Visualizing hematopoiesis as a stochastic process.

Stochastic simulation has played an important role in understanding hematopoiesis, but implementing and interpreting mathematical models requires a strong statistical background, often preventing their use by many clinical and translational researchers. Here, we introduce a user-friendly graphical interface with capabilities for visualizing hematopoiesis as a stochastic process, applicable to a variety of mammal systems and experimental designs. We describe the visualization tool and underlying mathematical model, and then use this to simulate serial transplantations in mice, human cord blood cell expansion, and clonal hematopoiesis of indeterminate potential. The outcomes of these virtual experiments challenge previous assumptions and provide examples of the flexible range of hypotheses easily testable via the visualization tool.

Discovering early diabetic neuropathy from epidermal nerve fiber patterns.

Epidermal nerve fibre (ENF) density and morphology are used to study small fibre involvement in diabetic, HIV, chemotherapy induced and other neuropathies. ENF density and summed length of ENFs per epidermal surface area are reduced, and ENFs may appear more clustered within the epidermis in subjects with small fibre neuropathy than in healthy subjects. Therefore, it is important to understand the spatial structure of ENFs. In this paper, we compare the ENF patterns between healthy subjects and subjects suffering from mild diabetic neuropathy. The study is based on suction skin blister specimens from the right foot of 32 healthy subjects and eight subjects with mild diabetic neuropathy. We regard the ENF entry point (location where the trunks of a nerve enters the epidermis) and ENF end point (termination of the nerve fibres) patterns as realizations of spatial point processes, and develop tools that can be used in the analysis and modelling of ENF patterns. We use spatial summary statistics and shift plots and define a new tool, reactive territory, to study the spatial patterns and to compare the patterns of the two groups. We will also introduce a simple model for these data in order to understand the growth process of the nerve fibres. Copyright © 2016 John Wiley & Sons, Ltd.

Likelihood-based inference for discretely observed birth-death-shift processes, with applications to evolution of mobile genetic elements.

Continuous-time birth-death-shift (BDS) processes are frequently used in stochastic modeling, with many applications in ecology and epidemiology. In particular, such processes can model evolutionary dynamics of transposable elements-important genetic markers in molecular epidemiology. Estimation of the effects of individual covariates on the birth, death, and shift rates of the process can be accomplished by analyzing patient data, but inferring these rates in a discretely and unevenly observed setting presents computational challenges. We propose a multi-type branching process approximation to BDS processes and develop a corresponding expectation maximization algorithm, where we use spectral techniques to reduce calculation of expected sufficient statistics to low-dimensional integration. These techniques yield an efficient and robust optimization routine for inferring the rates of the BDS process, and apply broadly to multi-type branching processes whose rates can depend on many covariates. After rigorously testing our methodology in simulation studies, we apply our method to study intrapatient time evolution of IS6110 transposable element, a genetic marker frequently used during estimation of epidemiological clusters of Mycobacterium tuberculosis infections.

The replication rate of human hematopoietic stem cells in vivo.

Hematopoietic stem cells (HSCs) replicate (self-renew) to create 2 daughter cells with capabilities equivalent to their parent, as well as differentiate, and thus can both maintain and restore blood cell production. Cell labeling with division-sensitive markers and competitive transplantation studies have been used to estimate the replication rate of murine HSCs in vivo. However, these methods are not feasible in humans and surrogate assays are required. In this report, we analyze the changing ratio with age of maternal/paternal X-chromosome phenotypes in blood cells from females and infer that human HSCs replicate on average once every 40 weeks (range, 25-50 weeks). We then confirm this estimate with 2 independent approaches, use the estimate to simulate human hematopoiesis, and show that the simulations accurately reproduce marrow transplantation data. Our simulations also provide evidence that the number of human HSCs increases from birth until adolescence and then plateaus, and that the ratio of contributing to quiescent HSCs in humans significantly differs from mouse. In addition, they suggest that human marrow failure, such as the marrow failure that occurs after umbilical cord blood transplantation and with aplastic anemia, results from insufficient numbers of early progenitor cells, and not the absence of HSCs.

BAYESIAN INFERENCE AND MODEL CHOICE IN A HIDDEN STOCHASTIC TWO-COMPARTMENT MODEL OF HEMATOPOIETIC STEM CELL FATE DECISIONS.

Despite rapid advances in experimental cell biology, the in vivo behavior of hematopoietic stem cells (HSC) cannot be directly observed and measured. Previously we modeled feline hematopoiesis using a two-compartment hidden Markov process that had birth and emigration events in the first compartment. Here we perform Bayesian statistical inference on models which contain two additional events in the first compartment in order to determine if HSC fate decisions are linked to cell division or occur independently. Pareto Optimal Model Assessment approach is used to cross check the estimates from Bayesian inference. Our results show that HSC must divide symmetrically (i.e., produce two HSC daughter cells) in order to maintain hematopoiesis. We then demonstrate that the augmented model that adds asymmetric division events provides a better fit to the competitive transplantation data, and we thus provide evidence that HSC fate determination in vivo occurs both in association with cell division and at a separate point in time. Last we show that assuming each cat has a unique set of parameters leads to either a significant decrease or a nonsignificant increase in model fit, suggesting that the kinetic parameters for HSC are not unique attributes of individual animals, but shared within a species.

Hematopoietic stem-cell behavior in nonhuman primates.

Little is known about the behavior of hematopoietic stem cells (HSCs) in primates because direct observations and competitive-repopulation assays are not feasible. Therefore, we used 2 different and independent experimental strategies, the tracking of transgene expression after retroviral-mediated gene transfer (N = 11 baboons; N = 7 rhesus macaques) and quantitation of the average telomere length of granulocytes (N = 132 baboons; N = 14 macaques), together with stochastic methods, to study HSC kinetics in vivo. The average replication rate for baboon HSCs is once per 36 weeks according to gene-marking analyses and once per 23 weeks according to telomere-shortening analyses. Comparable results were derived from the macaque data. These rates are substantially slower than the average replication rates previously reported for HSCs in mice (once per 2.5 weeks) and cats (once per 8.3 weeks). Because baboons and macaques live for 25 to 45 years, much longer than mice ( approximately 2 years) and cats (12-18 years), we can compute that HSCs undergo a relatively constant number ( approximately 80-200) of lifetime replications. Thus, our data suggest that the self-renewal capacity of mammalian stem cells in vivo is defined and evolutionarily conserved.

The kinetics of clonal dominance in myeloproliferative disorders.

To study clonal evolution in myeloproliferative disorders, we used stochastic models of hematopoiesis for mouse and cat, species for which the in vivo kinetics of hematopoietic stem cells (HSCs) have been experimentally defined. We determined the consequence if 1 HSC became able to survive without the support of a microenvironmental niche while the rest of its behavior did not change. Neoplastic cells persisted and dominated hematopoiesis in 14% of mice and 17% of cats, requiring mean times of 2.5 +/- 0.5 and 7.0 +/- 1.2 years, respectively (n=1000 simulations/species). In both species, when the number of neoplastic HSCs exceeded 0.5% of all HSCs, clonal dominance was inevitable. Our results can explain the absence of clonal myeloproliferative disorders in mice (lifetime, 2 years), are consistent with clinical observations in cats, and provide insight into the progression of chronic myelogenous leukemia (CML) in humans. They also demonstrate that competition for microenvironmental support can lead to the suppression of normal hematopoiesis as neoplasia evolves. Toxic or immunologic suppression of normal HSCs is not required.

Estimating human hematopoietic stem cell kinetics using granulocyte telomere lengths.

OBJECTIVE: To study in vivo behavior of hematopoietic stem cells (HSC). MATERIALS AND METHODS: Behavior of HSC is difficult to study because one cannot observe and track cells within the marrow microenvironment. Therefore, information must be obtained from indirect means, such as competitive repopulation assays or surrogate studies, such as observations of telomere shortening in granulocytes. In this article, we use granulocyte telomere length data and a novel approach, stochastic simulation, to derive replication rates of HSC. The approach is first applied to cats and then to humans. RESULTS: Human HSC replicate infrequently, on average once per 45 weeks (range: once per 23 to once per 67 weeks). CONCLUSIONS: This rate is substantially slower than the average replication rates estimated for murine (once per 2.5 weeks) and feline (once per 8.3-10 weeks) HSC in vivo.

Strategies to expand transduced hematopoietic stem cells in vivo.

Data in mice suggest that in vivo selection strategies will expand the numbers of transduced hematopoietic stem cells (HSC) to levels sufficient for clinical therapies, and it is argued that comparable strategies will benefit larger animals and humans. To test this assumption, we performed virtual gene therapy in mouse and cat, species in which the in vivo kinetics of HSC are defined. In the simulated experiments, 10% of HSC and 50% of short-term repopulating cells were transduced with a gene allowing a conditional replication or apoptosis advantage. After transplantation, differentiation proceeded stochastically and contributions of transduced cells were tracked for 2 years. Fifty independent transplantations were simulated per species for each analysis. When transduced HSC had a 2-fold increased chance of replication (self-renewal) extending for 4, 10, or 20 weeks after transplantation, or a 5-fold replication advantage extending for 4 weeks, results in mice were far better than in cat, a larger animal, with slower baseline HSC cell cycle kinetics. Similarly, when transduced HSC had a 2-, 4-, or 10-fold decreased chance of apoptosis, extending for 20 or more weeks after transplantation, the murine studies were poor predictors of feline results. Simulation may allow one to optimize and/or understand the limitations of a gene therapy strategy.

Evidence that the number of hematopoietic stem cells per animal is conserved in mammals.

Humans and larger mammals require more blood cells per lifetime than mice because of their larger size and longer life expectancy. To investigate this evolutionary adaptation, we calculated the total number of nucleated marrow cells (NMCs) per cat, observing the distribution of (59)Fe to marrow, then multiplied this value (1.9 +/- 0.9 x 10(10) [mean +/- SD]) times the frequency of feline hematopoietic stem cells (HSCs) (6 HSCs/10(7) NMCs) to derive the total number of HSCs per cat (11 400 +/- 5400). Surprisingly, when the total number of HSCs per mouse was calculated with a similar experimental and computational approach, the value was equivalent. These data imply that the output of differentiated cells per feline HSC must vastly exceed that of murine HSCs. Furthermore, if the total number of human HSCs were also equivalent to the total number of HSCs in cat and mouse, the frequency of human HSCs would be 0.7 to 1.5 HSCs/10(8) NMCs, a frequency that is 20-fold less than estimated by the NOD/SCID repopulating assay.