UC Irvine

Hematopoiesis is the complex mechanism by which hematopoietic stem cells produce a variety of functional blood cells through multiple stages of differentiation. Since the numbers of various blood cell types need to be maintained in homeostasis, with occasional short-lived departures from it, hematopoiesis must have multiple regulatory mechanisms. However, these are still not fully understood. Although many mathematical models of hematopoiesis regulation have been proposed, more work on developing methods for fitting and interpreting experimental data that integrate statistical and mechanistic models is needed. Here, using a new chemical reaction ordinary differential equation model of negative feedback regulation in hematopoiesis, we develop a scalable, hierarchical Bayesian framework using a latent variables approach that takes cross heterogeneity into account and infers division, differentiation, and feedback regulation parameters of hematopoietic cells. We designed and performed an experiment where mice were injected with the chemotherapy drug 5-FU that reduces the number of stem and progenitor cells by blocking DNA synthesis and repair, to perturb the hematopoietic equilibrium. In order to count the number of cells in the BM, the mouse must be sacrificed. Therefore, each mouse can contribute their cell count data at a one time point only. To work with partially observed datasets, we use an ODE model to interpolate the noisy means of the experimental cell count data (the missing data is inferred). We evaluate the performance of the new model and inferential framework using synthetic data and find that we are able to distinguish between models that account for biological variation and models that include only technical variation/measurement error. We find that the experimental data are best described by a hierarchical model in which the hematopoiesis model parameters are allowed to vary among mice, suggesting the presence of significant biological variability. Our experimental data and the model show that, after perturbation, hematopoiesis returns to equilibrium via damped oscillations, with a notable overshoot of depleted cell counts that happens shortly after the system is perturbed from equilibrium. We then explore an alternative way of accounting for data heterogeneity by employing stochastic differential equations instead of letting division and feedback regulation parameters vary across mice. Computational tractability of the likelihood in a Bayesian inference framework is achieved by using the linear noise approximation (LNA) derived from the chemical Langevin equation. This enables us to approximate the joint posterior density for the hematopoietic rate value parameters and missing data. We evaluate the performance of the new Bayesian LNA model framework and compare it to the Bayesian ODE model frameworks we developed previously. We find that the new framework can further improve the out-of-sample prediction, as indicated by leave-one-out cross-validation. We identify limitations of inference for our LNA model when multiple sources of biological and technical variation of the dataset are significant and then develop a procedure for overcoming them. Finally, we investigate experimental designs that optimize the amount of information gained about the model parameter and missing data. We employ a new adversarial approach that uses a game theory framework for experimental design without the need for the calculation of the posterior probability distributions. This enables us to overcome the cost of traditional Bayesian optimal design methodology that requires repeated approximations of the posterior distributions, which are expensive to generate and prohibitively costly for high dimensional models.