Operon dynamics with state dependent transcription and/or translation delays.

Transcription and translation retrieve and operationalize gene encoded information in cells. These processes are not instantaneous and incur significant delays. In this paper we study Goodwin models of both inducible and repressible operons with state-dependent delays.

How can we describe density evolution under delayed dynamics?

Although the theory of density evolution in maps and ordinary differential equations is well developed, the situation is far from satisfactory in continuous time systems with delay. This paper reviews some of the work that has been done numerically, the interesting dynamics that have emerged, and the largely unsuccessful attempts that have been made to analytically treat the evolution of densities in differential delay equations. We also present a new approach to the problem and illustrate it with a simple example.

Characterizing Chemotherapy-Induced Neutropenia and Monocytopenia Through Mathematical Modelling.

In spite of the recent focus on the development of novel targeted drugs to treat cancer, cytotoxic chemotherapy remains the standard treatment for the vast majority of patients. Unfortunately, chemotherapy is associated with high hematopoietic toxicity that may limit its efficacy. We have previously established potential strategies to mitigate chemotherapy-induced neutropenia (a lack of circulating neutrophils) using a mechanistic model of granulopoiesis to predict the interactions defining the neutrophil response to chemotherapy and to define optimal strategies for concurrent chemotherapy/prophylactic granulocyte colony-stimulating factor (G-CSF).

Periodic hematological disorders: Quintessential examples of dynamical diseases.

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.

Gilteritinib in the treatment of relapsed and refractory acute myeloid leukemia with a FLT3 mutation.

Acute myeloid leukemia (AML) is a malignancy of uncontrolled proliferation of immature myeloid blasts characterized by clonal evolution and genetic heterogeneity. FMS-like tyrosine kinase 3 (FLT3) mutations occur in up to a third of AML cases and are associated with highly proliferative disease, shorter duration of remission, and increased rates of disease relapse. The known impact of activating mutations in FLT3 in AML on disease pathogenesis, prognosis, and response to therapy has led to the development of tyrosine kinase inhibitors targeting FLT3.

The timing of cyclic cytotoxic chemotherapy can worsen neutropenia and neutrophilia.

Despite recent advances in immunotherapies, cytotoxic chemotherapy continues to be a first-line treatment option for the majority of cancers. Unfortunately, a common side effect in patients undergoing chemotherapy treatment is neutropenia. To mitigate the risk of neutropenia and febrile neutropenia, prophylactic treatment with granulocyte-colony stimulating factor (G-CSF) is administered.

Response of an oscillatory differential delay equation to a periodic stimulus.

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.

Origins of oscillation patterns in cyclical thrombocytopenia.

Cyclical thrombocytopenia (CT) is a rare hematological disease characterized by periodic oscillations in circulating platelet counts. In almost all CT patients, other cell lines show no sign of oscillation, but recently a CT patient was reported with significant oscillations in circulating neutrophils (in the same period as the platelets). In this paper, we attempt to understand this phenomenon through a previously published model of human hematopoiesis.

Neutropenia in Barth syndrome: characteristics, risks, and management.

Purpose Of Review: Barth syndrome (BTHS) is an X-linked disease characterized by defective remodeling of phospholipid side chains in mitochondrial membranes. Major features include neutropenia, dilated cardiomyopathy, motor delay and proximal myopathy, feeding problems, and constitutional growth delay. We conducted this review of neutropenia in BTHS to aid in the diagnosis of this disease, and to improve understanding of both the consequences of neutropenia and the benefits of treatment with granulocyte colony-stimulating factor (G-CSF).

Cyclic thrombocytopenia with statistically significant neutrophil oscillations.

Cyclic thrombocytopenia is often misdiagnosed as immune thrombocytopenia due to similar clinical features, a fact of significance because cyclic thrombocytopenia generally responds poorly to treatments used successfully in immune thrombocytopenia. A precise diagnosis must establish the statistical significance of periodicity of the platelet counts using statistical methods (eg, Lomb-Scargle periodogram).

Normal and pathological dynamics of platelets in humans.

We develop a mathematical model of platelet, megakaryocyte, and thrombopoietin dynamics in humans. We show that there is a single stationary solution that can undergo a Hopf bifurcation, and use this information to investigate both normal and pathological platelet production, specifically cyclic thrombocytopenia. Carefully estimating model parameters from laboratory and clinical data, we then argue that a subset of parameters are involved in the genesis of cyclic thrombocytopenia based on clinical information.

A Mathematical Model of Granulopoiesis Incorporating the Negative Feedback Dynamics and Kinetics of G-CSF/Neutrophil Binding and Internalization.

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.

Response of an oscillatory differential delay equation to a single stimulus.

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.

Mathematical model of galactose regulation and metabolic consumption in yeast.

The galactose network has been extensively studied at the unicellular level to broaden our understanding of the regulatory mechanisms governing galactose metabolism in multicellular organisms. Although the key molecular players involved in the metabolic and regulatory processes of this system have been known for decades, their interactions and chemical kinetics remain incompletely understood. Mathematical models can provide an alternative method to study the dynamics of this network from a quantitative and a qualitative perspective.

The limiting dynamics of a bistable molecular switch with and without noise.

We consider the dynamics of a population of organisms containing two mutually inhibitory gene regulatory networks, that can result in a bistable switch-like behaviour. We completely characterize their local and global dynamics in the absence of any noise, and then go on to consider the effects of either noise coming from bursting (transcription or translation), or Gaussian noise in molecular degradation rates when there is a dominant slow variable in the system. We show analytically how the steady state distribution in the population can range from a single unimodal distribution through a bimodal distribution and give the explicit analytic form for the invariant stationary density which is globally asymptotically stable.

Neutrophil dynamics during concurrent chemotherapy and G-CSF administration: Mathematical modelling guides dose optimisation to minimise neutropenia.

The choice of chemotherapy regimens is often constrained by the patient's tolerance to the side effects of chemotherapeutic agents. This dose-limiting issue is a major concern in dose regimen design, which is typically focused on maximising drug benefits. Chemotherapy-induced neutropenia is one of the most prevalent toxic effects patients experience and frequently threatens the efficient use of chemotherapy.

Phosphate and ADP differently inhibit coordinated smooth muscle myosin groups.

Actin filaments propelled in vitro by groups of skeletal muscle myosin motors exhibit distinct phases of active sliding or arrest, whose occurrence depends on actin length (L) within a range of up to 1.0 μm. Smooth muscle myosin filaments are exponentially distributed with ≈150 nm average length in vivo--suggesting relevance of the L-dependence of myosin group kinetics.

Understanding and treating cytopenia through mathematical modeling.

Here, we briefly review how the study of dynamic hematological diseases with mathematical modeling tools has led to a better understanding of the origin of some types of neutropenia and thrombocytopenia and to improved treatment strategies. In addition, we have briefly discussed how these models suggest improved ways to minimize and/or treat cytopenia induced by chemotherapy.

The utility of simple mathematical models in understanding gene regulatory dynamics.

In this review, we survey work that has been carried out in the attempts of biomathematicians to understand the dynamic behaviour of simple bacterial operons starting with the initial work of the 1960's. We concentrate on the simplest of situations, discussing both repressible and inducible systems and then turning to concrete examples related to the biology of the lactose and tryptophan operons. We conclude with a brief discussion of the role of both extrinsic noise and so-called intrinsic noise in the form of translational and/or transcriptional bursting.

Understanding, treating and avoiding hematological disease: better medicine through mathematics?

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.

Molecular mechanical differences between isoforms of contractile actin in the presence of isoforms of smooth muscle tropomyosin.

The proteins involved in smooth muscle's molecular contractile mechanism - the anti-parallel motion of actin and myosin filaments driven by myosin heads interacting with actin - are found as different isoforms. While their expression levels are altered in disease states, their relevance to the mechanical interaction of myosin with actin is not sufficiently understood. Here, we analyzed in vitro actin filament propulsion by smooth muscle myosin for [Formula: see text]-actin ([Formula: see text]A), [Formula: see text]-actin-tropomyosin-[Formula: see text] ([Formula: see text]A-Tm[Formula: see text]), [Formula: see text]-actin-tropomyosin-[Formula: see text] ([Formula: see text]A-Tm[Formula: see text]), [Formula: see text]-actin ([Formula: see text]A), [Formula: see text]-actin-tropomyosin-[Formula: see text] ([Formula: see text]A-Tm[Formula: see text]), and [Formula: see text]-actin-tropomoysin-[Formula: see text] ([Formula: see text]A-Tm[Formula: see text]).

The kinetics of mechanically coupled myosins exhibit group size-dependent regimes.

Naturally occurring groups of muscle myosin behave differently from individual myosins or small groups commonly assayed in vitro. Here, we investigate the emergence of myosin group behavior with increasing myosin group size. Assuming the number of myosin binding sites (N) is proportional to actin length (L) (N = L/35.

Adiabatic reduction of a model of stochastic gene expression with jump Markov process.

This paper considers adiabatic reduction in a model of stochastic gene expression with bursting transcription considered as a jump Markov process. In this model, the process of gene expression with auto-regulation is described by fast/slow dynamics. The production of mRNA is assumed to follow a compound Poisson process occurring at a rate depending on protein levels (the phenomena called bursting in molecular biology) and the production of protein is a linear function of mRNA numbers.