Stochasticity and determinism in models of hematopoiesis

Chronic arsenic exposure induces malignant transformation of human HaCaT cells through both deterministic and stochastic changes in transcriptome expression

Biological processes are inherently stochastic, i.e., are partially driven by hard to predict random probabilistic processes. Carcinogenesis is driven both by stochastic and deterministic (predictable non-random) changes. However, very few studies systematically examine the contribution of stochastic events leading to cancer development. In differential gene expression studies, the established data analysis paradigms incentivize expression changes that are uniformly different across the experimental versus control groups, introducing preferential inclusion of deterministic changes at the expense of stochastic processes that might also play a crucial role in the process of carcinogenesis. In this study, we applied simple computational techniques to quantify: (i) The impact of chronic arsenic (iAs) exposure as well as passaging time on stochastic gene expression and (ii) Which genes were expressed deterministically and which were expressed stochastically at each of the three stages of cancer development. Using biological coefficient of variation as an empirical measure of stochasticity we demonstrate that chronic iAs exposure consistently suppressed passaging related stochastic gene expression at multiple time points tested, selecting for a homogenous cell population that undergo transformation. Employing multiple balanced removal of outlier data, we show that chronic iAs exposure induced deterministic and stochastic changes in the expression of unique set of genes, that populate largely unique biological pathways. Together, our data unequivocally demonstrate that both deterministic and stochastic changes in transcriptome-wide expression are critical in driving biological processes, pathways and networks towards clonal selection, carcinogenesis, and tumor heterogeneity.

Predicting Time to Relapse in Acute Myeloid Leukemia through Stochastic Modeling of Minimal Residual Disease Based on Clonality Data

Event-free and overall survival remain poor for patients with acute myeloid leukemia. Chemoresistant clones contributing to relapse arise from minimal residual disease (MRD) or newly-acquired mutations. However, the dynamics of clones comprising MRD is poorly understood. We developed a predictive stochastic model, based on a multitype age-dependent Markov branching process, to describe how random events in MRD contribute to the heterogeneity in treatment response. We employed training and validation sets of patients who underwent whole genome sequencing and for whom mutant clone frequencies at diagnosis and relapse were available. The disease evolution and treatment outcome are subject to stochastic fluctuations. Estimates of malignant clone growth rates, obtained by model fitting, are consistent with published data. Using the estimates from the training set, we developed a function linking MRD and time of relapse, with MRD inferred from the model fits to clone frequencies and other data. An independent validation set confirmed our model. In a third data set, we fitted the model to data at diagnosis and remission and predicted the time to relapse. As a conclusion, given bone marrow genome at diagnosis and MRD at or past remission, the model can predict time to relapse, and help guide treatment decisions to mitigate relapse.

Optimal experimental design for mathematical models of haematopoiesis

The haematopoietic system has a highly regulated and complex structure in which cells are organized to successfully create and maintain new blood cells. It is known that feedback regulation is crucial to tightly control this system, but the specific mechanisms by which control is exerted are not completely understood. In this work, we aim to uncover the underlying mechanisms in haematopoiesis by conducting perturbation experiments, where animal subjects are exposed to an external agent in order to observe the system response and evolution. We have developed a novel Bayesian hierarchical framework for optimal design of perturbation experiments and proper analysis of the data collected. We use a deterministic model that accounts for feedback and feedforward regulation on cell division rates and self-renewal probabilities. A significant obstacle is that the experimental data are not longitudinal, rather each data point corresponds to a different animal. We overcome this difficulty by modelling the unobserved cellular levels as latent variables. We then use principles of Bayesian experimental design to optimally distribute time points at which the haematopoietic cells are quantified. We evaluate our approach using synthetic and real experimental data and show that an optimal design can lead to better estimates of model parameters.

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.

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.

Towards Quantitative Systems Pharmacology Models of Chemotherapy-Induced Neutropenia

Neutropenia is a serious toxic complication of chemotherapeutic treatment. For years, mathematical models have been developed to better predict hematological outcomes during chemotherapy in both the traditional pharmaceutical sciences and mathematical biology disciplines. An increasing number of quantitative systems pharmacology (QSP) models that combine systems approaches, physiology, and pharmacokinetics/pharmacodynamics have been successfully developed. Here, I detail the shift towards QSP efforts, emphasizing the importance of incorporating systems-level physiological considerations in pharmacometrics.