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El Hajj W, El Khatib N, Volpert V. Inflammation propagation modeled as a reaction-diffusion wave. Math Biosci 2023; 365:109074. [PMID: 37689347 DOI: 10.1016/j.mbs.2023.109074] [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: 04/07/2023] [Revised: 08/28/2023] [Accepted: 08/29/2023] [Indexed: 09/11/2023]
Abstract
Inflammation is a physiological process aimed to protect the organism in various diseases and injuries. This work presents a generic inflammation model based on the reaction-diffusion equations for the concentrations of uninflamed cells, inflamed cells, immune cells and the inflammatory cytokines. The analysis of the model shows the existence of three different regimes of inflammation progression depending on the value of a parameter R called the inflammation number. If R>1, then inflammation propagates in cell culture or tissue as a reaction-diffusion wave due to diffusion of inflammatory cytokines produced by inflamed cells. If 0
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Affiliation(s)
- W El Hajj
- Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, 69622 Villeurbanne, France
| | - N El Khatib
- Department of Computer Science and Mathematics, Lebanese American University, P.O. Box 36, Byblos, Lebanon.
| | - V Volpert
- Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, 69622 Villeurbanne, France; Peoples' Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow 117198, Russian Federation
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2
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Yu Z, Sohail A, Arif R, Nutini A, Nofal TA, Tunc S. Modeling the crossover behavior of the bacterial infection with the COVID-19 epidemics. RESULTS IN PHYSICS 2022; 39:105774. [PMID: 35812469 PMCID: PMC9254571 DOI: 10.1016/j.rinp.2022.105774] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/19/2022] [Revised: 06/27/2022] [Accepted: 06/27/2022] [Indexed: 06/15/2023]
Abstract
To explore the crossover linkage of the bacterial infections resulting from the viral infection, within the host body, a computational framework is developed. It analyzes the additional pathogenic effect of Streptococcus pneumonia, one of the bacteria that can trigger the super-infection mechanism in the COVID-19 syndrome and the physiological effects of innate immunity for the control or eradication of this bacterial infection. The computational framework, in a novel manner, takes into account the action of pro-inflammatory and anti-inflammatory cytokines in response to the function of macrophages. A hypothetical model is created and is transformed to a system of non-dimensional mathematical equations. The dynamics of three main parameters (macrophages sensitivity κ , sensitivity to cytokines η and bacterial sensitivity ϵ ), analyzes a "threshold value" termed as the basic reproduction number R 0 which is based on a sub-model of the inflammatory state. Piece-wise differentiation approach is used and dynamical analysis for the inflammatory response of macrophages is studied in detail. The results shows that the inflamatory response, with high probability in bacterial super-infection, is concomitant with the COVID-19 infection. The mechanism of action of the anti-inflammatory cytokines is discussed during this research and it is observed that these cytokines do not prevent inflammation chronic, but only reduce its level while increasing the activation threshold of macrophages. The results of the model quantifies the probable deficit of the biological mechanisms linked with the anti-inflammatory cytokines. The numerical results shows that for such mechanisms, a minimal action of the pathogens is strongly amplified, resulting in the "chronicity" of the inflammatory process.
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Affiliation(s)
- Zhenhua Yu
- Institute of Systems Security and Control, College of Computer Science and Technology, Xi'an University of Science and Technology, Xi'an 710054, China
| | - Ayesha Sohail
- Department of Mathematics, Comsats University Islamabad, Lahore Campus, 54000, Pakistan
| | - Robia Arif
- Department of Mathematics, Comsats University Islamabad, Lahore Campus, 54000, Pakistan
| | - Alessandro Nutini
- Centro Studi Attività Motore - Biology and Biomechanics Dept., Via di tiglio 94 Lucca, Italy
| | - Taher A Nofal
- Department of Mathematics and Statistics, Faculty of Science, Taif University, Taif, Saudi Arabia
| | - Sümeyye Tunc
- Medipol University, Vocational School of Sciences, Physiotherapy Programme, Unkapanı, Atatürk Bulvarı, No:27, 34083, Halic Campus, Fatih-Istanbul, Turkey
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Nadin G, Ogier-Denis E, Toledo AI, Zaag H. A Turing mechanism in order to explain the patchy nature of Crohn's disease. J Math Biol 2021; 83:12. [PMID: 34223970 DOI: 10.1007/s00285-021-01635-w] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2020] [Revised: 04/22/2021] [Accepted: 06/14/2021] [Indexed: 11/24/2022]
Abstract
Crohn's disease is an inflammatory bowel disease (IBD) that is not well understood. In particular, unlike other IBDs, the inflamed parts of the intestine compromise deep layers of the tissue and are not continuous but separated and distributed through the whole gastrointestinal tract, displaying a patchy inflammatory pattern. In the present paper, we introduce a toy-model which might explain the appearance of such patterns. We consider a reaction-diffusion system involving bacteria and phagocyte and prove that, under certain conditions, this system might reproduce an activator-inhibitor dynamic leading to the occurrence of Turing-type instabilities. In other words, we prove the existence of stable stationary solutions that are spatially periodic and do not vanish in time. We also propose a set of parameters for which the system exhibits such phenomena and compare it with realistic parameters found in the literature. This is the first time, as far as we know, that a Turing pattern is investigated in inflammatory models.
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Affiliation(s)
- Grégoire Nadin
- Laboratoire Jaques-Louis Lions, Université Pierre et Marie Curie, Paris, France
| | - Eric Ogier-Denis
- Institut national de la santé et de la recherche médicale, Paris, France
| | - Ana I Toledo
- Laboratoire d'Analyse Géométrie et Applications, Université Sorbonne Paris Nord, Villetaneuse, France.
| | - Hatem Zaag
- Laboratoire d'Analyse Géométrie et Applications, Université Sorbonne Paris Nord, Villetaneuse, France
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Lahoz-Beltra R, Rodriguez RJ. Modeling a cancerous tumor development in a virtual patient suffering from a depressed state of mind: Simulation of somatic evolution with a customized genetic algorithm. Biosystems 2020; 198:104261. [DOI: 10.1016/j.biosystems.2020.104261] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2020] [Revised: 09/26/2020] [Accepted: 09/27/2020] [Indexed: 12/19/2022]
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Jarrett AM, Cogan NG. The ups and downs of S. aureus nasal carriage. MATHEMATICAL MEDICINE AND BIOLOGY-A JOURNAL OF THE IMA 2020; 36:157-177. [PMID: 29767719 DOI: 10.1093/imammb/dqy006] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/14/2017] [Accepted: 04/17/2018] [Indexed: 11/15/2022]
Abstract
Staphylococcus aureus infections are a growing concern worldwide due to the increasing number of strains that exhibit antibiotic resistance. Recent studies have indicated that some percentage of people carry the bacteria in the nasal cavity and therefore are at a higher risk of subsequent, and more serious, infections in other parts of the body. However, individuals carrying the infection can be classified as only intermittent carriers versus persistent carriers, being able to eliminate the bacteria and later colonized again. Using a model of bacterial colonization of the anterior nares, we investigate oscillatory patterns related to intermittent carriage of S. aureus. Following several studies using global sensitivity analysis techniques, various insights into the model's behaviour were made including interacting effects of the bacteria's growth rate and movement in the mucus, suggesting parameter connections associated with biofilm-like behaviour. Here the bacterial growth rate and bacterial movement are explicitly connected, leading to expanded oscillatory behaviour in the model. We suggest possible implications that this oscillatory behaviour can have on the definition of intermittent carriage and discuss differences in the bacterial virulence dependent upon individual host health. Furthermore, we show that connecting the bacterial growth and movement also expands the region of the parameter space for which the bacteria are able to survive and persist.
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Affiliation(s)
- Angela M Jarrett
- Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, USA
| | - Nicholas G Cogan
- Department of Mathematics, Academic Way, Florida State University, Tallahassee, USA
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Ottesen JT, Pedersen RK, Sajid Z, Gudmand-Hoeyer J, Bangsgaard KO, Skov V, Kjær L, Knudsen TA, Pallisgaard N, Hasselbalch HC, Andersen M. Bridging blood cancers and inflammation: The reduced Cancitis model. J Theor Biol 2019; 465:90-108. [PMID: 30615883 DOI: 10.1016/j.jtbi.2019.01.001] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/05/2018] [Revised: 12/11/2018] [Accepted: 01/02/2019] [Indexed: 11/28/2022]
Abstract
A novel mechanism-based model - the Cancitis model - describing the interaction of blood cancer and the inflammatory system is proposed, analyzed and validated. The immune response is divided into two components, one where the elimination rate of malignant stem cells is independent of the level of the blood cancer and one where the elimination rate depends on the level of the blood cancer. A dimensional analysis shows that the full 6-dimensional system of nonlinear ordinary differential equations may be reduced to a 2-dimensional system - the reduced Cancitis model - using Fenichel theory. The original 18 parameters appear in the reduced model in 8 groups of parameters. The reduced model is analyzed. Especially the steady states and their dependence on the exogenous inflammatory stimuli are analyzed. A semi-analytic investigation reveals the stability properties of the steady states. Finally, positivity of the system and the existence of an attracting trapping region in the positive octahedron guaranteeing global existence and uniqueness of solutions are proved. The possible topologies of the dynamical system are completely determined as having a Janus structure, where two qualitatively different topologies appear for different sets of parameters. To classify this Janus structure we propose a novel concept in blood cancer - a reproduction ratio R. It determines the topological structure depending on whether it is larger or smaller than a threshold value. Furthermore, it follows that inflammation, affected by the exogenous inflammatory stimulation, may determine the onset and development of blood cancers. The body may manage initial blood cancer as long as the self-renewal rate is not too high, but fails to manage it if an inflammation appears. Thus, inflammation may trigger and drive blood cancers. Finally, the mathematical analysis suggests novel treatment strategies and it is used to discuss the in silico effect of existing treatment, e.g. interferon-α or T-cell therapy, and the impact of malignant cells becoming resistant.
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Affiliation(s)
- Johnny T Ottesen
- Department of Science and Environment, Roskilde University, Denmark.
| | | | - Zamra Sajid
- Department of Science and Environment, Roskilde University, Denmark
| | | | | | - Vibe Skov
- Department of Hematology, Zealand University Hospital, University of Copenhagen, Denmark
| | - Lasse Kjær
- Department of Hematology, Zealand University Hospital, University of Copenhagen, Denmark
| | - Trine A Knudsen
- Department of Hematology, Zealand University Hospital, University of Copenhagen, Denmark
| | - Niels Pallisgaard
- Department of Hematology, Zealand University Hospital, University of Copenhagen, Denmark
| | - Hans C Hasselbalch
- Department of Hematology, Zealand University Hospital, University of Copenhagen, Denmark
| | - Morten Andersen
- Department of Science and Environment, Roskilde University, Denmark
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Andersen M, Sajid Z, Pedersen RK, Gudmand-Hoeyer J, Ellervik C, Skov V, Kjær L, Pallisgaard N, Kruse TA, Thomassen M, Troelsen J, Hasselbalch HC, Ottesen JT. Mathematical modelling as a proof of concept for MPNs as a human inflammation model for cancer development. PLoS One 2017; 12:e0183620. [PMID: 28859112 PMCID: PMC5578482 DOI: 10.1371/journal.pone.0183620] [Citation(s) in RCA: 42] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/16/2017] [Accepted: 08/08/2017] [Indexed: 12/15/2022] Open
Abstract
The chronic Philadelphia-negative myeloproliferative neoplasms (MPNs) are acquired stem cell neoplasms which ultimately may transform to acute myelogenous leukemia. Most recently, chronic inflammation has been described as an important factor for the development and progression of MPNs in the biological continuum from early cancer stage to the advanced myelofibrosis stage, the MPNs being described as "A Human Inflammation Model for Cancer Development". This novel concept has been built upon clinical, experimental, genomic, immunological and not least epidemiological studies. Only a few studies have described the development of MPNs by mathematical models, and none have addressed the role of inflammation for clonal evolution and disease progression. Herein, we aim at using mathematical modelling to substantiate the concept of chronic inflammation as an important trigger and driver of MPNs.The basics of the model describe the proliferation from stem cells to mature cells including mutations of healthy stem cells to become malignant stem cells. We include a simple inflammatory coupling coping with cell death and affecting the basic model beneath. First, we describe the system without feedbacks or regulatory interactions. Next, we introduce inflammatory feedback into the system. Finally, we include other feedbacks and regulatory interactions forming the inflammatory-MPN model. Using mathematical modeling, we add further proof to the concept that chronic inflammation may be both a trigger of clonal evolution and an important driving force for MPN disease progression. Our findings support intervention at the earliest stage of cancer development to target the malignant clone and dampen concomitant inflammation.
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Affiliation(s)
- Morten Andersen
- Department of Science and Environment, Roskilde University, Roskilde, Denmark
| | - Zamra Sajid
- Department of Science and Environment, Roskilde University, Roskilde, Denmark
| | - Rasmus K. Pedersen
- Department of Science and Environment, Roskilde University, Roskilde, Denmark
| | | | - Christina Ellervik
- Department of Laboratory Medicine at Boston Children’s Hospital, Boston, Massachusetts, United States of America
| | - Vibe Skov
- Department of Hematology, Zealand University Hospital, University of Copenhagen, Roskilde, Denmark
| | - Lasse Kjær
- Department of Hematology, Zealand University Hospital, University of Copenhagen, Roskilde, Denmark
| | - Niels Pallisgaard
- Department of Pathology, Zealand University Hospital, University of Copenhagen, Roskilde, Denmark
| | - Torben A. Kruse
- Department of Clinical Genetics, Odense University Hospital, Odense, Denmark
| | - Mads Thomassen
- Department of Clinical Genetics, Odense University Hospital, Odense, Denmark
| | - Jesper Troelsen
- Department of Science and Environment, Roskilde University, Roskilde, Denmark
| | - Hans Carl Hasselbalch
- Department of Hematology, Zealand University Hospital, University of Copenhagen, Roskilde, Denmark
| | - Johnny T. Ottesen
- Department of Science and Environment, Roskilde University, Roskilde, Denmark
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Baker M, Brook BS, Owen MR. Mathematical modelling of cytokines, MMPs and fibronectin fragments in osteoarthritic cartilage. J Math Biol 2017; 75:985-1024. [PMID: 28213682 PMCID: PMC5562782 DOI: 10.1007/s00285-017-1104-y] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2016] [Revised: 01/29/2017] [Indexed: 12/11/2022]
Abstract
Osteoarthritis (OA) is a degenerative disease which causes pain and stiffness in joints. OA progresses through excessive degradation of joint cartilage, eventually leading to significant joint degeneration and loss of function. Cytokines, a group of cell signalling proteins, present in raised concentrations in OA joints, can be classified into pro-inflammatory and anti-inflammatory groups. They mediate cartilage degradation through several mechanisms, primarily the up-regulation of matrix metalloproteinases (MMPs), a group of collagen-degrading enzymes. In this paper we show that the interactions of cytokines within cartilage have a crucial role to play in OA progression and treatment. We develop a four-variable ordinary differential equation model for the interactions between pro- and anti-inflammatory cytokines, MMPs and fibronectin fragments (Fn-fs), a by-product of cartilage degradation and up-regulator of cytokines. We show that the model has four classes of dynamic behaviour: homoeostasis, bistable inflammation, tristable inflammation and persistent inflammation. We show that positive and negative feedbacks controlling cytokine production rates can determine either a pre-disposition to OA or initiation of OA. Further, we show that manipulation of cytokine, MMP and Fn-fs levels can be used to treat OA, but we suggest that multiple treatment targets may be essential to halt or slow disease progression.
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Affiliation(s)
- Michelle Baker
- School of Computer Science, University of Nottingham, Nottingham, UK
| | - Bindi S. Brook
- Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, UK
| | - Markus R. Owen
- Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, UK
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11
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Lombardo MC, Barresi R, Bilotta E, Gargano F, Pantano P, Sammartino M. Demyelination patterns in a mathematical model of multiple sclerosis. J Math Biol 2016; 75:373-417. [DOI: 10.1007/s00285-016-1087-0] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2016] [Revised: 11/25/2016] [Indexed: 11/29/2022]
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12
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Dunster JL. The macrophage and its role in inflammation and tissue repair: mathematical and systems biology approaches. WILEY INTERDISCIPLINARY REVIEWS-SYSTEMS BIOLOGY AND MEDICINE 2015; 8:87-99. [PMID: 26459225 DOI: 10.1002/wsbm.1320] [Citation(s) in RCA: 40] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2015] [Revised: 08/25/2015] [Accepted: 08/28/2015] [Indexed: 02/05/2023]
Abstract
Macrophages are central to the inflammatory response and its ability to resolve effectively. They are complex cells that adopt a range of subtypes depending on the tissue type and stimulus that they find themselves under. This flexibility allows them to play multiple, sometimes opposing, roles in inflammation and tissue repair. Their central role in the inflammatory process is reflected in macrophage dysfunction being implicated in chronic inflammation and poorly healing wounds. In this study, we discuss recent attempts to model mathematically and computationally the macrophage and how it partakes in the complex processes of inflammation and tissue repair. There are increasing data describing the variety of macrophage phenotypes and their underlying transcriptional programs. Dynamic mathematical and computational models are an ideal way to test biological hypotheses against experimental data and could aid in understanding this multi-functional cell and its potential role as an attractive therapeutic target for inflammatory conditions and tissue repair.
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Affiliation(s)
- Joanne L Dunster
- Department of Mathematics and Statistics, University of Reading, Reading, UK.,Institute for Cardiovascular and Metabolic Research and School of Biological Sciences, University of Reading, Reading, UK
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13
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Global sensitivity analysis used to interpret biological experimental results. J Math Biol 2014; 71:151-70. [PMID: 25059426 DOI: 10.1007/s00285-014-0818-3] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2013] [Revised: 04/18/2014] [Indexed: 12/27/2022]
Abstract
Modeling host/pathogen interactions provides insight into immune defects that allow bacteria to overwhelm the host, mechanisms that allow vaccine strategies to be successful, and illusive interactions between immune components that govern the immune response to a challenge. However, even simplified models require a fairly high dimensional parameter space to be explored. Here we use global sensitivity analysis for parameters in a simple model for biofilm infections in mice. The results indicate which parameters are insignificant and are 'frozen' to yield a reduced model. The reduced model replicates the full model with high accuracy, using approximately half of the parameter space. We used the sensitivity to investigate the results of the combined biological and mathematical experiments for osteomyelitis. We are able to identify parts of the compartmentalized immune system that were responsible for each of the experimental outcomes. This model is one example for a technique that can be used generally.
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Jarrett AM, Cogan NG, Shirtliff ME. Modelling the interaction between the host immune response, bacterial dynamics and inflammatory damage in comparison with immunomodulation and vaccination experiments. MATHEMATICAL MEDICINE AND BIOLOGY-A JOURNAL OF THE IMA 2014; 32:285-306. [PMID: 24814512 DOI: 10.1093/imammb/dqu008] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/18/2013] [Accepted: 03/26/2014] [Indexed: 12/20/2022]
Abstract
The immune system is a complex system of chemical and cellular interactions that responds quickly to queues that signal infection and then reverts to a basal level once the challenge is eliminated. Here, we present a general, four-component model of the immune system's response to a Staphylococcal aureus (S. aureus) infection, using ordinary differential equations. To incorporate both the infection and the immune system, we adopt the style of compartmenting the system to include bacterial dynamics, damage and inflammation to the host, and the host response. We incorporate interactions not previously represented including cross-talk between inflammation/damage and the infection and the suppression of the anti-inflammatory pathway in response to inflammation/damage. As a result, the most relevant equilibrium of the system, representing the health state, is an all-positive basal level. The model is able to capture eight different experimental outcomes for mice challenged with intratibial osteomyelitis due to S. aureus, primarily involving immunomodulation and vaccine therapies. For further validation and parameter exploration, we perform a parameter sensitivity analysis which suggests that the model is very stable with respect to variations in parameters, indicates potential immunomodulation strategies and provides a possible explanation for the difference in immune potential for different mouse strains.
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Affiliation(s)
- Angela M Jarrett
- Department of Mathematics, Florida State University, 1017 Academic Way, Tallahassee, FL 32306, USA
| | - N G Cogan
- Department of Mathematics, Florida State University, 1017 Academic Way, Tallahassee, FL 32306, USA
| | - M E Shirtliff
- Department of Microbial Pathogenesis, Dental School, University of Maryland, Baltimore, MD, USA
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Phagocytosis of bacteria adhering to a biomaterial surface in a surface thermodynamic perspective. PLoS One 2013; 8:e70046. [PMID: 23894585 PMCID: PMC3716708 DOI: 10.1371/journal.pone.0070046] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2012] [Accepted: 06/17/2013] [Indexed: 11/19/2022] Open
Abstract
Bacterial biofilms can increase the pathogenicity of infection and constitute a major problem in modern health-care, especially on biomaterial implants and devices. Biofilms are difficult to eradicate by the host immune system, even with antibiotics, and have been the number one cause of biomaterial implant and device failure for decades. Therefore, it is important to understand how immune cells interact with adhering pathogens. This study firstly aims to develop a simple method to quantify phagocytosis of six different strains of staphylococci adhering on a surface with phase-contrast-microscopy. Phagocytosis of adhering staphylococci to a glass surface by phagocytes was quantified in a parallel plate flow chamber, and expressed as a phagocytosis rate, accounting for the number of adhering staphylococci initially present and for the duration of phagocytosis. Murine macrophages were more effective in clearing staphylococci from a surface than human phagocytes, which require differentiation from their monocyte or promyelocytic state during an experiment. Direct visualization of internalization of a GFP-modified S. aureus strain inside phagocytes confirmed the validity of the method proposed. As a second aim, the differences in phagocytosis rates observed were investigated on a surface thermodynamic basis using measured contact angles of liquids on macroscopic lawns of staphylococci and phagocytes, confirming that phagocytosis of adhering pathogens can be regarded as a surface phenomenon. In addition, surface thermodynamics revealed that phagocytosis of adhering pathogens is determined by an interplay of physical attraction between pathogens and phagocytes and the influence of chemo-attractants. For future studies, these results will help to place in vitro experiments and murine infection models in better perspective with respect to human ones.
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Hidalgo A, Tello L, Toro EF. Numerical and analytical study of an atherosclerosis inflammatory disease model. J Math Biol 2013; 68:1785-814. [PMID: 23719743 DOI: 10.1007/s00285-013-0688-0] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2012] [Revised: 05/06/2013] [Indexed: 11/24/2022]
Abstract
We study a reaction-diffusion mathematical model for the evolution of atherosclerosis as an inflammation process by combining analytical tools with computer-intensive numerical calculations. The computational work involved the calculation of more than sixty thousand solutions of the full reaction-diffusion system and lead to the complete characterisation of the ω-limit for every initial condition. Qualitative properties of the solution are rigorously proved, some of them hinted at by the numerical study.
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Affiliation(s)
- A Hidalgo
- Dept. Matemática Aplicada y Métodos Informáticos. E.T.S.I., Minas, Universidad Politécnica de Madrid, Rios Rosas 21, 28003 , Madrid, Spain,
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Malka R, Rom-Kedar V. Bacteria-phagocyte dynamics, axiomatic modelling and mass-action kinetics. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2011; 8:475-502. [PMID: 21631141 DOI: 10.3934/mbe.2011.8.475] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
Axiomatic modeling is ensued to provide a family of models that describe bacterial growth in the presence of phagocytes, or, more generally, prey dynamics in a large spatially homogenous eco-system. A classification of the possible bifurcation diagrams that arise in such models is presented. It is shown that other commonly used models that do not belong to this class may miss important features that are associated with the limited growth curve of the bacteria (prey) and the saturation associated with the phagocytosis (predator kill) term. Notably, these features appear at relatively low concentrations, much below the saturation range. Finally, combining this model with a model of neutrophil dynamics in the blood after chemotherapy treatments we obtain new insights regarding the development of infections under neutropenic conditions.
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Affiliation(s)
- Roy Malka
- Department of Computer Science and Applied Mathematics, The Weizmann Institute, Rehovot, Israel.
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18
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Childs LM, Paskow M, Morris SM, Hesse M, Strogatz S. From inflammation to wound healing: using a simple model to understand the functional versatility of murine macrophages. Bull Math Biol 2011; 73:2575-604. [PMID: 21347813 DOI: 10.1007/s11538-011-9637-5] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2010] [Accepted: 01/27/2011] [Indexed: 12/18/2022]
Abstract
Macrophages are fundamental cells of the innate immune system. Their activation is essential for such distinct immune functions as inflammation (pathogen-killing) and tissue repair (wound healing). An open question has been the functional stability of an individual macrophage cell: whether it can change its functional profile between different immune responses such as between the repair pathway and the inflammatory pathway. We studied this question theoretically by constructing a rate equation model for the key substrate, enzymes and products of the pathways; we then tested the model experimentally. Both our model and experiments show that individual macrophages can switch from the repair pathway to the inflammation pathway but that the reverse switch does not occur.
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Affiliation(s)
- Lauren M Childs
- Center for Applied Mathematics, Cornell University, Ithaca, NY 14853, USA.
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