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. 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.

Origin of bistability in the lac Operon.

Multistability is an emergent dynamic property that has been invoked to explain multiple coexisting biological states. In this work, we investigate the origin of bistability in the lac operon. To do this, we develop a mathematical model for the regulatory pathway in this system and compare the model predictions with other experimental results in which a nonmetabolizable inducer was employed. We investigate the effect of lactose metabolism using this model, and show that it greatly modifies the bistable region in the external lactose (Le) versus external glucose (Ge) parameter space. The model also predicts that lactose metabolism can cause bistability to disappear for very low Ge. We have also carried out stochastic numerical simulations of the model for several values of Ge and Le. Our results indicate that bistability can help guarantee that Escherichia coli consumes glucose and lactose in the most efficient possible way. Namely, the lac operon is induced only when there is almost no glucose in the growing medium, but if Le is high, the operon induction level increases abruptly when the levels of glucose in the environment decrease to very low values. We demonstrate that this behavior could not be obtained without bistability if the stability of the induced and uninduced states is to be preserved. Finally, we point out that the present methods and results may be useful to study the emergence of multistability in biological systems other than the lac operon.

Stimulus-dependent onset latency of inhibitory recurrent activity.

This paper gives an explanation for the experimentally observed onset latencies of the inhibitory responses that vary from a few milliseconds to hundreds of milliseconds in systems where the conduction delays are only several milliseconds in the feedback pathways. To do this we use a simple mathematical model. The model consists of two delay differential equations (DDE) where the nonlinear relation between the postsynaptic potential and the firing frequency of the neuron population arises from the stoichiometry of the transmitter-receptor kinetics. The parameters of the model refer to the hippocampal feedback system, and the modeling results are compared with corresponding experiments.

Information capacity and pattern formation in a tent map network featuring statistical periodicity.

We provide quantitative support to the observation that lattices of coupled maps are "efficient" information coding devices. It has been suggested recently that lattices of coupled maps may provide a model of information coding in the nervous system because of their ability to create structured and stimulus-dependent activity patterns which have the potential to be used for storing information. In this paper, we give an upper bound to the effective number of patterns that can be used to store information in the lattice by evaluating numerically its information capacity or information rate as a function of the coupling strength between the maps. We also estimate the time taken by the lattice to establish a limiting activity pattern.

The rate of apoptosis in post mitotic neutrophil precursors of normal and neutropenic humans.

Using data on the fraction of post-mitotic neutrophil precursors (CD15+ cells) displaying positive markers for apoptosis in 12 normal humans, and a simple mathematical model, we have estimated the apoptotic rate to be about 0.28/day in this compartment. This implies that the influx of myelocytes into the post-mitotic compartment exceeds twice the granulocyte turnover rate (GTR), and that about 55% of the cells entering this compartment die before being released into the blood. The normal half life of apoptotic post-mitotic neutrophil precursors is calculated to be 10.4 h. Comparable calculations for patients indicate apoptosis rates in the post-mitotic compartment of about 17 times normal for one myelokathexis patient and rates of about 13 times normal for the one cyclical neutropenic patient and two severe congenital neutropenic patients. The estimated half life for apoptotic post-mitotic neutrophil precursors in the myelokathexis patient was about 0.4 h, 1.4 h in the cyclical neutropenia patient, and about 0.6 h in the severe congenital neutropenic patients.

Cell kinetic status of haematopoietic stem cells.

The haematopoietic stem cell (HSC) population supports a tremendous cellular production over the course of an animal's lifetime, e.g. adult humans produce their body weight in red cells, white cells and platelets every 7 years, while the mouse produces about 60% of its body weight in the course of a 2 year lifespan. Understanding how the HSC population carries this out is of interest and importance, and a first step in that understanding involves the characterization of HSC kinetics. Using previously published continuous labelling data (of Bradford et al. 1997 and Cheshier et al. 1999) from mouse HSC and a standard G0 model for the cell cycle, the steady state parameters characterizing these HSC populations are derived. It is calculated that in the mouse the differentiation rate ranges between about 0.01 and 0.02, the rate of cell re-entry from G0 back into the proliferative phase is between 0.02 and 0.05, the rate of apoptosis from the proliferative phase is between 0.07 and 0.23 (all units are days(-1)), and the duration of the proliferative phase is between 1.4 and 4.3 days. These values are compared with previously obtained values derived from the modelling by Abkowitz and colleagues of long-term haematopoietic reconstitution in the cat (Abkowitz et al. 1996) and the mouse (Abkowitz et al. 2000). It is further calculated using the estimates derived in this paper and other data on mice that between the HSC and the circulating blood cells there are between 17 and 19.5 effective cell divisions giving a net amplification of between approximately 170 000 and approximately 720 000.

Resonance in periodic chemotherapy: a case study of acute myelogenous leukemia.

The effects of periodic chemotherapy administration are evaluated within the context of a G(0)model of the cell cycle. Parameters are estimated for normal bone marrow cells and malignant cells in acute myelogenous leukemia (AML). This model explicitly includes the resting G(0)phase and the feedback mechanism that recruits the cells back into the cell cycle. Periodic chemotherapy administration can induce resonance within our model under high cell kill rate where the average cell cycle times may change during the course of treatment, and therapeutic benefits from these resonances cannot be solely based on cell cycle times in untreated tissue. The depletion rate under chemotherapy and the regrowth rate may differ between the cell populations, and our analysis suggests that this favors the tumour cells. We were able to distinguish between the effects of cycle-non-specific, S -phase-specific and M -phase-specific drugs, and found that these can show differences in sharpness and location of the resonance phenomenon. We conclude that resonance chemotherapy (chronotherapy) is unlikely to be efficacious in the treatment of AML.

Dynamic regulation of the tryptophan operon: a modeling study and comparison with experimental data.

A mathematical model for regulation of the tryptophan operon is presented. This model takes into account repression, feedback enzyme inhibition, and transcriptional attenuation. Special attention is given to model parameter estimation based on experimental data. The model's system of delay differential equations is numerically solved, and the results are compared with experimental data on the temporal evolution of enzyme activity in cultures of Escherichia coli after a nutritional shift (minimal + tryptophan medium to minimal medium). Good agreement is obtained between the numeric simulations and the experimental results for wild-type E. coli, as well as for two different mutant strains.

Regulation of platelet production: the normal response to perturbation and cyclical platelet disease.

An age-structured model for the regulation of platelet production is developed, and compared with both normal and pathological platelet production. We consider the role of thrombopoietin (TPO) in this process, how TPO affects the transition between megakaryocytes of various ploidy classes, and their individual contributions to platelet production. After the estimation of the relevant parameters of the model from both in vivo and in vitro data, we use the model to numerically reproduce the normal human response to a bolus injection of TPO. We further show that our model reproduces the dynamic characteristics of autoimmune cyclical thromobocytopenia if the rate of platelet destruction in the circulation is elevated to more than twice the normal value.

Stress, pre-term labour and birth outcomes.

Stress, pre-term labour and birth outcomes Preliminary studies have suggested that stress may be associated with the onset, treatment and outcomes of pre-term labour; however, a systematic comparison of the stress of women with and without pre-term labour has not been reported. Therefore, the purpose of this exploratory study was to compare the stress (daily hassles and mood states) and birth outcomes of black and white women who experienced pre-term labour (PTL) during pregnancy with those who did not. The convenience sample consisted of 35 pregnant women hospitalized in 1996-1997 for the treatment of PTL (24-35 weeks gestation) and 35 controls matched on age, race, parity, gestational age and method of hospital payment. Women in the PTL group had significantly higher tension-anxiety and depression-dejection on the Profile of Mood States (POMS), lower mean birthweight and mean gestational age, and a higher percentage of babies born <37 weeks and weighing 2500 g or less. Black women in the PTL group and white women in the control group had significantly higher scores on the fatigue sub-scale of the POMS and the work and future security sub-scales of the Daily Hassles Scale. Women in the PTL group whose babies weighed 2500 g or less had significantly higher scores on the health, inner concern and financial responsibility sub-scales of the Daily Hassles Scale. The findings from this study indicate the need for further exploration of the interaction of race and stress in understanding and preventing PTL and low birthweight and the need to examine the role of social support in preventing pre-term birth after an episode of PTL.

Modeling complex neutrophil dynamics in the grey collie.

We have developed a mathematical model for the peripheral regulation of neutrophil production mediated by granulocyte colony-stimulating factor. We have used that model to show that the pattern of neutrophil oscillations in nine grey collies is consistent with the hypothesis that cyclical neutropenia is due to an oscillatory stem cell input to the neutrophil regulatory system, and not due to autonomous oscillations in the peripheral neutrophil regulatory system. In the process of interfacing our model with the laboratory data, we have estimated parameters for the peripheral neutrophil control system consistent with higher than normal apoptotic cell loss within the recognizable neutrophil precursors. This is in agreement with other experimental data. Our estimated model parameters also predict that the peripheral neutrophil production system is globally stable in the grey collies we studied. This further supports our hypothesis that the origin of the oscillatory behavior in cyclical neutropenia is in the stem cell population, consistent with other clinical and experimental evidence.

Alienation from self and others: the psychosocial problem of rural alcoholic women.

The purpose of this study was to describe women's perspectives in becoming and being alcohol dependent. Using grounded theory techniques, 14 adult Black and White women receiving treatment for alcohol addiction at rural substance abuse centers participated in an intensive interview. Data analysis focused on the identification of the basic psychosocial problem and the process of becoming alcohol dependent. The results are presented in 2 parts. Part 1, "Alienation From Self and Others," focuses on the basic psychosocial problem faced by women in becoming alcohol dependent. Part 2, "Running Away to Nowhere," on page 142 of this issue of Archives, describes the process used by women to resolve this problem.

Running away to nowhere: rural women's experiences of becoming alcohol dependent.

The purpose of this study was to describe women's perspectives in becoming and being alcohol dependent. Part 1, "Alienation From Self and Others," on page 134 in this issue of Archives, describes the study methods, the sample, and the basic psychosocial problem faced by rural, alcoholic women. Part 2, "Running Away to Nowhere," focuses on the basic psychosocial process that women used to resolve the pain caused by their "Alienation From Self and Others." The article concludes with suggestions for nursing intervention.

Neural ensemble coding and statistical periodicity: speculations on the operation of the mind's eye.

Statistical periodicity is a statistical property of densities which arises in the description of retarded dynamical systems. This property is particularly attractive as a possible mechanism for the ensemble coding of information in the nervous system because it operates rapidly and has high storage capacity. For a population of neurons which exhibits statistical periodicity, information would not be encoded by the periodicity, but rather by the spatio-temporal distributions of neural activity. Statistical periodicity is discussed in relation to the temporal binding hypothesis and to the occurrence of multistability in neural systems.

An explanatory model of preterm labor.

The purpose of this article is to describe women's explanatory model of their preterm labor (PTL) experiences. Fourteen young adult (20 to 23 years of age) women living in the southeast, who were hospitalized for the treatment of PTL, participated in this naturalistic study. Stress was the dominant theme that all participants used to explain what had precipitated PTL. All women described multiple stressors and chaos in their lives, which preceded their admission to the hospital for PTL. Meanings of PTL were intertwined with dysfunctional families and problematic relationships. All 9 women who delivered at term were able to find a friend or family member to provide support that allowed the women to relax and reduce the stress in their lives. In contrast, women who delivered preterm had no one in their lives that could provide help and support. Women's conceptualizations of PTL suggest that culturally appropriate interventions to reduce stress and mobilize support may help improve birth outcomes after an episode of PTL.

Pica: sorting it out.

Pica, a culture-bound illness, has occurred for centuries. The ingestion of nonfood substances such as starch, cornstarch, clay, dirt, and other material is fairly common, although the distribution of the condition varies by cultural and socioeconomic factors. The underlying cause of pica is not known, although the condition often is associated with pregnancy. There is conflicting evidence about the association of nutrient deficiencies and pica. This article presents a clinical example of pica in a pregnant 33-year-old African American woman. Implications for culturally appropriate care are discussed.

Hematopoietic dynamics in grey collies.

Using Lomb periodogram analysis we have quantified variations in the peripheral neutrophil and platelet counts of the cyclical neutropenia animal model-the grey collie. We found that the amplitudes of the oscillations in these two cell lineages vary concomitantly. Further, the power spectrum and the shape of the oscillations in the absolute neutrophil counts vary together with the amplitude of the oscillations. As the amplitude of the oscillations increases, the height of the second subharmonic increases, giving rise to a distorted oscillation with two peaks per cycle. The particular dynamics of the absolute neutrophil counts can be reproduced by a combination of a delayed peripheral feedback, representing the peripheral control of granulopoiesis through granulocyte colony stimulating factor, together with a sinusoidal input representing an oscillatory input from the pluripotential stem cells to the granulocytic lineage. The same pluripotential stem cell input is probably responsible for the sinusoidal oscillations observed in the other cell lineages.

Women's experiences of preterm labor: a feminist critique.

Using a feminist perspective, women's experiences of preterm labor (PTL) were critiqued and compared with the medical establishment's perspective on PTL as described in the medical literature. Interview data from 29 women who participated in a larger study on the PTL experience were revisited and examined based on principles of feminist theory. The persistent "medicalization" of women's bodies was discussed and used as a framework to explore several issues: (a) the diagnosis of PTL and what it means to be at risk for this phenomenon; and (b) the treatment of PTL including the role of medications, activity, and home monitoring for uterine contractions. Based on the differences that emerged when PTL--was examined from two divergent standpoints--the women's perspective and the physician's perspective--some alternative approaches to PTL management that place women's lives at the center of the treatment process were suggested.

Periodic chronic myelogenous leukaemia: spectral analysis of blood cell counts and aetiological implications.

Of 24 published clinical reports of periodic chronic myelogenous leukaemia (PCML), 21 had sufficient data to analyse for periodicity, and 12 showed significant periodicity (p < or = 0.05) using the Lomb periodogram. Leucocyte oscillations had periods T ranging from 37 to 83d. When data were also reported for platelets and reticulocytes there was no significant difference between their periods and those of the leucocytes. These data and their analysis provide strong circumstantial evidence for a haemopoietic stem cell origin of PCML. Namely, the known chromosomal changes in CML patients may, on occasion, also be accompanied by a destabilization resulting in an oscillatory efflux into the leucocyte, platelet and erythrocytic pathways.

Occurrence of periodic oscillations in the differential blood counts of congenital, idiopathic, and cyclical neutropenic patients before and during treatment with G-CSF.

Using techniques developed in astrophysics to deal with unequally sampled data sets, we have analyzed serial differential cell counts from 45 congenital, idiopathic, and cyclic neutropenic patients before and during treatment with recombinant human G-CSF (rhG-CSF). Our results show that the occurrence of significant cycling in the absolute neutrophil count (ANC) of neutropenics not classified as cyclical is much more prevalent than had been previously thought, and that not all the patients classified as cyclic show significant ANC periodicity. In these patients, cycling in more than one cell line may be involved. The range of periods encountered in these patients is much broader (between 11 and 52 days) than is usually associated with classical cyclical neutropenia, and there is no obvious connection between the range of periods and the patient's diagnostic category. Administration of rhG-CSF is able to induce significant cycling in neutropenic patients that were not cycling prior to treatment. In patients who had significant cycling before treatment, rhG-CSF may either decrease the period to between 11 and 14 days, or may obliterate any statistical evidence of cycling.