1
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Nolte DD. Coherent light scattering from cellular dynamics in living tissues. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2024; 87:036601. [PMID: 38433567 DOI: 10.1088/1361-6633/ad2229] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/01/2022] [Accepted: 01/24/2024] [Indexed: 03/05/2024]
Abstract
This review examines the biological physics of intracellular transport probed by the coherent optics of dynamic light scattering from optically thick living tissues. Cells and their constituents are in constant motion, composed of a broad range of speeds spanning many orders of magnitude that reflect the wide array of functions and mechanisms that maintain cellular health. From the organelle scale of tens of nanometers and upward in size, the motion inside living tissue is actively driven rather than thermal, propelled by the hydrolysis of bioenergetic molecules and the forces of molecular motors. Active transport can mimic the random walks of thermal Brownian motion, but mean-squared displacements are far from thermal equilibrium and can display anomalous diffusion through Lévy or fractional Brownian walks. Despite the average isotropic three-dimensional environment of cells and tissues, active cellular or intracellular transport of single light-scattering objects is often pseudo-one-dimensional, for instance as organelle displacement persists along cytoskeletal tracks or as membranes displace along the normal to cell surfaces, albeit isotropically oriented in three dimensions. Coherent light scattering is a natural tool to characterize such tissue dynamics because persistent directed transport induces Doppler shifts in the scattered light. The many frequency-shifted partial waves from the complex and dynamic media interfere to produce dynamic speckle that reveals tissue-scale processes through speckle contrast imaging and fluctuation spectroscopy. Low-coherence interferometry, dynamic optical coherence tomography, diffusing-wave spectroscopy, diffuse-correlation spectroscopy, differential dynamic microscopy and digital holography offer coherent detection methods that shed light on intracellular processes. In health-care applications, altered states of cellular health and disease display altered cellular motions that imprint on the statistical fluctuations of the scattered light. For instance, the efficacy of medical therapeutics can be monitored by measuring the changes they induce in the Doppler spectra of livingex vivocancer biopsies.
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Affiliation(s)
- David D Nolte
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN 47907, United States of America
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2
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Glass DS, Bren A, Vaisbourd E, Mayo A, Alon U. A synthetic differentiation circuit in Escherichia coli for suppressing mutant takeover. Cell 2024; 187:931-944.e12. [PMID: 38320549 PMCID: PMC10882425 DOI: 10.1016/j.cell.2024.01.024] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2023] [Revised: 11/27/2023] [Accepted: 01/16/2024] [Indexed: 02/08/2024]
Abstract
Differentiation is crucial for multicellularity. However, it is inherently susceptible to mutant cells that fail to differentiate. These mutants outcompete normal cells by excessive self-renewal. It remains unclear what mechanisms can resist such mutant expansion. Here, we demonstrate a solution by engineering a synthetic differentiation circuit in Escherichia coli that selects against these mutants via a biphasic fitness strategy. The circuit provides tunable production of synthetic analogs of stem, progenitor, and differentiated cells. It resists mutations by coupling differentiation to the production of an essential enzyme, thereby disadvantaging non-differentiating mutants. The circuit selected for and maintained a positive differentiation rate in long-term evolution. Surprisingly, this rate remained constant across vast changes in growth conditions. We found that transit-amplifying cells (fast-growing progenitors) underlie this environmental robustness. Our results provide insight into the stability of differentiation and demonstrate a powerful method for engineering evolutionarily stable multicellular consortia.
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Affiliation(s)
- David S Glass
- Department of Molecular Cell Biology, Weizmann Institute of Science, Rehovot 76100, Israel.
| | - Anat Bren
- Department of Molecular Cell Biology, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Elizabeth Vaisbourd
- Department of Molecular Cell Biology, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Avi Mayo
- Department of Molecular Cell Biology, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Uri Alon
- Department of Molecular Cell Biology, Weizmann Institute of Science, Rehovot 76100, Israel.
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3
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ADIMY MOSTAFA, CHEKROUN ABDENNASSER, EL ABDLLAOUI ABDERRAHIM, MARZORATI ARSÈNE. DISCRETE MATURITY AND DELAY DIFFERENTIAL-DIFFERENCE MODEL OF HEMATOPOIETIC CELL DYNAMICS WITH APPLICATIONS TO ACUTE MYELOGENOUS LEUKEMIA. J BIOL SYST 2022. [DOI: 10.1142/s0218339022500176] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
In the last few years, many efforts were oriented towards describing the hematopoiesis phenomenon in normal and pathological situations. This complex biological process is organized as a hierarchical system that begins with primitive hematopoietic stem cells (HSCs) and ends with mature blood cells: red blood cells, white blood cells and platelets. Regarding acute myelogenous leukemia (AML), a cancer of the bone marrow and blood, characterized by a rapid proliferation of immature cells, which eventually invade the bloodstream, there is a consensus about the target cells during the HSCs development which are susceptible to leukemic transformation. We propose and analyze a mathematical model of HSC dynamics taking into account two phases in the cell cycle, a resting and a proliferating one, by allowing just after division a part of HSCs to enter the resting phase and the other part to come back to the proliferating phase to divide again. The resulting mathematical model is a system of nonlinear differential-difference equations. Due to the hierarchical organization of the hematopoiesis, we consider [Formula: see text] stages of HSCs characterized by their maturity levels. We obtain a system of [Formula: see text] nonlinear differential-difference equations. We study the existence, uniqueness, positivity, boundedness and unboundedness of the solutions. We then investigate the existence of positive and axial steady states for the system, and obtain conditions for their stability. Sufficient conditions for the global asymptotic stability of the trivial steady state as well as conditions for its instability are obtained. Using neutral differential equation associated to the differential-difference system, we also obtain results on the local asymptotic stability of the positive steady state. Numerical simulations are carried out to show the influence of variations of the differentiation rates and self-renewal coefficients of the HSCs on the behavior of the system. In particular, we show that a blocking of differentiation at an early stage of HSC development can lead in an overexpression of very immature cells. Such situation corresponds to the observation in the case of AML.
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Affiliation(s)
- MOSTAFA ADIMY
- Inria, Univ Lyon, Université Lyon 1, CNRS UMR 5208, Institut Camille Jordan, 43 Bd. du 11 Novembre 1918, F-69200 Villeurbanne Cedex, France
| | - ABDENNASSER CHEKROUN
- Laboratoire d’Analyse Nonlinéaire et Mathématiques Appliquées, University of Tlemcen Tlemcen 13000, Algeria
| | - ABDERRAHIM EL ABDLLAOUI
- Laboratory of Mathematics, Computer Science and Applications, Security of Information Department of Mathematics, Faculty of Sciences, Mohammed V University in Rabat, Morocco
| | - ARSÈNE MARZORATI
- Inria, Univ Lyon, Université Lyon 1, CNRS UMR 5208, Institut Camille Jordan, 43 Bd. du 11 Novembre 1918, F-69200 Villeurbanne Cedex, France
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4
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Adimy M, Babin L, Pujo-Menjouet L. Why Are Periodic Erythrocytic Diseases so Rare in Humans? Bull Math Biol 2021; 84:19. [PMID: 34923612 DOI: 10.1007/s11538-021-00973-6] [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: 07/07/2021] [Accepted: 11/15/2021] [Indexed: 10/19/2022]
Abstract
Many studies have shown that periodic erythrocytic (red blood cell linked) diseases are extremely rare in humans. To explain this observation, we develop here a simple model of erythropoiesis in mammals and investigate its stability in the parameter space. A bifurcation analysis enables us to sketch stability diagrams in the plane of key parameters. Contrary to some other mammal species such as rabbits, mice or dogs, we show that human-specific parameter values prevent periodic oscillations of red blood cells levels. In other words, human erythropoiesis seems to lie in a region of parameter space where oscillations exclusively concerning red blood cells cannot appear. Further mathematical analysis show that periodic oscillations of red blood cells levels are highly unusual and if exist, might only be due to an abnormally high erythrocytes destruction rate or to an abnormal hematopoietic stem cell commitment into the erythrocytic lineage. We also propose numerical results only for an improved version of our approach in order to give a more realistic but more complex approach of our problem.
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Affiliation(s)
- Mostafa Adimy
- Univ Lyon, Inria, Université Claude Bernard Lyon 1, CNRS UMR5208, Institut Camille Jordan, 43 Bd. du 11 Novembre 1918, 69200, Villeurbanne Cedex, France.,INRIA, Lyon, France
| | - Louis Babin
- Univ Lyon, Inria, Université Claude Bernard Lyon 1, CNRS UMR5208, Institut Camille Jordan, 43 Bd. du 11 Novembre 1918, 69200, Villeurbanne Cedex, France
| | - Laurent Pujo-Menjouet
- Univ Lyon, Inria, Université Claude Bernard Lyon 1, CNRS UMR5208, Institut Camille Jordan, 43 Bd. du 11 Novembre 1918, 69200, Villeurbanne Cedex, France. .,INRIA, Lyon, France.
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5
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Abstract
In this paper, two control problems for a symmetric model of cell dynamics related to leukemia are considered. The first one, in connection with classical chemotherapy, is that the evolution of the disease under treatment should follow a prescribed trajectory assuming that the drug works by increasing the cell death rates of both malignant and normal cells. In the case of the second control problem, as for targeted therapies, the drug is assumed to work by decreasing the multiplication rate of leukemic cells only, and the control objective is that the disease state reaches a desired endpoint. The solvability of the two problems as well as their stability are proved by using a general method of analysis. Some numerical simulations are included to illustrate the theoretical results and prove their applicability. The results can possibly be used to design therapeutic scenarios such that an expected clinical evolution can be achieved.
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6
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Nonlinear delay differential equations and their application to modeling biological network motifs. Nat Commun 2021; 12:1788. [PMID: 33741909 PMCID: PMC7979834 DOI: 10.1038/s41467-021-21700-8] [Citation(s) in RCA: 23] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2020] [Accepted: 02/01/2021] [Indexed: 12/24/2022] Open
Abstract
Biological regulatory systems, such as cell signaling networks, nervous systems and ecological webs, consist of complex dynamical interactions among many components. Network motif models focus on small sub-networks to provide quantitative insight into overall behavior. However, such models often overlook time delays either inherent to biological processes or associated with multi-step interactions. Here we systematically examine explicit-delay versions of the most common network motifs via delay differential equation (DDE) models, both analytically and numerically. We find many broadly applicable results, including parameter reduction versus canonical ordinary differential equation (ODE) models, analytical relations for converting between ODE and DDE models, criteria for when delays may be ignored, a complete phase space for autoregulation, universal behaviors of feedforward loops, a unified Hill-function logic framework, and conditions for oscillations and chaos. We conclude that explicit-delay modeling simplifies the phenomenology of many biological networks and may aid in discovering new functional motifs. Network motif models focus on small sub-networks in biological systems to quantitatively describe overall behavior but they often overlook time delays. Here, the authors systematically examine the most common network motifs via delay differential equations (DDE), often leading to more concise descriptions.
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7
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Solé R, Aguadé-Gorgorió G. The ecology of cancer differentiation therapy. J Theor Biol 2020; 511:110552. [PMID: 33309530 DOI: 10.1016/j.jtbi.2020.110552] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2020] [Revised: 10/21/2020] [Accepted: 11/17/2020] [Indexed: 11/29/2022]
Abstract
A promising, yet still under development approach to cancer treatment is based on the idea of differentiation therapy (DTH). Most tumours are characterized by poorly differentiated cell populations exhibiting a marked loss of traits associated to communication and tissue homeostasis. DTH has been suggested as an alternative (or complement) to cytotoxic-based approaches, and has proven successful in some specific types of cancer such as acute promyelocytic leukemia (APL). While novel drugs favouring the activation of differentiation therapies are being tested, several open problems emerge in relation to its effectiveness on solid tumors. Here we present a mathematical framework to DTH based on a well-known ecological model used to describe habitat loss. The models presented here account for some of the observed clinical and in vitro outcomes of DTH, providing relevant insight into potential therapy design. Furthermore, the same ecological approach is tested in a hierarchical model that accounts for cancer stem cells, highlighting the role of niche specificity in CSC therapy resistance. We show that the lessons learnt from metapopulation ecology can help guide future developments and potential difficulties of DTH.
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Affiliation(s)
- Ricard Solé
- ICREA-Complex Systems Lab, Universitat Pompeu Fabra, 08003 Barcelona, Catalonia, Spain; Institut de Biologia Evolutiva (CSIC-UPF), Psg Maritim Barceloneta, 37, 08003 Barcelona, Catalonia, Spain; Santa Fe Institute, 1399 Hyde Park Road, Santa Fe NM 87501, USA
| | - Guim Aguadé-Gorgorió
- ICREA-Complex Systems Lab, Universitat Pompeu Fabra, 08003 Barcelona, Catalonia, Spain; Institut de Biologia Evolutiva (CSIC-UPF), Psg Maritim Barceloneta, 37, 08003 Barcelona, Catalonia, Spain
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8
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Alfonso S, Jenner AL, Craig M. Translational approaches to treating dynamical diseases through in silico clinical trials. CHAOS (WOODBURY, N.Y.) 2020; 30:123128. [PMID: 33380031 DOI: 10.1063/5.0019556] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2020] [Accepted: 11/20/2020] [Indexed: 06/12/2023]
Abstract
The primary goal of drug developers is to establish efficient and effective therapeutic protocols. Multifactorial pathologies, including dynamical diseases and complex disorders, can be difficult to treat, given the high degree of inter- and intra-patient variability and nonlinear physiological relationships. Quantitative approaches combining mechanistic disease modeling and computational strategies are increasingly leveraged to rationalize pre-clinical and clinical studies and to establish effective treatment strategies. The development of clinical trials has led to new computational methods that allow for large clinical data sets to be combined with pharmacokinetic and pharmacodynamic models of diseases. Here, we discuss recent progress using in silico clinical trials to explore treatments for a variety of complex diseases, ultimately demonstrating the immense utility of quantitative methods in drug development and medicine.
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Affiliation(s)
- Sofia Alfonso
- Department of Physiology, McGill University, Montreal, Quebec H3A 0G4, Canada
| | - Adrianne L Jenner
- Department of Mathematics and Statistics, Université de Montréal, Montreal, Quebec H3C 3J7, Canada
| | - Morgan Craig
- Department of Physiology, McGill University, Montreal, Quebec H3A 0G4, Canada
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9
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Mackey MC. Periodic hematological disorders: Quintessential examples of dynamical diseases. CHAOS (WOODBURY, N.Y.) 2020; 30:063123. [PMID: 32611100 DOI: 10.1063/5.0006517] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/04/2020] [Accepted: 05/21/2020] [Indexed: 06/11/2023]
Abstract
This paper summarizes the evidence supporting the classification of cyclic neutropenia as a dynamical disease and periodic chronic myelogenous leukemia is also considered. The unsatisfactory state of knowledge concerning the genesis of cyclic thrombocytopenia and periodic autoimmune hemolytic anemia is detailed.
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Affiliation(s)
- Michael C Mackey
- Department of Physiology, Department of Physics, and Department of Mathematics McGill University, Montreal, Quebec H4X 2C1, Canada
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10
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Lei J. A general mathematical framework for understanding the behavior of heterogeneous stem cell regeneration. J Theor Biol 2020; 492:110196. [PMID: 32067937 DOI: 10.1016/j.jtbi.2020.110196] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2019] [Revised: 12/28/2019] [Accepted: 02/11/2020] [Indexed: 11/21/2022]
Abstract
Stem cell heterogeneity is essential for homeostasis in tissue development. This paper establishes a general mathematical framework to model the dynamics of stem cell regeneration with cell heterogeneity and random transitions of epigenetic states. The framework generalizes the classical G0 cell cycle model and incorporates the epigenetic states of individual cells represented by a continuous multidimensional variable. In the model, the kinetic rates of cell behaviors, including proliferation, differentiation, and apoptosis, are dependent on their epigenetic states, and the random transitions of epigenetic states between cell cycles are represented by an inheritance probability function that describes the conditional probability of cell state changes. Moreover, the model can be extended to include genotypic changes and describe the process of gene mutation-induced tumor development. The proposed mathematical framework provides a generalized formula that helps us to understand various dynamic processes of stem cell regeneration, including tissue development, degeneration, and abnormal growth.
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Affiliation(s)
- Jinzhi Lei
- Zhou Pei-Yuan Center for Applied Mathematics, MOE Key Laboratory of Bioinformatics, Tsinghua University, Beijing 100084, China.
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11
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A Mathematical Model of the Transition from Normal Hematopoiesis to the Chronic and Accelerated-Acute Stages in Myeloid Leukemia. MATHEMATICS 2020. [DOI: 10.3390/math8030376] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
A mathematical model given by a two-dimensional differential system is introduced in order to understand the transition process from the normal hematopoiesis to the chronic and accelerated-acute stages in chronic myeloid leukemia. A previous model of Dingli and Michor is refined by introducing a new parameter in order to differentiate the bone marrow microenvironment sensitivities of normal and mutant stem cells. In the light of the new parameter, the system now has three distinct equilibria corresponding to the normal hematopoietic state, to the chronic state, and to the accelerated-acute phase of the disease. A characterization of the three hematopoietic states is obtained based on the stability analysis. Numerical simulations are included to illustrate the theoretical results.
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12
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Paquin-Lefebvre F, Bélair J. On the Effect of Age-Dependent Mortality on the Stability of a System of Delay-Differential Equations Modeling Erythropoiesis. Acta Biotheor 2020; 68:5-19. [PMID: 31350630 DOI: 10.1007/s10441-019-09351-1] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/04/2019] [Accepted: 07/10/2019] [Indexed: 11/26/2022]
Abstract
We present an age-structured model for erythropoiesis in which the mortality of mature cells is described empirically by a physiologically realistic probability distribution of survival times. Under some assumptions, the model can be transformed into a system of delay differential equations with both constant and distributed delays. The stability of the equilibrium of this system and possible Hopf bifurcations are described for a number of probability distributions. Physiological motivation and interpretation of our results are provided.
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Affiliation(s)
| | - Jacques Bélair
- Département de mathématiques et de statistique and Centre de recherches mathématiques, Université de Montréal, CP 6128 Succ. centre-ville, Montréal, QC, H3C 3J7, Canada.
- Centre for Applied Mathematics in Bioscience and Medicine, McGill University, Montréal, Canada.
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13
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Attarakih M, Bart HJ, Abu-Khader M. On the solution of the population balance equation: From global to local constrained maximum entropy method. Chem Eng Sci 2019. [DOI: 10.1016/j.ces.2019.115168] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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14
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Duchesne R, Guillemin A, Crauste F, Gandrillon O. Calibration, Selection and Identifiability Analysis of a Mathematical Model of the in vitro Erythropoiesis in Normal and Perturbed Contexts. In Silico Biol 2019; 13:55-69. [PMID: 31006682 PMCID: PMC6597985 DOI: 10.3233/isb-190471] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023]
Abstract
The in vivo erythropoiesis, which is the generation of mature red blood cells in the bone marrow of whole organisms, has been described by a variety of mathematical models in the past decades. However, the in vitro erythropoiesis, which produces red blood cells in cultures, has received much less attention from the modelling community. In this paper, we propose the first mathematical model of in vitro erythropoiesis. We start by formulating different models and select the best one at fitting experimental data of in vitro erythropoietic differentiation obtained from chicken erythroid progenitor cells. It is based on a set of linear ODE, describing 3 hypothetical populations of cells at different stages of differentiation. We then compute confidence intervals for all of its parameters estimates, and conclude that our model is fully identifiable. Finally, we use this model to compute the effect of a chemical drug called Rapamycin, which affects all states of differentiation in the culture, and relate these effects to specific parameter variations. We provide the first model for the kinetics of in vitro cellular differentiation which is proven to be identifiable. It will serve as a basis for a model which will better account for the variability which is inherent to the experimental protocol used for the model calibration.
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Affiliation(s)
- Ronan Duchesne
- Laboratoire de Biologie et Modélisation de la Cellule, CNRS UMR 5239, École Normale Supérieure de Lyon, 46 allée d'Italie, Lyon.,Inria team Dracula, Inria center Grenoble-Rhône Alpes, 56 Boulevard Niels Bohr, Villeurbanne
| | - Anissa Guillemin
- Laboratoire de Biologie et Modélisation de la Cellule, CNRS UMR 5239, École Normale Supérieure de Lyon, 46 allée d'Italie, Lyon
| | - Fabien Crauste
- Institut Mathématiques de Bordeaux, CNRS UMR5251, Université de Bordeaux, Talence, France
| | - Olivier Gandrillon
- Laboratoire de Biologie et Modélisation de la Cellule, CNRS UMR 5239, École Normale Supérieure de Lyon, 46 allée d'Italie, Lyon.,Inria team Dracula, Inria center Grenoble-Rhône Alpes, 56 Boulevard Niels Bohr, Villeurbanne
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15
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Zhuge C, Mackey MC, Lei J. Origins of oscillation patterns in cyclical thrombocytopenia. J Theor Biol 2019; 462:432-445. [DOI: 10.1016/j.jtbi.2018.11.024] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2018] [Revised: 11/22/2018] [Accepted: 11/26/2018] [Indexed: 10/27/2022]
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16
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De Souza DC, Mackey MC. Response of an oscillatory differential delay equation to a periodic stimulus. J Math Biol 2019; 78:1637-1679. [PMID: 30637475 DOI: 10.1007/s00285-018-1322-y] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2018] [Revised: 09/21/2018] [Indexed: 11/26/2022]
Abstract
Periodic hematological diseases such as cyclical neutropenia or cyclical thrombocytopenia, with their characteristic oscillations of circulating neutrophils or platelets, may pose grave problems for patients. Likewise, periodically administered chemotherapy has the unintended side effect of establishing periodic fluctuations in circulating white cells, red cell precursors and/or platelets. These fluctuations, either spontaneous or induced, often have serious consequences for the patient (e.g. neutropenia, anemia, or thrombocytopenia respectively) which exogenously administered cytokines can partially correct. The question of when and how to administer these drugs is a difficult one for clinicians and not easily answered. In this paper we use a simple model consisting of a delay differential equation with a piecewise linear nonlinearity, that has a periodic solution, to model the effect of a periodic disease or periodic chemotherapy. We then examine the response of this toy model to both single and periodic perturbations, meant to mimic the drug administration, as a function of the drug dose and the duration and frequency of its administration to best determine how to avoid side effects.
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Affiliation(s)
- Daniel C De Souza
- Department of Mathematics and Statistics, McGill University, Montreal, QC, H3A 0B9, Canada.
- Institute of Immunology and Infection Research, University of Edinburgh, Ashworth Labs, Edinburgh, EH9 3FL, Scotland.
| | - Michael C Mackey
- Departments of Physiology, Physics and Mathematics, McGill University, 3655 Promenade Sir William Osler, Montreal, QC, H3G 1Y6, Canada
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17
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Fan Y, Antonijević D, Zhong X, Komlev VS, Li Z, Đurić M, Fan Y. Three-Dimensional Reconstruction of Erythrocytes Using the Novel Method For Corrective Realignment of the Transmission Electron Microscopy Cross-Section Images. MICROSCOPY AND MICROANALYSIS : THE OFFICIAL JOURNAL OF MICROSCOPY SOCIETY OF AMERICA, MICROBEAM ANALYSIS SOCIETY, MICROSCOPICAL SOCIETY OF CANADA 2018; 24:676-683. [PMID: 30588909 DOI: 10.1017/s1431927618015325] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
The detailed kinetics study of erythrocyte deformability is useful for the early diagnosis of blood diseases and for monitoring the blood rheology. Present solutions for a three-dimensional (3D) reconstruction of erythrocytes has a limited potential. This study aimed to use erythrocyte transmission electron images (ETIs) to evaluate the morphological relationship between adjacent ETIs and generate erythrocytes 3D model. First, ultrathin serial sections of skeletal muscle tissue were obtained using an ultramicrotome. Further, the set of ETIs in a capillary were captured by transmission electron microscopy. The images were aligned by translations and rotations using custom software to optimize the morphological relationship between adjacent ETIs. These coordinate transformations exploit the unique principal axis of inertia of each image to define the body coordinate system and hence provide the means to accurately reconnect the adjacent ETIs. The sum of the distances between the corresponding points on the boundary of adjacent ETIs was minimized and, further, was optimized by using physiological relationship between the adjacent ETIs. The analysis allowed to define precise virtual relationship between the adjacent erythrocytes. Finally, extracted erythrocytes' cross-section images allowed to generate 3D model of the erythrocytes.
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Affiliation(s)
- Yuzhou Fan
- 1School of Physical Education and Sport Science,Fujian Normal University,350108 Fuzhou,China
| | - Djordje Antonijević
- 1School of Physical Education and Sport Science,Fujian Normal University,350108 Fuzhou,China
| | - Xing Zhong
- 5Medical Imaging Center,The First Affiliated Hospital of Jinan University,510632 Guangzhou,China
| | - Vladimir S Komlev
- 6A. A. Baikov Institute of Metallurgy and Materials Science,119334 Moscow,Russia
| | - Zhiyu Li
- 7College of Foreign Studies,Jinan University,510632 Guangzhou,China
| | - Marija Đurić
- 3Laboratory for Anthropology,Institute for Anatomy,School of Medicine,University of Belgrade,11000 Belgrade,Serbia
| | - Yifang Fan
- 1School of Physical Education and Sport Science,Fujian Normal University,350108 Fuzhou,China
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18
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A stochastic model of myeloid cell lineages in hematopoiesis and pathway mutations in acute myeloid leukemia. PLoS One 2018; 13:e0204393. [PMID: 30273383 PMCID: PMC6166954 DOI: 10.1371/journal.pone.0204393] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/17/2017] [Accepted: 09/07/2018] [Indexed: 01/13/2023] Open
Abstract
A model for hematopoiesis is presented that explicitly includes the erythrocyte, granulocyte, and thrombocyte lineages and their common precursors. A small number of stem cells proliferate and differentiate through different compartments to produce the vast number of blood cells needed every day. Growth factors regulate the proliferation of cells dependent on the current demand. We provide a steady state analysis of the model and rough parameter estimates. Furthermore, we extend the model to include mutations that alter the replicative capacity of cells and introduce differentiation blocks. With these mutations the model develops signs of acute myeloid leukemia.
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19
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Djema W, Bonnet C, Mazenc F, Clairambault J, Fridman E, Hirsch P, Delhommeau F. Control in dormancy or eradication of cancer stem cells: Mathematical modeling and stability issues. J Theor Biol 2018; 449:103-123. [PMID: 29678688 DOI: 10.1016/j.jtbi.2018.03.038] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/11/2017] [Revised: 02/17/2018] [Accepted: 03/31/2018] [Indexed: 12/12/2022]
Abstract
OBJECTIVE Modeling and analysis of cell population dynamics enhance our understanding of cancer. Here we introduce and explore a new model that may apply to many tissues. ANALYSES An age-structured model describing coexistence between mutated and ordinary stem cells is developed and explored. The model is transformed into a nonlinear time-delay system governing the dynamics of healthy cells, coupled to a nonlinear differential-difference system describing dynamics of unhealthy cells. Its main features are highlighted and an advanced stability analysis of several steady states is performed, through specific Lyapunov-like functionals for descriptor-type systems. RESULTS We propose a biologically based model endowed with rich dynamics. It incorporates a new parameter representing immunoediting processes, including the case where proliferation of cancer cells is locally kept under check by the immune cells. It also considers the overproliferation of cancer stem cells, modeled as a subpopulation of mutated cells that is constantly active in cell division. The analysis that we perform here reveals the conditions of existence of several steady states, including the case of cancer dormancy, in the coupled model of interest. Our study suggests that cancer dormancy may result from a plastic sensitivity of mutated cells to their shared environment, different from that - fixed - of healthy cells, and this is related to an action (or lack of action) of the immune system. Next, the stability analysis that we perform is essentially oriented towards the determination of sufficient conditions, depending on all the model parameters, that ensure either a regionally (i.e., locally) stable dormancy steady state or eradication of unhealthy cells. Finally, we discuss some biological interpretations, with regards to our findings, in light of current and emerging therapeutics. These final insights are particularly formulated in the paradigmatic case of hematopoiesis and acute leukemia, which is one of the best known malignancies for which it is always hard, in presence of a clinical and histological remission, to decide between cure and dormancy of a tumoral clone.
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Affiliation(s)
- Walid Djema
- Inria Saclay, CentraleSupélec, Université Paris-Saclay & Inria Sophia-Antipolis, Biocore and McTao teams, Université Côte d'Azur (UCA), France.
| | - Catherine Bonnet
- Inria Saclay, Disco team, Université Paris-Saclay, CentraleSupélec, L2S (CNRS), France.
| | - Frédéric Mazenc
- Inria Saclay, Disco team, Université Paris-Saclay, CentraleSupélec, L2S (CNRS), France.
| | - Jean Clairambault
- Inria, Mamba team and Sorbonne Université, Paris 6, UPMC, Laboratoire Jacques-Louis Lions, Paris, France.
| | - Emilia Fridman
- Department of Electrical Engineering and Systems at the School of Electrical Engineering, Tel-Aviv, Israel.
| | - Pierre Hirsch
- Sorbonne Université, GRC n7, Groupe de Recherche Clinique sur les Myéloproliferations Aiguës et Chroniques, AP-HP, Hôpital Saint-Antoine, Paris F-75012, France.
| | - François Delhommeau
- Sorbonne Université, GRC n7, Groupe de Recherche Clinique sur les Myéloproliferations Aiguës et Chroniques, AP-HP, Hôpital Saint-Antoine, Paris F-75012, France.
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20
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Transit and lifespan in neutrophil production: implications for drug intervention. J Pharmacokinet Pharmacodyn 2017; 45:59-77. [DOI: 10.1007/s10928-017-9560-y] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2017] [Accepted: 12/06/2017] [Indexed: 01/08/2023]
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21
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Abstract
The Mackey-Glass equation is the representative example of delay induced chaotic behavior. Here, we propose various control mechanisms so that otherwise erratic solutions are forced to converge to the positive equilibrium or to a periodic orbit oscillating around that equilibrium. We take advantage of some recent results of the delay differential literature, when a sufficiently large domain of the phase space has been shown to be attractive and invariant, where the system is governed by monotone delayed feedback and chaos is not possible due to some Poincaré-Bendixson type results. We systematically investigate what control mechanisms are suitable to drive the system into such a situation and prove that constant perturbation, proportional feedback control, Pyragas control, and state dependent delay control can all be efficient to control Mackey-Glass chaos with properly chosen control parameters.
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Affiliation(s)
- Gábor Kiss
- Bolyai Institute, University of Szeged, Szeged H-6720, Hungary
| | - Gergely Röst
- Bolyai Institute, University of Szeged, Szeged H-6720, Hungary
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22
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Abstract
Sustained oscillations abound in biological systems. They occur at all levels of biological organization over a wide range of periods, from a fraction of a second to years, and with a variety of underlying mechanisms. They control major physiological functions, and their dysfunction is associated with a variety of physiological disorders. The goal of this review is (i) to give an overview of the main rhythms observed at the cellular and supracellular levels, (ii) to briefly describe how the study of biological rhythms unfolded in the course of time, in parallel with studies on chemical oscillations, (iii) to present the major roles of biological rhythms in the control of physiological functions, and (iv) the pathologies associated with the alteration, disappearance, or spurious occurrence of biological rhythms. Two tables present the main examples of cellular and supracellular rhythms ordered according to their period, and their role in physiology and pathophysiology. Among the rhythms discussed are neural and cardiac rhythms, metabolic oscillations such as those occurring in glycolysis in yeast, intracellular Ca++ oscillations, cyclic AMP oscillations in Dictyostelium amoebae, the segmentation clock that controls somitogenesis, pulsatile hormone secretion, circadian rhythms which occur in all eukaryotes and some bacteria with a period close to 24 h, the oscillatory dynamics of the enzymatic network driving the cell cycle, and oscillations in transcription factors such as NF-ΚB and tumor suppressors such as p53. Ilya Prigogine's concept of dissipative structures applies to temporal oscillations and allows us to unify within a common framework the various rhythms observed at different levels of biological organization, regardless of their period and underlying mechanism.
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Affiliation(s)
- Albert Goldbeter
- Unité de Chronobiologie théorique, Service de Chimie physique et Biologie théorique, Faculté des Sciences, Université Libre de Bruxelles (ULB), Campus Plaine, CP 231, B-1050 Brussels, Belgium
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23
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Craig M. Towards Quantitative Systems Pharmacology Models of Chemotherapy-Induced Neutropenia. CPT Pharmacometrics Syst Pharmacol 2017; 6:293-304. [PMID: 28418603 PMCID: PMC5445232 DOI: 10.1002/psp4.12191] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/09/2017] [Revised: 02/21/2017] [Accepted: 02/21/2017] [Indexed: 12/22/2022] Open
Abstract
Neutropenia is a serious toxic complication of chemotherapeutic treatment. For years, mathematical models have been developed to better predict hematological outcomes during chemotherapy in both the traditional pharmaceutical sciences and mathematical biology disciplines. An increasing number of quantitative systems pharmacology (QSP) models that combine systems approaches, physiology, and pharmacokinetics/pharmacodynamics have been successfully developed. Here, I detail the shift towards QSP efforts, emphasizing the importance of incorporating systems-level physiological considerations in pharmacometrics.
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Affiliation(s)
- M Craig
- Program for Evolutionary Dynamics, Harvard UniversityCambridgeMassachusettsUSA
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24
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Domschke P, Trucu D, Gerisch A, Chaplain MAJ. Structured models of cell migration incorporating molecular binding processes. J Math Biol 2017; 75:1517-1561. [PMID: 28405746 DOI: 10.1007/s00285-017-1120-y] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2016] [Revised: 03/07/2017] [Indexed: 10/19/2022]
Abstract
The dynamic interplay between collective cell movement and the various molecules involved in the accompanying cell signalling mechanisms plays a crucial role in many biological processes including normal tissue development and pathological scenarios such as wound healing and cancer. Information about the various structures embedded within these processes allows a detailed exploration of the binding of molecular species to cell-surface receptors within the evolving cell population. In this paper we establish a general spatio-temporal-structural framework that enables the description of molecular binding to cell membranes coupled with the cell population dynamics. We first provide a general theoretical description for this approach and then illustrate it with three examples arising from cancer invasion.
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Affiliation(s)
- Pia Domschke
- Fachbereich Mathematik, Technische Universität Darmstadt, Dolivostr. 15, 64293, Darmstadt, Germany.
| | - Dumitru Trucu
- Division of Mathematics, University of Dundee, Dundee, DD1 4HN, UK
| | - Alf Gerisch
- Fachbereich Mathematik, Technische Universität Darmstadt, Dolivostr. 15, 64293, Darmstadt, Germany
| | - Mark A J Chaplain
- School of Mathematics and Statistics, Mathematical Institute, University of St Andrews, St Andrews, KY16 9SS, UK
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25
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Normal and pathological dynamics of platelets in humans. J Math Biol 2017; 75:1411-1462. [DOI: 10.1007/s00285-017-1125-6] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/28/2016] [Revised: 01/23/2017] [Indexed: 11/26/2022]
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26
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Mackey MC, Tyran-Kamińska M, Walther HO. Response of an oscillatory differential delay equation to a single stimulus. J Math Biol 2016; 74:1139-1196. [PMID: 27613016 DOI: 10.1007/s00285-016-1051-z] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/01/2015] [Revised: 08/18/2016] [Indexed: 12/17/2022]
Abstract
Here we analytically examine the response of a limit cycle solution to a simple differential delay equation to a single pulse perturbation of the piecewise linear nonlinearity. We construct the unperturbed limit cycle analytically, and are able to completely characterize the perturbed response to a pulse of positive amplitude and duration with onset at different points in the limit cycle. We determine the perturbed minima and maxima and period of the limit cycle and show how the pulse modifies these from the unperturbed case.
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Affiliation(s)
- Michael C Mackey
- Departments of Physiology, Physics and Mathematics, McGill University, 3655 Promenade Sir William Osler, Montreal, QC, H3G 1Y6, Canada.
| | - Marta Tyran-Kamińska
- Institute of Mathematics, University of Silesia, Bankowa 14, 40-007, Katowice, Poland
| | - Hans-Otto Walther
- Mathematisches Institut, Universität Giessen, Arndtstrasse 2, 35392, Giessen, Germany
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27
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Craig M, Humphries AR, Mackey MC. A Mathematical Model of Granulopoiesis Incorporating the Negative Feedback Dynamics and Kinetics of G-CSF/Neutrophil Binding and Internalization. Bull Math Biol 2016; 78:2304-2357. [PMID: 27324993 DOI: 10.1007/s11538-016-0179-8] [Citation(s) in RCA: 40] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2015] [Accepted: 05/19/2016] [Indexed: 11/24/2022]
Abstract
We develop a physiological model of granulopoiesis which includes explicit modelling of the kinetics of the cytokine granulocyte colony-stimulating factor (G-CSF) incorporating both the freely circulating concentration and the concentration of the cytokine bound to mature neutrophils. G-CSF concentrations are used to directly regulate neutrophil production, with the rate of differentiation of stem cells to neutrophil precursors, the effective proliferation rate in mitosis, the maturation time, and the release rate from the mature marrow reservoir into circulation all dependent on the level of G-CSF in the system. The dependence of the maturation time on the cytokine concentration introduces a state-dependent delay into our differential equation model, and we show how this is derived from an age-structured partial differential equation model of the mitosis and maturation and also detail the derivation of the rest of our model. The model and its estimated parameters are shown to successfully predict the neutrophil and G-CSF responses to a variety of treatment scenarios, including the combined administration of chemotherapy and exogenous G-CSF. This concomitant treatment was reproduced without any additional fitting to characterize drug-drug interactions.
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Affiliation(s)
- M Craig
- Faculté de Pharmacie, Université de Montréal, Montréal, QC, H3T 1J4, Canada.
- Program for Evolutionary Dynamics, Harvard University, Cambridge, MA, 02138, USA.
| | - A R Humphries
- Department of Mathematics and Statistics, McGill University, Montréal, QC, H3A 0B9, Canada
| | - M C Mackey
- Departments of Mathematics, Physics and Physiology, McGill University, Montréal, QC, H3G 1Y6, Canada
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28
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Wang MX, Ma YQ, Lai PY. Regulatory effects on the population dynamics and wave propagation in a cell lineage model. J Theor Biol 2016; 393:105-17. [PMID: 26796226 DOI: 10.1016/j.jtbi.2015.12.035] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2014] [Revised: 11/26/2015] [Accepted: 12/29/2015] [Indexed: 11/28/2022]
Abstract
We consider the interplay of cell proliferation, cell differentiation (and de-differentiation), cell movement, and the effect of feedback regulations on the population and propagation dynamics of different cell types in a cell lineage model. Cells are assumed to secrete and respond to negative feedback molecules which act as a control on the cell lineage. The cell densities are described by coupled reaction-diffusion partial differential equations, and the propagating wave front solutions in one dimension are investigated analytically and by numerical solutions. In particular, wavefront propagation speeds are obtained analytically and verified by numerical solutions of the equations. The emphasis is on the effects of the feedback regulations on different stages in the cell lineage. It is found that when the progenitor cell is negatively regulated, the populations of the cell lineage are strongly down-regulated with the steady growth rate of the progenitor cell being driven to zero beyond a critical regulatory strength. An analytic expression for the critical regulation strength in terms of the model parameters is derived and verified by numerical solutions. On the other hand, if the inhibition is acting on the differentiated cells, the change in the population dynamics and wave propagation speed is small. In addition, it is found that only the propagating speed of the progenitor cells is affected by the regulation when the diffusion of the differentiated cells is large. In the presence of de-differentiation, the effect on down-regulating the progenitor population is weakened and there is no effect on the propagation speed due to regulation, suggesting that the effect of regulatory control is diminished by de-differentiation pathways.
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Affiliation(s)
- Mao-Xiang Wang
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China; School of Science, Nanjing University of Science and Technology, Nanjing 210094, China.
| | - Yu-Qiang Ma
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China; Center for Soft Condensed Matter Physics and Interdisciplinary Research, Soochow University, Suzhou 215006, China
| | - Pik-Yin Lai
- Department of Physics, Graduate Institute of Biophysics, National Central University, Chungli 320, Taiwan, ROC.
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29
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Stiehl T, Baran N, Ho AD, Marciniak-Czochra A. Cell division patterns in acute myeloid leukemia stem-like cells determine clinical course: a model to predict patient survival. Cancer Res 2015; 75:940-9. [PMID: 25614516 DOI: 10.1158/0008-5472.can-14-2508] [Citation(s) in RCA: 66] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Acute myeloid leukemia (AML) is a heterogeneous disease in which a variety of distinct genetic alterations might occur. Recent attempts to identify the leukemia stem-like cells (LSC) have also indicated heterogeneity of these cells. On the basis of mathematical modeling and computer simulations, we have provided evidence that proliferation and self-renewal rates of the LSC population have greater impact on the course of disease than proliferation and self-renewal rates of leukemia blast populations, that is, leukemia progenitor cells. The modeling approach has enabled us to estimate the LSC properties of 31 individuals with relapsed AML and to link them to patient survival. On the basis of the estimated LSC properties, the patients can be divided into two prognostic groups that differ significantly with respect to overall survival after first relapse. The results suggest that high LSC self-renewal and proliferation rates are indicators of poor prognosis. Nevertheless, high LSC self-renewal rate may partially compensate for slow LSC proliferation and vice versa. Thus, model-based interpretation of clinical data allows estimation of prognostic factors that cannot be measured directly. This may have clinical implications for designing treatment strategies.
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Affiliation(s)
- Thomas Stiehl
- Institute of Applied Mathematics, University of Heidelberg, Heidelberg, Germany. Bioquant Center, University of Heidelberg, Heidelberg, Germany. Interdisciplinary Center for Scientific Computing (IWR), University of Heidelberg, Heidelberg, Germany.
| | - Natalia Baran
- Department of Medicine V, Medical Center, University of Heidelberg, Heidelberg, Germany
| | - Anthony D Ho
- Department of Medicine V, Medical Center, University of Heidelberg, Heidelberg, Germany
| | - Anna Marciniak-Czochra
- Institute of Applied Mathematics, University of Heidelberg, Heidelberg, Germany. Bioquant Center, University of Heidelberg, Heidelberg, Germany. Interdisciplinary Center for Scientific Computing (IWR), University of Heidelberg, Heidelberg, Germany
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30
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Jayachandran D, Rundell AE, Hannemann RE, Vik TA, Ramkrishna D. Optimal chemotherapy for leukemia: a model-based strategy for individualized treatment. PLoS One 2014; 9:e109623. [PMID: 25310465 PMCID: PMC4195683 DOI: 10.1371/journal.pone.0109623] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/19/2014] [Accepted: 09/12/2014] [Indexed: 12/11/2022] Open
Abstract
Acute Lymphoblastic Leukemia, commonly known as ALL, is a predominant form of cancer during childhood. With the advent of modern healthcare support, the 5-year survival rate has been impressive in the recent past. However, long-term ALL survivors embattle several treatment-related medical and socio-economic complications due to excessive and inordinate chemotherapy doses received during treatment. In this work, we present a model-based approach to personalize 6-Mercaptopurine (6-MP) treatment for childhood ALL with a provision for incorporating the pharmacogenomic variations among patients. Semi-mechanistic mathematical models were developed and validated for i) 6-MP metabolism, ii) red blood cell mean corpuscular volume (MCV) dynamics, a surrogate marker for treatment efficacy, and iii) leukopenia, a major side-effect. With the constraint of getting limited data from clinics, a global sensitivity analysis based model reduction technique was employed to reduce the parameter space arising from semi-mechanistic models. The reduced, sensitive parameters were used to individualize the average patient model to a specific patient so as to minimize the model uncertainty. Models fit the data well and mimic diverse behavior observed among patients with minimum parameters. The model was validated with real patient data obtained from literature and Riley Hospital for Children in Indianapolis. Patient models were used to optimize the dose for an individual patient through nonlinear model predictive control. The implementation of our approach in clinical practice is realizable with routinely measured complete blood counts (CBC) and a few additional metabolite measurements. The proposed approach promises to achieve model-based individualized treatment to a specific patient, as opposed to a standard-dose-for-all, and to prescribe an optimal dose for a desired outcome with minimum side-effects.
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Affiliation(s)
- Devaraj Jayachandran
- School of Chemical Engineering, Purdue University, West Lafayette, Indiana, United States of America
| | - Ann E. Rundell
- Weldon School of Biomedical Engineering, Purdue University, West Lafayette, Indiana, United States of America
| | - Robert E. Hannemann
- School of Chemical Engineering, Purdue University, West Lafayette, Indiana, United States of America
- Weldon School of Biomedical Engineering, Purdue University, West Lafayette, Indiana, United States of America
| | - Terry A. Vik
- Riley Hospital for Children, Indianapolis, Indiana, United States of America
| | - Doraiswami Ramkrishna
- School of Chemical Engineering, Purdue University, West Lafayette, Indiana, United States of America
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31
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Dale DC, Mackey MC. Understanding, treating and avoiding hematological disease: better medicine through mathematics? Bull Math Biol 2014; 77:739-57. [PMID: 25213154 DOI: 10.1007/s11538-014-9995-x] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/19/2014] [Accepted: 07/08/2014] [Indexed: 10/24/2022]
Abstract
This paper traces the experimental, clinical and mathematical modeling efforts to understand a periodic hematological disease-cyclical neutropenia. It is primarily a highly personal account by two scientists from quite different backgrounds of their interactions over almost 40 years and their attempts to understand this intriguing disease. It's also a story of their efforts to offer effective treatments for the patients who suffer from cyclic neutropenia and other conditions causing neutropenia and infections.
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Affiliation(s)
- David C Dale
- Department of Medicine, University of Washington, Seattle, WA, 98195, USA,
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32
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Abstract
Population balance modeling is undergoing phenomenal growth in its applications, and this growth is accompanied by multifarious reviews. This review aims to fortify the model's fundamental base, as well as point to a variety of new applications, including modeling of crystal morphology, cell growth and differentiation, gene regulatory processes, and transfer of drug resistance. This is accomplished by presenting the many faces of population balance equations that arise in the foregoing applications.
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Affiliation(s)
| | - Meenesh R. Singh
- School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, California 94704
- Joint Center for Artificial Photosynthesis, Lawrence Berkeley National Laboratory, Berkeley, California 94720
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33
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Stiehl T, Baran N, Ho AD, Marciniak-Czochra A. Clonal selection and therapy resistance in acute leukaemias: mathematical modelling explains different proliferation patterns at diagnosis and relapse. J R Soc Interface 2014; 11:20140079. [PMID: 24621818 PMCID: PMC3973374 DOI: 10.1098/rsif.2014.0079] [Citation(s) in RCA: 66] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
Abstract
Recent experimental evidence suggests that acute myeloid leukaemias may originate from multiple clones of malignant cells. Nevertheless, it is not known how the observed clones may differ with respect to cell properties, such as proliferation and self-renewal. There are scarcely any data on how these cell properties change due to chemotherapy and relapse. We propose a new mathematical model to investigate the impact of cell properties on the multi-clonal composition of leukaemias. Model results imply that enhanced self-renewal may be a key mechanism in the clonal selection process. Simulations suggest that fast proliferating and highly self-renewing cells dominate at primary diagnosis, while relapse following therapy-induced remission is triggered mostly by highly self-renewing but slowly proliferating cells. Comparison of simulation results to patient data demonstrates that the proposed model is consistent with clinically observed dynamics based on a clonal selection process.
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Affiliation(s)
- Thomas Stiehl
- Institute of Applied Mathematics, BIOQUANT and IWR, Im Neuenheimer Feld 294, University of Heidelberg, , 69120 Heidelberg, Germany
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34
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Dynamic spatial pattern formation in the sea urchin embryo. J Math Biol 2014; 68:581-608. [DOI: 10.1007/s00285-012-0640-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/07/2012] [Revised: 12/16/2012] [Indexed: 10/27/2022]
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35
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Kimmel M. Stochasticity and determinism in models of hematopoiesis. ADVANCES IN EXPERIMENTAL MEDICINE AND BIOLOGY 2014; 844:119-52. [PMID: 25480640 DOI: 10.1007/978-1-4939-2095-2_7] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
Abstract
This chapter represents a novel view of modeling in hematopoiesis, synthesizing both deterministic and stochastic approaches. Whereas the stochastic models work in situations where chance dominates, for example when the number of cells is small, or under random mutations, the deterministic models are more important for large-scale, normal hematopoiesis. New types of models are on the horizon. These models attempt to account for distributed environments such as hematopoietic niches and their impact on dynamics. Mixed effects of such structures and chance events are largely unknown and constitute both a challenge and promise for modeling. Our discussion is presented under the separate headings of deterministic and stochastic modeling; however, the connections between both are frequently mentioned. Four case studies are included to elucidate important examples. We also include a primer of deterministic and stochastic dynamics for the reader's use.
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Affiliation(s)
- Marek Kimmel
- Department of Statistics and Bioengineering, Rice University, 2102 Duncan Hall, 6100 Main St., 77005, Houston, TX, USA,
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36
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Understanding and Treating Cytopenia Through Mathematical Modeling. ADVANCES IN EXPERIMENTAL MEDICINE AND BIOLOGY 2014; 844:279-302. [DOI: 10.1007/978-1-4939-2095-2_14] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
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37
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Avila JL, Bonnet C, Clairambault J, Özbay H, Niculescu SI, Merhi F, Ballesta A, Tang R, Marie JP. Analysis of a New Model of Cell Population Dynamics in Acute Myeloid Leukemia. DELAY SYSTEMS 2014. [DOI: 10.1007/978-3-319-01695-5_23] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
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38
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Adimy M, Angulo O, Marquet C, Sebaa L. A mathematical model of multistage hematopoietic cell lineages. ACTA ACUST UNITED AC 2014. [DOI: 10.3934/dcdsb.2014.19.1] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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39
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Global dynamics of two-compartment models for cell production systems with regulatory mechanisms. Math Biosci 2013; 245:258-68. [DOI: 10.1016/j.mbs.2013.07.006] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/12/2011] [Revised: 07/12/2013] [Accepted: 07/15/2013] [Indexed: 01/17/2023]
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40
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Stiehl T, Ho AD, Marciniak-Czochra A. The impact of CD34+ cell dose on engraftment after SCTs: personalized estimates based on mathematical modeling. Bone Marrow Transplant 2013; 49:30-7. [DOI: 10.1038/bmt.2013.138] [Citation(s) in RCA: 38] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2013] [Revised: 07/05/2013] [Accepted: 08/03/2013] [Indexed: 11/09/2022]
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41
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Parameter identification of hematopoiesis mathematical model - periodic chronic myelogenous leukemia. Contemp Oncol (Pozn) 2013; 17:73-7. [PMID: 23788966 PMCID: PMC3685348 DOI: 10.5114/wo.2013.33778] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2012] [Revised: 05/17/2012] [Accepted: 05/23/2012] [Indexed: 12/01/2022] Open
Abstract
Periodic chronic myelogenous leukemia (PCML) is a dynamic hematopoietic disease which causes oscillations of circulating leukocytes, platelets and reticulocytes. Mathematical modeling is an invaluable tool to help in predicting hematopoiesis behavior. In this paper we modify the existing models based on improving the parameters of the model. Also more parameters are estimated regarding the proposed model. It is our major intention to construct a physiological model which can map major identified mechanisms of leukopoiesis to provide a deeper insight into this complex biological process. In the proposed model the leukocytes line has been modeled more precisely. In fact, precursor cells have been considered as two separate groups: proliferating precursor cells and non-proliferating precursor cells. As a result, more parameters have appeared in the model and identifying the new parameters has resulted in a better fit of clinical data and the data extracted from the model for both platelets and leukocytes. That is, the new model describes the leukocytes and platelets of the system in a way that is closer to clinical data, so the proposed model can be more useful for predicting the behavior of leukocytes and platelets for PCML disease. Compared with the previous works, it is shown that the new model has a better fit of the quantitative data on leukocytes and platelets.
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Serna S, Nirody JA, Rácz MZ. Analysis of unstable behavior in a mathematical model for erythropoiesis. J Math Biol 2013; 66:595-625. [DOI: 10.1007/s00285-012-0524-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2011] [Revised: 03/07/2012] [Indexed: 10/28/2022]
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Billy F, Clairambault J. Designing proliferating cell population models with functional targets for control by anti-cancer drugs. ACTA ACUST UNITED AC 2013. [DOI: 10.3934/dcdsb.2013.18.865] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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Abstract
The circadian timing system controls cell cycle, apoptosis, drug bioactivation, and transport and detoxification mechanisms in healthy tissues. As a consequence, the tolerability of cancer chemotherapy varies up to several folds as a function of circadian timing of drug administration in experimental models. Best antitumor efficacy of single-agent or combination chemotherapy usually corresponds to the delivery of anticancer drugs near their respective times of best tolerability. Mathematical models reveal that such coincidence between chronotolerance and chronoefficacy is best explained by differences in the circadian and cell cycle dynamics of host and cancer cells, especially with regard circadian entrainment and cell cycle variability. In the clinic, a large improvement in tolerability was shown in international randomized trials where cancer patients received the same sinusoidal chronotherapy schedule over 24h as compared to constant-rate infusion or wrongly timed chronotherapy. However, sex, genetic background, and lifestyle were found to influence optimal chronotherapy scheduling. These findings support systems biology approaches to cancer chronotherapeutics. They involve the systematic experimental mapping and modeling of chronopharmacology pathways in synchronized cell cultures and their adjustment to mouse models of both sexes and distinct genetic background, as recently shown for irinotecan. Model-based personalized circadian drug delivery aims at jointly improving tolerability and efficacy of anticancer drugs based on the circadian timing system of individual patients, using dedicated circadian biomarker and drug delivery technologies.
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Avila J, Bonnet C, Clairambault J, Özbay H, Niculescu S, Merhi F, Tang R, Marie J. A new model of cell dynamics in Acute Myeloid Leukemia involving distributed delays1. ACTA ACUST UNITED AC 2012. [DOI: 10.3182/20120622-3-us-4021.00047] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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PRECUP RADU, ARGHIRESCU SMARANDA, CUCUIANU ANDREI, ŞERBAN MARGIT. MATHEMATICAL MODELING OF CELL DYNAMICS AFTER ALLOGENEIC BONE MARROW TRANSPLANTATION. INT J BIOMATH 2012. [DOI: 10.1142/s1793524511001684] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
In this paper a basic mathematical model is introduced to describe the dynamics of three cell lines after allogeneic stem cell transplantation: normal host cells, leukemic host cells and donor cells. Their evolution is one of competitive type and depends upon kinetic and cell–cell interaction parameters. Numerical simulations prove that the evolution can ultimately lead either to the normal hematopoietic state achieved by the expansion of the donor cells and the elimination of the host cells, or to the leukemic hematopoietic state characterized by the proliferation of the cancer line and the suppression of the other cell lines. One state or the other is reached depending on cell–cell interactions (anti-host, anti-leukemia and anti-graft effects) and initial cell concentrations at transplantation. The model also provides a theoretical basis for the control of post-transplant evolution aimed at the achievement of normal hematopoiesis.
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Affiliation(s)
- RADU PRECUP
- Department of Applied Mathematics, "Babeş–Bolyai" University, Cluj 400084, Romania
| | - SMARANDA ARGHIRESCU
- Department of Hematology, "Victor Babeş" University of Medicine and Pharmacy, Timişoara 300041, Romania
| | - ANDREI CUCUIANU
- Department of Hematology, "Iuliu Haţieganu" University of Medicine and Pharmacy, Cluj 400012, Romania
| | - MARGIT ŞERBAN
- Department of Hematology, "Victor Babeş" University of Medicine and Pharmacy, Timişoara 300041, Romania
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Batzel JJ, Kappel F. Time delay in physiological systems: analyzing and modeling its impact. Math Biosci 2011; 234:61-74. [PMID: 21945380 DOI: 10.1016/j.mbs.2011.08.006] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/10/2011] [Revised: 08/22/2011] [Accepted: 08/25/2011] [Indexed: 10/17/2022]
Abstract
This article examines the functional and clinical impact of time delays that arise in human physiological systems, especially control systems. An overview of the mathematical and physiological contexts for considering time delays will be illustrated, from the system level to cell level, by examining models that incorporate time delays. This examination will highlight how such delays in combination with other system structures and parameters influence system dynamics. Model analysis that reveals the influence of delays can also reveal related physiological effects which may have medical consequences and clinical applications.
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Affiliation(s)
- Jerry J Batzel
- Institute for Mathematics and Scientific Computing, University of Graz, Austria.
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Nakaoka S, Aihara K. Mathematical study on kinetics of hematopoietic stem cells--theoretical conditions for successful transplantation. JOURNAL OF BIOLOGICAL DYNAMICS 2011; 6:836-854. [PMID: 22873618 DOI: 10.1080/17513758.2011.588343] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
Numerous haematological diseases occur due to dysfunctions during homeostasis processes of blood cell production. Haematopoietic stem cell transplantation (HSCT) is a therapeutic option for the treatment of haematological malignancy and congenital immunodeficiency. Today, HSCT is widely applied as an alternative method to bone marrow transplantation; however, HSCT can be a risky procedure because of potential side effects and complications after transplantations. Although an optimal regimen to achieve successful HSCT while maintaining quality of life is to be developed, even theoretical considerations such as the evaluations of successful engraftments and proposals of clinical management strategies have not been fully discussed yet. In this paper, we construct and investigate mathematical models that describe the kinetics of hematopoietic stem cell self-renewal and granulopoiesis under the influence of growth factors. Moreover, we derive theoretical conditions for successful HSCT, primarily on the basis of the idea that the basic reproduction number R (0) represents a threshold condition for a population to successfully grow in a given steady-state environment. Successful engraftment of transplanted haematopoietic stem cells (HSCs) is subsequently ensured by employing a concept of dynamical systems theory known as 'persistence'. On the basis of the implications from the modelling study, we discuss how the conditions derived for a successful HSCT are used to link to experimental studies.
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Affiliation(s)
- Shinji Nakaoka
- FIRST, Aihara Innovative Mathematical Modelling Project, Japan Science and Technology Agency, Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo, 153-8505, Japan.
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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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Akushevich IV, Veremeyeva GA, Dimov GP, Ukraintseva SV, Arbeev KG, Akleyev AV, Yashin AI. Modeling hematopoietic system response caused by chronic exposure to ionizing radiation. RADIATION AND ENVIRONMENTAL BIOPHYSICS 2011; 50:299-311. [PMID: 21259022 PMCID: PMC3830531 DOI: 10.1007/s00411-011-0351-3] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/15/2010] [Accepted: 01/04/2011] [Indexed: 05/30/2023]
Abstract
A new model of the hematopoietic system response in humans chronically exposed to ionizing radiation describes the dynamics of the hematopoietic stem cell compartment as well as the dynamics of each of the four blood cell types (lymphocytes, neutrophiles, erythrocytes, and platelets). The required model parameters were estimated based on available results of human and experimental animal studies. They include the steady-state number of hematopoietic stem cells and peripheral blood cell lines in an unexposed organism, amplification parameters for each blood line, parameters describing proliferation and apoptosis, parameters of feedback functions regulating the steady-state numbers, and characteristics of radiosensitivity related to cell death and non-lethal cell damage. The model predictions were tested using data on hematological measurements (e.g., blood counts) performed in 1950-1956 in the Techa River residents chronically exposed to ionizing radiation since 1949. The suggested model of hematopoiesis is capable of describing experimental findings in the Techa River Cohort, including: (1) slopes of the dose-effect curves reflecting the inhibition of hematopoiesis due to chronic ionizing radiation, (2) delay in effect of chronic exposure and accumulated character of the effect, and (3) dose-rate patterns for different cytopenic states (e.g., leukopenia, thrombocytopenia).
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Affiliation(s)
- Igor V Akushevich
- Center for Population Health and Aging, Duke University, 002 Trent Hall, Box 90408, Durham, NC 27708-0408, USA.
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