Modeling the architecture and dynamics of hematopoiesis

Scalable inference of cell differentiation networks in gene therapy clonal tracking studies of haematopoiesis

MOTIVATION

Investigating cell differentiation under a genetic disorder offers the potential for improving current gene therapy strategies. Clonal tracking provides a basis for mathematical modelling of population stem cell dynamics that sustain the blood cell formation, a process known as haematopoiesis. However, many clonal tracking protocols rely on a subset of cell types for the characterization of the stem cell output, and the data generated are subject to measurement errors and noise.

RESULTS

We propose a stochastic framework to infer dynamic models of cell differentiation from clonal tracking data. A state-space formulation combines a stochastic quasi-reaction network, describing cell differentiation, with a Gaussian measurement model accounting for data errors and noise. We developed an inference algorithm based on an extended Kalman filter, a nonlinear optimization, and a Rauch-Tung-Striebel smoother. Simulations show that our proposed method outperforms the state-of-the-art and scales to complex structures of cell differentiations in terms of nodes size and network depth. The application of our method to five in vivo gene therapy studies reveals different dynamics of cell differentiation. Our tool can provide statistical support to biologists and clinicians to better understand cell differentiation and haematopoietic reconstitution after a gene therapy treatment. The equations of the state-space model can be modified to infer other dynamics besides cell differentiation.

AVAILABILITY AND IMPLEMENTATION

The stochastic framework is implemented in the R package Karen which is available for download at https://cran.r-project.org/package=Karen. The code that supports the findings of this study is openly available at https://github.com/delcore-luca/CellDifferentiationNetworks.

Global dynamics of healthy and cancer cells competing in the hematopoietic system

Stem cells in the bone marrow differentiate to ultimately become mature, functioning blood cells through a tightly regulated process (hematopoiesis) including a stem cell niche interaction and feedback through the immune system. Mutations in a hematopoietic stem cell can create a cancer stem cell leading to a less controlled production of malfunctioning cells in the hematopoietic system. This was mathematically modelled by Andersen et al. (2017) including the dynamic variables: healthy and cancer stem cells and mature cells, dead cells and an immune system response. Here, we apply a quasi steady state approximation to this model to construct a two dimensional model with four algebraic equations denoted the simple cancitis model. The two dynamic variables are the clinically available quantities JAK2V617F allele burden and the number of white blood cells. The simple cancitis model represents the original model very well. Complete phase space analysis of the simple cancitis model is performed, including proving the existence and location of globally attracting steady states. Hence, parameter values from compartments of stem cells, mature cells and immune cells are directly linked to disease and treatment prognosis, showing the crucial importance of early intervention. The simple cancitis model allows for a complete analysis of the long term evolution of trajectories. In particular, the value of the self renewal of the hematopoietic stem cells divided by the self renewal of the cancer stem cells is found to be an important diagnostic marker and perturbing this parameter value at intervention allows the model to reproduce clinical data. Treatment at low cancer cell numbers allows returning to healthy blood production while the same intervention at a later disease stage can lead to eradication of healthy blood producing cells. Assuming the total number of white blood cells is constant in the early cancer phase while the allele burden increases, a one dimensional model is suggested and explicitly solved, including parameters from all original compartments. The solution explicitly shows that exogenous inflammation promotes blood cancer when cancer stem cells reproduce more efficiently than hematopoietic stem cells.

Calibration, Selection and Identifiability Analysis of a Mathematical Model of the in vitro Erythropoiesis in Normal and Perturbed Contexts

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.

The relationship of mammal survivorship and body mass modeled by metabolic and vitality theories

A model describes the relationship between mammal body mass and survivorship by combining replicative senescence theory postulating a cellular basis of aging, metabolic theory relating metabolism to body mass, and vitality theory relating survival to vitality loss and extrinsic mortality. In the combined framework, intrinsic mortality results from replicative senescence of the hematopoietic stem cells and extrinsic mortality results from environmental challenges. Because the model expresses the intrinsic and extrinsic rates with different powers of body mass, across the spectrum of mammals, survivorship changes from Type I to Type II curve shapes with decreasing body mass. Fitting the model to body mass and maximum lifespan data of 494 nonvolant mammals yields allometric relationships of body mass to the vitality parameters, from which full survivorship profiles were generated from body mass alone. Because maximum lifespan data is predominantly derived from captive populations, the generated survivorship curves were dominated by intrinsic mortality. Comparison of the mass-derived and observed survivorship curves provides insights into how specific populations deviate from the aggregate of populations observed under captivity.

Mechanisms of blood homeostasis: lineage tracking and a neutral model of cell populations in rhesus macaques

Background

How a potentially diverse population of hematopoietic stem cells (HSCs) differentiates and proliferates to supply more than 10¹¹ mature blood cells every day in humans remains a key biological question. We investigated this process by quantitatively analyzing the clonal structure of peripheral blood that is generated by a population of transplanted lentivirus-marked HSCs in myeloablated rhesus macaques. Each transplanted HSC generates a clonal lineage of cells in the peripheral blood that is then detected and quantified through deep sequencing of the viral vector integration sites (VIS) common within each lineage. This approach allowed us to observe, over a period of 4-12 years, hundreds of distinct clonal lineages.

Results

While the distinct clone sizes varied by three orders of magnitude, we found that collectively, they form a steady-state clone size-distribution with a distinctive shape. Steady-state solutions of our model show that the predicted clone size-distribution is sensitive to only two combinations of parameters. By fitting the measured clone size-distributions to our mechanistic model, we estimate both the effective HSC differentiation rate and the number of active HSCs.

Conclusions

Our concise mathematical model shows how slow HSC differentiation followed by fast progenitor growth can be responsible for the observed broad clone size-distribution. Although all cells are assumed to be statistically identical, analogous to a neutral theory for the different clone lineages, our mathematical approach captures the intrinsic variability in the times to HSC differentiation after transplantation.

Electronic supplementary material

The online version of this article (doi:10.1186/s12915-015-0191-8) contains supplementary material, which is available to authorized users.

Prep1 (pKnox1) regulates mouse embryonic HSC cycling and self-renewal affecting the Stat1-Sca1 IFN-dependent pathway

A hypomorphic Prep1 mutation results in embryonic lethality at late gestation with a pleiotropic embryonic phenotype that includes defects in all hematopoietic lineages. Reduced functionality of the hematopoietic stem cells (HSCs) compartment might be responsible for the hematopoietic phenotype observed at mid-gestation. In this paper we demonstrate that Prep1 regulates the number of HSCs in fetal livers (FLs), their clonogenic potential and their ability to de novo generate the hematopoietic system in ablated hosts. Furthermore, we show that Prep1 controls the self-renewal ability of the FL HSC compartment as demonstrated by serial transplantation experiments. The premature exhaustion of Prep1 mutant HSCs correlates with the reduced quiescent stem cell pool thus suggesting that Prep1 regulates the self-renewal ability by controlling the quiescence/proliferation balance. Finally, we show that in FL HSCs Prep1 absence induces the interferon signaling pathway leading to premature cycling and exhaustion of fetal HSCs.

Higher-order orchestration of hematopoiesis: is cohesin a new player?

Hematopoiesis-the process that generates distinct lineage-committed blood cells from a single multipotent hematopoietic stem cell-is a complex process of cellular differentiation regulated by a set of dynamic transcriptional programs. Cytokines and growth factors, transcription factors, chromatin remodeling, and modifying enzymes have been suggested to enact critical roles during hematopoiesis, leading to the development of myeloid, lymphoid, erythroid and platelet precursors. How is such a complex process orchestrated? Is there a higher order of hematopoiesis regulation? These are some of the unresolved questions in the field of hematopoiesis. Here, we suggest that cohesin, which is known to mediate chromosomal cohesion between sister chromatids, may have a central role in the orchestration of hematopoiesis and serve as a master transcriptional regulator.

MATHEMATICAL MODELING OF CELL DYNAMICS AFTER ALLOGENEIC BONE MARROW TRANSPLANTATION

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.

Modeling hematopoietic system response caused by chronic exposure to ionizing radiation

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).

Systems biology and medicine--meta-issues and frameworks

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