMW fibrin matrices. Our model suggests that cells digest fibrin, thus creating space for ingrowth. At the same time, digestion frees growth factors bound to fibrin, that activates further secretion of digestive enzymes by the cells. We propose that the resulting positive feedback loop spontaneously selects cells in the endothelial monolayer for ingrowth and helps the blood vessel sprout move deeper into the fibrin. This could be a complementary mechanism to lateral-inhibition by Delta-Notch for the selection of leader cells, also called ‘tip cells’. Our model predicts that endothelial cells in LMW fibrin compared to HMW fibrin show reduced sprouting due to a lower bio-availability of TGFβ1.
Collapse
Affiliation(s)
- Sonja E. M. Boas
- Centrum Wiskunde & Informatica (CWI), Amsterdam, The Netherlands
- Mathematical Institute, Leiden University, Leiden, The Netherlands
| | - Joao Carvalho
- Centrum Wiskunde & Informatica (CWI), Amsterdam, The Netherlands
- CFisUC, Department of Physics, University of Coimbra, Coimbra, Portugal
| | - Marloes van den Broek
- Amsterdam Cardiovascular Sciences, VU University medical Center, Dept. of Physiology, Amsterdam, The Netherlands
| | - Ester M. Weijers
- Amsterdam Cardiovascular Sciences, VU University medical Center, Dept. of Physiology, Amsterdam, The Netherlands
| | - Marie-José Goumans
- Department of Cell and Chemical Biology, Leiden University Medical Center, Leiden, The Netherlands
| | - Pieter Koolwijk
- Amsterdam Cardiovascular Sciences, VU University medical Center, Dept. of Physiology, Amsterdam, The Netherlands
| | - Roeland M. H. Merks
- Centrum Wiskunde & Informatica (CWI), Amsterdam, The Netherlands
- Mathematical Institute, Leiden University, Leiden, The Netherlands
- * E-mail:
| |
Collapse
|
14
|
Alves AP, Mesquita ON, Gómez-Gardeñes J, Agero U. Graph analysis of cell clusters forming vascular networks. ROYAL SOCIETY OPEN SCIENCE 2018; 5:171592. [PMID: 29657767 PMCID: PMC5882691 DOI: 10.1098/rsos.171592] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/09/2017] [Accepted: 01/02/2018] [Indexed: 05/07/2023]
Abstract
This manuscript describes the experimental observation of vasculogenesis in chick embryos by means of network analysis. The formation of the vascular network was observed in the area opaca of embryos from 40 to 55 h of development. In the area opaca endothelial cell clusters self-organize as a primitive and approximately regular network of capillaries. The process was observed by bright-field microscopy in control embryos and in embryos treated with Bevacizumab (Avastin®), an antibody that inhibits the signalling of the vascular endothelial growth factor (VEGF). The sequence of images of the vascular growth were thresholded, and used to quantify the forming network in control and Avastin-treated embryos. This characterization is made by measuring vessels density, number of cell clusters and the largest cluster density. From the original images, the topology of the vascular network was extracted and characterized by means of the usual network metrics such as: the degree distribution, average clustering coefficient, average short path length and assortativity, among others. This analysis allows to monitor how the largest connected cluster of the vascular network evolves in time and provides with quantitative evidence of the disruptive effects that Avastin has on the tree structure of vascular networks.
Collapse
Affiliation(s)
- A. P. Alves
- Departamento de Física, Universidade Federal de Minas Gerais- 31270-901 Belo Horizonte, MG, Brazil
- Author for correspondence: A. P. Alves e-mail:
| | - O. N. Mesquita
- Departamento de Física, Universidade Federal de Minas Gerais- 31270-901 Belo Horizonte, MG, Brazil
| | - J. Gómez-Gardeñes
- Departamento de Física de la Materia Condensada, Universidad de Zaragoza, 50009 Zaragoza, Spain
- GOTHAM Lab, Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza, 50018 Zaragoza, Spain
| | - U. Agero
- Departamento de Física, Universidade Federal de Minas Gerais- 31270-901 Belo Horizonte, MG, Brazil
| |
Collapse
|
15
|
Sasaki D, Nakajima H, Yamaguchi Y, Yokokawa R, Ei SI, Miura T. Mathematical modeling for meshwork formation of endothelial cells in fibrin gels. J Theor Biol 2017. [PMID: 28648563 DOI: 10.1016/j.jtbi.2017.06.012] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Abstract
Vasculogenesis is the earliest process in development for spontaneous formation of a primitive capillary network from endothelial progenitor cells. When human umbilical vein endothelial cells (HUVECs) are cultured on Matrigel, they spontaneously form a network structure which is widely used as an in vitro model of vasculogenesis. Previous studies indicated that chemotaxis or gel deformation was involved in spontaneous pattern formation. In our study, we analyzed the mechanism of vascular pattern formation using a different system, meshwork formation by HUVECs embedded in fibrin gels. Unlike the others, this experimental system resulted in a perfusable endothelial network in vitro. We quantitatively observed the dynamics of endothelial cell protrusion and developed a mathematical model for one-dimensional dynamics. We then extended the one-dimensional model to two-dimensions. The model showed that random searching by endothelial cells was sufficient to generate the observed network structure in fibrin gels.
Collapse
Affiliation(s)
- Daiki Sasaki
- Department of Anatomy and Cell Biology, Kyushu University Graduate School of Medicine, Fukuoka, Japan
| | - Hitomi Nakajima
- Department of Biomedical Science,Kyushu University Faculty of Medicine, Fukuoka, Japan
| | - Yoshimi Yamaguchi
- Department of Anatomy and Cell Biology, Kyushu University Graduate School of Medicine, Fukuoka, Japan
| | - Ryuji Yokokawa
- Department of Micro Engineering, Kyoto University, Kyoto, Japan
| | - Shin-Ichiro Ei
- Department of Mathematics, Hokkaido University, Hokkaido, Japan
| | - Takashi Miura
- Department of Anatomy and Cell Biology, Kyushu University Graduate School of Medicine, Fukuoka, Japan
| |
Collapse
|
16
|
Hirashima T, Rens EG, Merks RMH. Cellular Potts modeling of complex multicellular behaviors in tissue morphogenesis. Dev Growth Differ 2017; 59:329-339. [DOI: 10.1111/dgd.12358] [Citation(s) in RCA: 54] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/13/2017] [Accepted: 03/24/2017] [Indexed: 12/14/2022]
Affiliation(s)
- Tsuyoshi Hirashima
- Institute for Frontier Life and Medical Sciences Kyoto University 53 Kawahara, Shogoin, Sakyo‐ku Kyoto 606‐8507 Japan
| | - Elisabeth G. Rens
- Centrum Wiskunde & Informatica Life Sciences Group Science Park 123 1098 XG Amsterdam the Netherlands
- Mathematical Institute Leiden University Niels Bohrweg 1 2333 CA Leiden the Netherlands
| | - Roeland M. H. Merks
- Centrum Wiskunde & Informatica Life Sciences Group Science Park 123 1098 XG Amsterdam the Netherlands
- Mathematical Institute Leiden University Niels Bohrweg 1 2333 CA Leiden the Netherlands
| |
Collapse
|
17
|
Boas SEM, Merks RMH. Tip cell overtaking occurs as a side effect of sprouting in computational models of angiogenesis. BMC SYSTEMS BIOLOGY 2015; 9:86. [PMID: 26589386 PMCID: PMC4654812 DOI: 10.1186/s12918-015-0230-7] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/04/2015] [Accepted: 11/10/2015] [Indexed: 11/10/2022]
Abstract
BACKGROUND During angiogenesis, the formation of new blood vessels from existing ones, endothelial cells differentiate into tip and stalk cells, after which one tip cell leads the sprout. More recently, this picture has changed. It has become clear that endothelial cells compete for the tip position during angiogenesis: a phenomenon named tip cell overtaking. The biological function of tip cell overtaking is not yet known. From experimental observations, it is unclear to what extent tip cell overtaking is a side effect of sprouting or to what extent it is regulated through a VEGF-Dll4-Notch signaling network and thus might have a biological function. To address this question, we studied tip cell overtaking in computational models of angiogenic sprouting in absence and in presence of VEGF-Dll4-Notch signaling. RESULTS We looked for tip cell overtaking in two existing Cellular Potts models of angiogenesis. In these simulation models angiogenic sprouting-like behavior emerges from a small set of plausible cell behaviors. In the first model, cells aggregate through contact-inhibited chemotaxis. In the second model the endothelial cells assume an elongated shape and aggregate through (non-inhibited) chemotaxis. In both these sprouting models the endothelial cells spontaneously migrate forwards and backwards within sprouts, suggesting that tip cell overtaking might occur as a side effect of sprouting. In accordance with other experimental observations, in our simulations the cells' tendency to occupy the tip position can be regulated when two cell lines with different levels of Vegfr2 expression are contributing to sprouting (mosaic sprouting assay), where cell behavior is regulated by a simple VEGF-Dll4-Notch signaling network. CONCLUSIONS Our modeling results suggest that tip cell overtaking can occur spontaneously due to the stochastic motion of cells during sprouting. Thus, tip cell overtaking and sprouting dynamics may be interdependent and should be studied and interpreted in combination. VEGF-Dll4-Notch can regulate the ability of cells to occupy the tip cell position in our simulations. We propose that the function of VEGF-Dll4-Notch signaling might not be to regulate which cell ends up at the tip, but to assure that the cell that randomly ends up at the tip position acquires the tip cell phenotype.
Collapse
Affiliation(s)
- Sonja E M Boas
- Life Sciences, Centrum Wiskunde & Informatica (CWI), Science Park 123, 1098 XG, Amsterdam, The Netherlands.
- Mathematical Institute, Leiden University, Niels Bohrweg 1, 2333 CA, Leiden, The Netherlands.
| | - Roeland M H Merks
- Life Sciences, Centrum Wiskunde & Informatica (CWI), Science Park 123, 1098 XG, Amsterdam, The Netherlands.
- Mathematical Institute, Leiden University, Niels Bohrweg 1, 2333 CA, Leiden, The Netherlands.
| |
Collapse
|
18
|
A cellular Potts model analyzing differentiated cell behavior during in vivo vascularization of a hypoxic tissue. Comput Biol Med 2015; 63:143-56. [DOI: 10.1016/j.compbiomed.2015.05.020] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2015] [Revised: 05/25/2015] [Accepted: 05/26/2015] [Indexed: 02/07/2023]
|
19
|
Abstract
Swarming or collective motion of living entities is one of the most common and spectacular manifestations of living systems that have been extensively studied in recent years. A number of general principles have been established. The interactions at the level of cells are quite different from those among individual animals, therefore the study of collective motion of cells is likely to reveal some specific important features which we plan to overview in this paper. In addition to presenting the most appealing results from the quickly growing related literature we also deliver a critical discussion of the emerging picture and summarize our present understanding of collective motion at the cellular level. Collective motion of cells plays an essential role in a number of experimental and real-life situations. In most cases the coordinated motion is a helpful aspect of the given phenomenon and results in making a related process more efficient (e.g., embryogenesis or wound healing), while in the case of tumor cell invasion it appears to speed up the progression of the disease. In these mechanisms cells both have to be motile and adhere to one another, the adherence feature being the most specific to this sort of collective behavior. One of the central aims of this review is to present the related experimental observations and treat them in light of a few basic computational models so as to make an interpretation of the phenomena at a quantitative level as well.
Collapse
Affiliation(s)
- Előd Méhes
- Department of Biological Physics, Eötvös University, Budapest, Hungary.
| | | |
Collapse
|
20
|
|
21
|
Daub JT, Merks RMH. Cell-based computational modeling of vascular morphogenesis using Tissue Simulation Toolkit. Methods Mol Biol 2015; 1214:67-127. [PMID: 25468600 DOI: 10.1007/978-1-4939-1462-3_6] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Computational modeling has become a widely used tool for unraveling the mechanisms of higher level cooperative cell behavior during vascular morphogenesis. However, experimenting with published simulation models or adding new assumptions to those models can be daunting for novice and even for experienced computational scientists. Here, we present a step-by-step, practical tutorial for building cell-based simulations of vascular morphogenesis using the Tissue Simulation Toolkit (TST). The TST is a freely available, open-source C++ library for developing simulations with the two-dimensional cellular Potts model, a stochastic, agent-based framework to simulate collective cell behavior. We will show the basic use of the TST to simulate and experiment with published simulations of vascular network formation. Then, we will present step-by-step instructions and explanations for building a recent simulation model of tumor angiogenesis. Demonstrated mechanisms include cell-cell adhesion, chemotaxis, cell elongation, haptotaxis, and haptokinesis.
Collapse
Affiliation(s)
- Josephine T Daub
- Institute of Ecology and Evolution, University of Bern, Bern, Switzerland
| | | |
Collapse
|
22
|
van Oers RFM, Rens EG, LaValley DJ, Reinhart-King CA, Merks RMH. Mechanical cell-matrix feedback explains pairwise and collective endothelial cell behavior in vitro. PLoS Comput Biol 2014; 10:e1003774. [PMID: 25121971 PMCID: PMC4133044 DOI: 10.1371/journal.pcbi.1003774] [Citation(s) in RCA: 97] [Impact Index Per Article: 9.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/05/2013] [Accepted: 06/20/2014] [Indexed: 12/14/2022] Open
Abstract
In vitro cultures of endothelial cells are a widely used model system of the collective behavior of endothelial cells during vasculogenesis and angiogenesis. When seeded in an extracellular matrix, endothelial cells can form blood vessel-like structures, including vascular networks and sprouts. Endothelial morphogenesis depends on a large number of chemical and mechanical factors, including the compliancy of the extracellular matrix, the available growth factors, the adhesion of cells to the extracellular matrix, cell-cell signaling, etc. Although various computational models have been proposed to explain the role of each of these biochemical and biomechanical effects, the understanding of the mechanisms underlying in vitro angiogenesis is still incomplete. Most explanations focus on predicting the whole vascular network or sprout from the underlying cell behavior, and do not check if the same model also correctly captures the intermediate scale: the pairwise cell-cell interactions or single cell responses to ECM mechanics. Here we show, using a hybrid cellular Potts and finite element computational model, that a single set of biologically plausible rules describing (a) the contractile forces that endothelial cells exert on the ECM, (b) the resulting strains in the extracellular matrix, and (c) the cellular response to the strains, suffices for reproducing the behavior of individual endothelial cells and the interactions of endothelial cell pairs in compliant matrices. With the same set of rules, the model also reproduces network formation from scattered cells, and sprouting from endothelial spheroids. Combining the present mechanical model with aspects of previously proposed mechanical and chemical models may lead to a more complete understanding of in vitro angiogenesis.
Collapse
Affiliation(s)
- René F. M. van Oers
- Life Sciences group, Centrum Wiskunde & Informatica, Amsterdam, The Netherlands
- Netherlands Consortium for System Biology - Netherlands Institute for Systems Biology, Amsterdam, The Netherlands
| | - Elisabeth G. Rens
- Life Sciences group, Centrum Wiskunde & Informatica, Amsterdam, The Netherlands
- Netherlands Consortium for System Biology - Netherlands Institute for Systems Biology, Amsterdam, The Netherlands
| | - Danielle J. LaValley
- Department of Biomedical Engineering, Cornell University, Ithaca, New York, United States of America
| | - Cynthia A. Reinhart-King
- Department of Biomedical Engineering, Cornell University, Ithaca, New York, United States of America
| | - Roeland M. H. Merks
- Life Sciences group, Centrum Wiskunde & Informatica, Amsterdam, The Netherlands
- Netherlands Consortium for System Biology - Netherlands Institute for Systems Biology, Amsterdam, The Netherlands
- Mathematical Institute, Leiden University, Leiden, The Netherlands
| |
Collapse
|
23
|
Starruß J, de Back W, Brusch L, Deutsch A. Morpheus: a user-friendly modeling environment for multiscale and multicellular systems biology. ACTA ACUST UNITED AC 2014; 30:1331-2. [PMID: 24443380 PMCID: PMC3998129 DOI: 10.1093/bioinformatics/btt772] [Citation(s) in RCA: 163] [Impact Index Per Article: 16.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023]
Abstract
Summary: Morpheus is a modeling environment for the simulation and integration of cell-based models with ordinary differential equations and reaction-diffusion systems. It allows rapid development of multiscale models in biological terms and mathematical expressions rather than programming code. Its graphical user interface supports the entire workflow from model construction and simulation to visualization, archiving and batch processing. Availability and implementation: Binary packages are available at http://imc.zih.tu-dresden.de/wiki/morpheus for Linux, Mac OSX and MS Windows. Contact:walter.deback@tu-dresden.de Supplementary information:Supplementary data are available at Bioinformatics online.
Collapse
Affiliation(s)
- Jörn Starruß
- Center for Information Services and High Performance Computing, Technische Universität Dresden, 01062 Dresden, Germany
| | | | | | | |
Collapse
|
24
|
Köhn-Luque A, de Back W, Yamaguchi Y, Yoshimura K, Herrero MA, Miura T. Dynamics of VEGF matrix-retention in vascular network patterning. Phys Biol 2013; 10:066007. [DOI: 10.1088/1478-3975/10/6/066007] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
|
25
|
Scianna M, Bell C, Preziosi L. A review of mathematical models for the formation of vascular networks. J Theor Biol 2013; 333:174-209. [DOI: 10.1016/j.jtbi.2013.04.037] [Citation(s) in RCA: 108] [Impact Index Per Article: 9.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/14/2012] [Revised: 02/15/2013] [Accepted: 04/30/2013] [Indexed: 02/08/2023]
|
26
|
Czirok A. Endothelial cell motility, coordination and pattern formation during vasculogenesis. WILEY INTERDISCIPLINARY REVIEWS-SYSTEMS BIOLOGY AND MEDICINE 2013; 5:587-602. [PMID: 23857825 DOI: 10.1002/wsbm.1233] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2012] [Revised: 05/24/2013] [Accepted: 05/28/2013] [Indexed: 01/13/2023]
Abstract
How vascular networks assemble is a fundamental problem of developmental biology that also has medical importance. To explain the organizational principles behind vascular patterning, we must understand how can tissue level structures be controlled through cell behavior patterns like motility and adhesion that, in turn, are determined by biochemical signal transduction processes? We discuss the various ideas that have been proposed as mechanisms for vascular network assembly: cell motility guided by extracellular matrix alignment (contact guidance), chemotaxis guided by paracrine and autocrine morphogens, and multicellular sprouting guided by cell-cell contacts. All of these processes yield emergent patterns, thus endothelial cells can form an interconnected structure autonomously, without guidance from an external pre-pattern.
Collapse
Affiliation(s)
- Andras Czirok
- Department of Anatomy and Cell Biology, University of Kansas Medical Center, Kansas City, KS, USA; Department of Biological Physics, Eötvös Loránd University, Budapest, Hungary
| |
Collapse
|
27
|
Kleinstreuer N, Dix D, Rountree M, Baker N, Sipes N, Reif D, Spencer R, Knudsen T. A computational model predicting disruption of blood vessel development. PLoS Comput Biol 2013; 9:e1002996. [PMID: 23592958 PMCID: PMC3616981 DOI: 10.1371/journal.pcbi.1002996] [Citation(s) in RCA: 89] [Impact Index Per Article: 8.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2012] [Accepted: 01/24/2013] [Indexed: 11/18/2022] Open
Abstract
Vascular development is a complex process regulated by dynamic biological networks that vary in topology and state across different tissues and developmental stages. Signals regulating de novo blood vessel formation (vasculogenesis) and remodeling (angiogenesis) come from a variety of biological pathways linked to endothelial cell (EC) behavior, extracellular matrix (ECM) remodeling and the local generation of chemokines and growth factors. Simulating these interactions at a systems level requires sufficient biological detail about the relevant molecular pathways and associated cellular behaviors, and tractable computational models that offset mathematical and biological complexity. Here, we describe a novel multicellular agent-based model of vasculogenesis using the CompuCell3D (http://www.compucell3d.org/) modeling environment supplemented with semi-automatic knowledgebase creation. The model incorporates vascular endothelial growth factor signals, pro- and anti-angiogenic inflammatory chemokine signals, and the plasminogen activating system of enzymes and proteases linked to ECM interactions, to simulate nascent EC organization, growth and remodeling. The model was shown to recapitulate stereotypical capillary plexus formation and structural emergence of non-coded cellular behaviors, such as a heterologous bridging phenomenon linking endothelial tip cells together during formation of polygonal endothelial cords. Molecular targets in the computational model were mapped to signatures of vascular disruption derived from in vitro chemical profiling using the EPA's ToxCast high-throughput screening (HTS) dataset. Simulating the HTS data with the cell-agent based model of vascular development predicted adverse effects of a reference anti-angiogenic thalidomide analog, 5HPP-33, on in vitro angiogenesis with respect to both concentration-response and morphological consequences. These findings support the utility of cell agent-based models for simulating a morphogenetic series of events and for the first time demonstrate the applicability of these models for predictive toxicology.
Collapse
Affiliation(s)
- Nicole Kleinstreuer
- National Center for Computational Toxicology, Office of Research and Development, U.S. Environmental Protection Agency, Research Triangle Park, North Carolina, United States of America
| | - David Dix
- National Center for Computational Toxicology, Office of Research and Development, U.S. Environmental Protection Agency, Research Triangle Park, North Carolina, United States of America
| | - Michael Rountree
- National Center for Computational Toxicology, Office of Research and Development, U.S. Environmental Protection Agency, Research Triangle Park, North Carolina, United States of America
| | - Nancy Baker
- Lockheed-Martin, Research Triangle Park, North Carolina, United States of America
| | - Nisha Sipes
- National Center for Computational Toxicology, Office of Research and Development, U.S. Environmental Protection Agency, Research Triangle Park, North Carolina, United States of America
| | - David Reif
- National Center for Computational Toxicology, Office of Research and Development, U.S. Environmental Protection Agency, Research Triangle Park, North Carolina, United States of America
| | - Richard Spencer
- Lockheed-Martin, Research Triangle Park, North Carolina, United States of America
| | - Thomas Knudsen
- National Center for Computational Toxicology, Office of Research and Development, U.S. Environmental Protection Agency, Research Triangle Park, North Carolina, United States of America
| |
Collapse
|
28
|
Daub JT, Merks RMH. A cell-based model of extracellular-matrix-guided endothelial cell migration during angiogenesis. Bull Math Biol 2013; 75:1377-99. [PMID: 23494144 PMCID: PMC3738846 DOI: 10.1007/s11538-013-9826-5] [Citation(s) in RCA: 59] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2012] [Accepted: 02/11/2013] [Indexed: 12/23/2022]
Abstract
Angiogenesis, the formation of new blood vessels sprouting from existing ones, occurs in several situations like wound healing, tissue remodeling, and near growing tumors. Under hypoxic conditions, tumor cells secrete growth factors, including VEGF. VEGF activates endothelial cells (ECs) in nearby vessels, leading to the migration of ECs out of the vessel and the formation of growing sprouts. A key process in angiogenesis is cellular self-organization, and previous modeling studies have identified mechanisms for producing networks and sprouts. Most theoretical studies of cellular self-organization during angiogenesis have ignored the interactions of ECs with the extra-cellular matrix (ECM), the jelly or hard materials that cells live in. Apart from providing structural support to cells, the ECM may play a key role in the coordination of cellular motility during angiogenesis. For example, by modifying the ECM, ECs can affect the motility of other ECs, long after they have left. Here, we present an explorative study of the cellular self-organization resulting from such ECM-coordinated cell migration. We show that a set of biologically-motivated, cell behavioral rules, including chemotaxis, haptotaxis, haptokinesis, and ECM-guided proliferation suffice for forming sprouts and branching vascular trees.
Collapse
Affiliation(s)
- Josephine T Daub
- Centrum Wiskunde & Informatica, Science Park 123, 1098 XG, Amsterdam, The Netherlands.
| | | |
Collapse
|
29
|
Palm MM, Merks RMH. Vascular networks due to dynamically arrested crystalline ordering of elongated cells. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:012725. [PMID: 23410377 DOI: 10.1103/physreve.87.012725] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/29/2012] [Revised: 12/29/2012] [Indexed: 06/01/2023]
Abstract
Recent experimental and theoretical studies suggest that crystallization and glass-like solidification are useful analogies for understanding cell ordering in confluent biological tissues. It remains unexplored how cellular ordering contributes to pattern formation during morphogenesis. With a computational model we show that a system of elongated, cohering biological cells can get dynamically arrested in a network pattern. Our model provides an explanation for the formation of cellular networks in culture systems that exclude intercellular interaction via chemotaxis or mechanical traction.
Collapse
|
30
|
Voss-Böhme A. Multi-scale modeling in morphogenesis: a critical analysis of the cellular Potts model. PLoS One 2012; 7:e42852. [PMID: 22984409 PMCID: PMC3439478 DOI: 10.1371/journal.pone.0042852] [Citation(s) in RCA: 39] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2012] [Accepted: 07/12/2012] [Indexed: 11/19/2022] Open
Abstract
Cellular Potts models (CPMs) are used as a modeling framework to elucidate mechanisms of biological development. They allow a spatial resolution below the cellular scale and are applied particularly when problems are studied where multiple spatial and temporal scales are involved. Despite the increasing usage of CPMs in theoretical biology, this model class has received little attention from mathematical theory. To narrow this gap, the CPMs are subjected to a theoretical study here. It is asked to which extent the updating rules establish an appropriate dynamical model of intercellular interactions and what the principal behavior at different time scales characterizes. It is shown that the longtime behavior of a CPM is degenerate in the sense that the cells consecutively die out, independent of the specific interdependence structure that characterizes the model. While CPMs are naturally defined on finite, spatially bounded lattices, possible extensions to spatially unbounded systems are explored to assess to which extent spatio-temporal limit procedures can be applied to describe the emergent behavior at the tissue scale. To elucidate the mechanistic structure of CPMs, the model class is integrated into a general multiscale framework. It is shown that the central role of the surface fluctuations, which subsume several cellular and intercellular factors, entails substantial limitations for a CPM's exploitation both as a mechanistic and as a phenomenological model.
Collapse
Affiliation(s)
- Anja Voss-Böhme
- Center for Information Services and High Performance Computing, Technical University Dresden, Dresden, Germany.
| |
Collapse
|
31
|
Czirok A, Little CD. Pattern formation during vasculogenesis. BIRTH DEFECTS RESEARCH. PART C, EMBRYO TODAY : REVIEWS 2012; 96:153-62. [PMID: 22692888 PMCID: PMC3465733 DOI: 10.1002/bdrc.21010] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
Vasculogenesis, the assembly of the first vascular network, is an intriguing developmental process that yields the first functional organ system of the embryo. In addition to being a fundamental part of embryonic development, vasculogenic processes also have medical importance. To explain the organizational principles behind vascular patterning, we must understand how morphogenesis of tissue level structures can be controlled through cell behavior patterns that, in turn, are determined by biochemical signal transduction processes. Mathematical analyses and computer simulations can help conceptualize how to bridge organizational levels and thus help in evaluating hypotheses regarding the formation of vascular networks. Here, we discuss the ideas that have been proposed to explain the formation of the first vascular pattern: cell motility guided by extracellular matrix alignment (contact guidance), chemotaxis guided by paracrine and autocrine morphogens, and sprouting guided by cell-cell contacts.
Collapse
Affiliation(s)
- Andras Czirok
- Department of Anatomy and Cell Biology, University of Kansas Medical Center, Kansas City, KS, USA.
| | | |
Collapse
|