Periodic Hematological Disorders: Quintessential Examples of Dynamical Diseases

Periodic hematological disorders: Quintessential examples of dynamical diseases Cite as: Chaos 30, 063123 (2020); https://doi.org/10.1063/5.0006517 Submitted: 04 March 2020 . Accepted: 21 May 2020 . Published Online: 08 June 2020 Michael C. Mackey Chaos 30, 063123 (2020); https://doi.org/10.1063/5.0006517 30, 063123 © 2020 Author(s). Chaos ARTICLE scitation.org/journal/cha Periodic hematological disorders: Quintessential examples of dynamical diseases Cite as: Chaos 30, 063123 (2020); doi: 10.1063/5.0006517 Submitted: 4 March 2020 · Accepted: 21 May 2020 · Published Online: 8 June 2020 View Online Export Citation CrossMark Michael C. Mackeya) AFFILIATIONS Department of Physiology, Department of Physics, and Department of Mathematics McGill University, Montreal, Quebec H4X 2C1, Canada Note: This paper is part of the Focus Issue on Dynamical Disease: A Translational Perspective. a)Author to whom correspondence should be addressed: [email protected]. URL: https://www.mcgill.ca/mathe matical-physiology-lab/ 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. Published under license by AIP Publishing. https://doi.org/10.1063/5.0006517 The concept of dynamical disease first appeared in 1977, and since the operation of a basically normal control system in a region of that time numerous investigators have searched for examples physiological parameters that produces pathological behavior.” (The that might fulfill the requirements of this hypothesized clini- concept of dynamical disease was preceded by a similar idea related cal entity. Here, I argue that some hematological disorders are to schizophrenia.13) The concept was later elaborated in Ref. 14 with beautiful examples of dynamical diseases and discuss the insights many examples from the biological and medical sciences. that have been obtained into the origin of cyclic neutropenia Here, I summarize the evidence that two periodic hematologi- (and its treatment) and periodic chronic myelogenous leukemia. I cal diseases (cyclic neutropenia and periodic chronic myelogenous also briefly discuss cyclic thrombocytopenia and periodic autoim- leukemia) are perfect examples of dynamical diseases and briefly mune hemolytic anemia. consider two others (periodic autoimmune hemolytic anemia and cyclic thrombocytopenia) for which the evidence is still incomplete. I. INTRODUCTION II. OUTLINE OF HUMAN HEMATOPOIESIS AND ITS Nearly 2400 years ago, Hippocrates associated disease with a change in the regularity of a physiological process. Present day REGULATION clinical medicine often focuses on diseases in which these changes Blood cells are formed from a hematopoietic stem cell (HSC) in occur on time scales ranging from milliseconds to hours, for exam- a process known as hematopoiesis. In humans, hematopoiesis pro- ple, the generation of cardiac and respiratory arrhythmias, tremors, duces the equivalent of our body weight in red blood cells, white and seizures. More puzzling have been those diseases, collectively blood cells, and platelets every decade of life.15 Throughout, this referred to as “periodic diseases,” in which symptoms recur in an process usually proceeds flawlessly, implying the existence of robust approximately periodic fashion.1 Among the latter are the periodic control mechanisms. This cellular renewal system is thus ideal for hematological diseases, i.e., cyclic neutropenia (CN, also known as the study of the normal regulation of tissue proliferation and differ- periodic hematopoiesis),2–5 cyclic thrombocytopenia (CT),6,7 and the entiation from the single cell to whole organ level, and the study of periodic variants of chronic myelogenous leukemia (PCML)8,9 and derangements of these processes. autoimmune hemolytic anemia.10,11 Though hematopoiesis is incredibly complicated,17,18 the broad In 1977, it was proposed12 that some periodic diseases (not just outlines can be summarized as in Fig. 1, which schematically in hematology) might be “dynamical diseases . characterized by shows the major aspects of the mammalian platelet, red blood cell, Chaos 30, 063123 (2020); doi: 10.1063/5.0006517 30, 063123-1 Published under license by AIP Publishing. Chaos ARTICLE scitation.org/journal/cha monocyte, and granulocyte production. Control is mediated by a Periodic hematological diseases fall into two broad classes. The large family of growth factors and cytokines. Three of the major first, with oscillations in numbers of a single circulating cell type, is players are thrombopoietin (TPO), erythropoietin (EPO), and gran- probably due to a destabilization of a peripheral control mechanism, ulocyte colony stimulating factor (G-CSF), which also have local reg- e.g., cyclic thrombocytopenia with periods of 13–65 days7,23,24 and ulatory (LR) effects within the HSC population. All three cytokines autoimmune hemolytic anemia.25 The second type has several cir- will play a major role in our discussion of the hematological dis- culating cell types and seemingly involves the stem cells. Examples ease. CFU/BFU refers to the various in vitro analogs of the in vivo are cyclic neutropenia with periods of 14–45 days26,27 and periodic committed stem cells. chronic myelogenous leukemia.28,29. Both classes of disorders illu- From a mathematical standpoint all of these are negative feed- minate aspects of hematopoietic regulation that would never have back mechanisms in the sense that a fall in a peripheral circulating been discovered in a laboratory setting because of the time scales cell numbers leads to a consequent increase in production of the involved. immature precursor and this response is mediated by a specific cytokine or group of them. The mathematics is further complicated by the fact that there are significant delays (often state dependent) III. MATHEMATICAL MODELING IN HEMATOLOGY between when a cytokine acts and the resulting effect is felt in the Since this is a non-technical survey, detailed consideration of circulation. the variety of mathematical modeling techniques that have been Investigations of whole animal dynamic behavior of cellular employed to understand normal and pathological hematopoiesis is replication systems is hampered by the lack of good quality temporal inappropriate. It suffices to simply note that there is an excellent data on cell numbers and cytokine levels in response to perturbation. recent survey30 of modeling efforts in the area over the past half Ironically, the best source of data currently available comes from century. These techniques range from differential equation models clinical studies of patients with hematological disease. Of the vast through delay differential equations, partial differential equations, array of documented hematological pathologies, the periodic hema- and also agent based models. tological diseases (periods from weeks to months) have been some In work with my collaborators, we have typically utilized non- of the most instructive in terms of elucidating the control mech- linear differential delay equations of variable complexity depend- anisms regulating hematopoiesis.19 See Fig. 2 for an illustration of ing on the question under consideration. Nonlinearities arise four of the most studied of these disorders which form the focus of because of the stoichiometry of cytokine receptor interactions, this paper. and the delays typically reflect maturation and cell cycle times. FIG. 1. The architecture and control of mammalian hematopoiesis. All blood cells are formed from hematopoietic stem cells (HSCs), and this figure summarizes mammalian platelet (P), red blood cell (RBC), monocyte, and granulocyte (G/M includ- ing neutrophil, basophil, and eosinophil) production. Control over these processes is mediated by a variety of cytokines [e.g., thrombopoietin (TPO), erythropoietin (EPO), and granulocyte colony stimulating factor (G-CSF) are the main ones but over 50 have so far been identi- fied], and there are also local regula- tory (LR) effects within the HSC population. CFU/BFU refers to the various in vitro analogs of the in vivo committed stem cells. Reprinted with permission fromC.Haurie et al., Blood 92, 2629–2640 (1998). Copyright 1998 American Society of Hematology. Chaos 30, 063123 (2020); doi: 10.1063/5.0006517 30, 063123-2 Published under license by AIP Publishing. Chaos ARTICLE scitation.org/journal/cha FIG. 2. Examples of data for four periodic hematological diseases. AIHA: reticulocyte numbers (×104 cells/µl) in an AIHA subject.20 CT: cyclic fluctuations in platelet counts (×103 cells/µl).21 CN: circulating neutrophils (×103 cells/µl), platelets (×105 cells/µl), and reticulocytes (×104 cells/µl) in a cyclic neutropenic patient.22 PCML: white blood cells (top) (×104 cells/µl), platelets (middle) (×105 cells/µl), and reticulocyte (bottom) (×104 cells/µl) counts in a PCML patient.9 Reprinted with permission from C. Foley and M. C. Mackey, J. Math. Biol. 58, 285–322 (2009). Copyright 2009 Springer. Representative examples of these models are easily found27,29,31 as are animal model has allowed for the collection of a variety of data that reviews.5,16,19,32–35 would have been difficult to obtain in humans. A major characteristic of CN is that the oscillations are not only present in neutrophils, but often are observed in platelets, IV. PERIODIC HEMATOLOGICAL

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