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Eymard N, Bessonov N, Volpert V, Kurbatova P, Gueyffier F, Nony P. Pharmacokinetic/pharmacodynamic model of a methionine starvation based anti-cancer drug. Med Biol Eng Comput 2023:10.1007/s11517-023-02786-2. [PMID: 36882575 DOI: 10.1007/s11517-023-02786-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/28/2020] [Accepted: 01/17/2023] [Indexed: 03/09/2023]
Abstract
A new therapeutic approach against cancer is developed by the firm Erytech. This approach is based on starved cancer cells of an amino acid essential to their growth (the L-methionine). The depletion of plasma methionine level can be induced by an enzyme, the methionine-Îł-lyase. The new therapeutic formulation is a suspension of erythrocytes encapsulating the activated enzyme. Our work reproduces a preclinical trial of a new anti-cancer drug with a mathematical model and numerical simulations in order to replace animal experiments and to have a deeper insight on the underlying processes. With a combination of a pharmacokinetic/pharmacodynamic model for the enzyme, substrate, and co-factor with a hybrid model for tumor, we develop a "global model" that can be calibrated to simulate different human cancer cell lines. The hybrid model includes a system of ordinary differential equations for the intracellular concentrations, partial differential equations for the concentrations of nutrients and drugs in the extracellular matrix, and individual based model for cancer cells. This model describes cell motion, division, differentiation, and death determined by the intracellular concentrations. The models are developed on the basis of experiments in mice carried out by Erytech. Parameters of the pharmacokinetics model were determined by fitting a part of experimental data on the concentration of methionine in blood. Remaining experimental protocols effectuated by Erytech were used to validate the model. The validated PK model allowed the investigation of pharmacodynamics of cell populations. Numerical simulations with the global model show cell synchronization and proliferation arrest due to treatment similar to the available experiments. Thus, computer modeling confirms a possible effect of treatment based on the decrease of methionine concentration. The main goal of the study is the development of an integrated pharmacokinetic/pharmacodynamic model for encapsulated methioninase and of a mathematical model of tumor growth/regression in order to determine the kinetics of L-methionine depletion after co-administration of Erymet product and Pyridoxine.
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Affiliation(s)
- N Eymard
- Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, 69622, Villeurbanne, France.
| | - N Bessonov
- Institute of Mechanical Engineering Problems, 199178, Saint Petersburg, Russia
| | - 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, Russia
| | - P Kurbatova
- Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, 69622, Villeurbanne, France
| | - F Gueyffier
- CNRS, Laboratoire de Biométrie et Biologie Evolutive UMR 5558, Université Lyon 1, F-69622, Villeurbanne, France
| | - P Nony
- Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, 69622, Villeurbanne, France.,CNRS, Laboratoire de Biométrie et Biologie Evolutive UMR 5558, Université Lyon 1, F-69622, Villeurbanne, France
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Bessonov N, Reinberg N, Banerjee M, Volpert V. The Origin of Species by Means of Mathematical Modelling. Acta Biotheor 2018; 66:333-344. [PMID: 29713844 DOI: 10.1007/s10441-018-9328-9] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/23/2017] [Accepted: 04/25/2018] [Indexed: 11/30/2022]
Abstract
Darwin described biological species as groups of morphologically similar individuals. These groups of individuals can split into several subgroups due to natural selection, resulting in the emergence of new species. Some species can stay stable without the appearance of a new species, some others can disappear or evolve. Some of these evolutionary patterns were described in our previous works independently of each other. In this work we have developed a single model which allows us to reproduce the principal patterns in Darwin's diagram. Some more complex evolutionary patterns are also observed. The relation between Darwin's definition of species, stated above, and Mayr's definition of species (group of individuals that can reproduce) is also discussed.
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Affiliation(s)
- Nikolai Bessonov
- Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, Saint Petersburg, Russian Federation, 199178
| | | | - Malay Banerjee
- Department of Mathematics and Statistics, IIT Kanpur, Kanpur, India
| | - Vitaly Volpert
- Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, 69622, Villeurbanne, France.
- INRIA, Universite de Lyon, Universite Lyon 1, Institut Camille Jordan, 43 Bd. du 11 Novembre 1918, 69200, Villeurbanne Cedex, France.
- Peoples Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow, Russian Federation, 117198.
- Poncelet Center, UMI 2615 CNRS, 11 Bolshoy Vlasyevskiy, Moscow, Russian Federation, 119002.
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Eymard N, Volpert V, Kurbatova P, Volpert V, Bessonov N, Ogungbenro K, Aarons L, Janiaud P, Nony P, Bajard A, Chabaud S, Bertrand Y, KassaĂŻ B, Cornu C, Nony P. Mathematical model of T-cell lymphoblastic lymphoma: disease, treatment, cure or relapse of a virtual cohort of patients. MATHEMATICAL MEDICINE AND BIOLOGY-A JOURNAL OF THE IMA 2018; 35:25-47. [PMID: 28082512 DOI: 10.1093/imammb/dqw019] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2015] [Accepted: 10/12/2016] [Indexed: 12/19/2022]
Abstract
T lymphoblastic lymphoma (T-LBL) is a rare type of lymphoma with a good prognosis with a remission rate of 85%. Patients can be completely cured or can relapse during or after a 2-year treatment. Relapses usually occur early after the remission of the acute phase. The median time of relapse is equal to 1 year, after the occurrence of complete remission (range 0.2-5.9 years) (Uyttebroeck et al., 2008). It can be assumed that patients may be treated longer than necessary with undue toxicity.The aim of our model was to investigate whether the duration of the maintenance therapy could be reduced without increasing the risk of relapses and to determine the minimum treatment duration that could be tested in a future clinical trial.We developed a mathematical model of virtual patients with T-LBL in order to obtain a proportion of virtual relapses close to the one observed in the real population of patients from the EuroLB database. Our simulations reproduced a 2-year follow-up required to study the onset of the disease, the treatment of the acute phase and the maintenance treatment phase.
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Affiliation(s)
- N Eymard
- Institut Camille Jordan, UMR, CNRS, University Lyon 1, Villeurbanne, France
| | - V Volpert
- Institut Camille Jordan, UMR, CNRS, University Lyon 1, Villeurbanne, France
| | - P Kurbatova
- Institut Camille Jordan, UMR, CNRS, University Lyon 1, Villeurbanne, France
| | - V Volpert
- INRIA Team Dracula, INRIA Antenne Lyon la Doua 69603 Villeurbanne, France
| | - N Bessonov
- Institute of Mechanical Engineering Problems, Saint Petersburg, Russia
| | - K Ogungbenro
- Centre for Applied Pharmacokinetic Research, Manchester Pharmacy School The University of Manchester, Manchester, UK
| | - L Aarons
- Centre for Applied Pharmacokinetic Research, Manchester Pharmacy School The University of Manchester, Manchester, UK
| | - P Janiaud
- University of Lyon 1, UMR, CNRS, Lyon, France
| | - P Nony
- University of Lyon 1, UMR, CNRS, Lyon, France
| | - A Bajard
- Unité de Biostatistique et d'Evaluation des Thérapeutiques Centre Léon Bérard, Lyon, France
| | - S Chabaud
- Unité de Biostatistique et d'Evaluation des Thérapeutiques Centre Léon Bérard, Lyon, France
| | - Y Bertrand
- Institute of Hematology and Oncology Paediatrics, Hospices Civils de Lyon, University Claude Bernard Lyon I, Lyon, France
| | - B KassaĂŻ
- Hospices Civils de Lyon, Centre d'Investigation Clinique, INSERM CIC1407, Lyon, France
| | - C Cornu
- Hospices Civils de Lyon, Centre d'Investigation Clinique, INSERM CIC1407, Lyon, France
| | - P Nony
- CHU Lyon, Service de Pharmacologie Clinique et Essais Thérapeutiques, Lyon, France
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Eymard N, Bessonov N, Gandrillon O, Koury MJ, Volpert V. The role of spatial organization of cells in erythropoiesis. J Math Biol 2014; 70:71-97. [PMID: 24496930 DOI: 10.1007/s00285-014-0758-y] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2013] [Revised: 01/16/2014] [Indexed: 10/25/2022]
Abstract
Erythropoiesis, the process of red blood cell production, occurs mainly in the bone marrow. The functional unit of mammalian erythropoiesis, the erythroblastic island, consists of a central macrophage surrounded by adherent erythroid progenitor cells (CFU-E/Pro-EBs) and their differentiating progeny, the erythroblasts. Central macrophages display on their surface or secrete various growth or inhibitory factors that influence the fate of the surrounding erythroid cells. CFU-E/Pro-EBs have three possible fates: (a) expansion of their numbers without differentiation, (b) differentiation into reticulocytes that are released into the blood, (c) death by apoptosis. CFU-E/Pro-EB fate is under the control of a complex molecular network, that is highly dependent upon environmental conditions in the erythroblastic island. In order to assess the functional role of space coupled with the complex network behavior in erythroblastic islands, we developed hybrid discrete-continuous models of erythropoiesis. A model was developed in which cells are considered as individual physical objects, intracellular regulatory networks are modeled with ordinary differential equations and extracellular concentrations by partial differential equations. We used the model to investigate the impact of an important difference between humans and mice in which mature late-stage erythroblasts produce the most Fas-ligand in humans, whereas early-stage erythroblasts produce the most Fas-ligand in mice. Although the global behaviors of the erythroblastic islands in both species were similar, differences were found, including a relatively slower response time to acute anemia in humans. Also, our modeling approach was very consistent with in vitro culture data, where the central macrophage in reconstituted erythroblastic islands has a strong impact on the dynamics of red blood cell production. The specific spatial organization of erythroblastic islands is key to the normal, stable functioning of mammalian erythropoiesis, both in vitro and in vivo. Our model of a simplified molecular network controlling cell decision provides a realistic functional unit of mammalian erythropoiesis that integrates multiple microenvironmental influences within the erythroblastic island with those of circulating regulators of erythropoiesis, such as EPO and glucocorticosteroids, that are produced at remote sites.
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Affiliation(s)
- N Eymard
- Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, Villeurbanne, France,
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Clairambault J. Optimizing cancer pharmacotherapeutics using mathematical modeling and a systems biology approach. Per Med 2011; 8:271-286. [PMID: 29783516 DOI: 10.2217/pme.11.20] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Abstract
Research in mathematics and in mathematical biology on cancer and its treatments has been soaring in the past 10 years at an unprecedented speed. Such thriving is likely due as much to new findings in fundamental biology as to an emerging general interest from mathematicians and engineers towards applications in biology and medicine and to their subsequently designed representations and predictions of tumor processes that are now allowed by modern means of computation and simulation. This article, which does not claim the status of an extended review paper on mathematical models of cancer and its treatment, is focused on modeling in a systems biology perspective. I will list here the most necessary mathematical methods, in my opinion, which, while enforcing already existing methods, should be further developed towards designing and applying optimized individualized treatments of cancer in the clinic.
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Affiliation(s)
- Jean Clairambault
- INRIA Paris-Rocquencourt, Domaine de Voluceau, F78153 Rocquencourt, France.
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Silva A, Anderson ARA, Gatenby R. A multiscale model of the bone marrow and hematopoiesis. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2011; 8:643-58. [PMID: 21631151 PMCID: PMC3754791 DOI: 10.3934/mbe.2011.8.643] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/14/2023]
Abstract
The bone marrow is necessary for renewal of all hematopoietic cells and critical for maintenance of a wide range of physiologic functions. Multiple human diseases result from bone marrow dysfunction. It is also the site in which liquid tumors, including leukemia and multiple myeloma, develop as well as a frequent site of metastases. Understanding the complex cellular and microenvironmental interactions that govern normal bone marrow function as well as diseases and cancers of the bone marrow would be a valuable medical advance. Our goal is the development of a spatially-explicit in silico model of the bone marrow to understand both its normal function and the evolutionary dynamics that govern the emergence of bone marrow malignancy. Here we introduce a multiscale computational model of the bone marrow that incorporates three distinct spatial scales, cell, hematopoietic subunit, whole marrow. Our results, using parameter estimates from literature, recapitulates normal bone marrow function and suggest an explanation for the fractal-like structure of trabeculae and sinuses in the marrow, which would be an optimization of the hematopoietic function in order to maximize the number of mature blood cells produced daily within the volumetric restrictions of the marrow.
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Affiliation(s)
- Ariosto Silva
- H Lee Moffitt Cancer Center, Tampa, FL 33612, United States.
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