A composite likelihood approach to the analysis of longitudinal clonal data on multitype cellular systems under an age-dependent branching process

Subcritical Sevastyanov branching processes with nonhomogeneous Poisson immigration

We consider a class of Sevastyanov branching processes with non-homogeneous Poisson immigration. These processes relax the assumption required by the Bellman-Harris process which imposes the lifespan and offspring of each individual to be independent. They find applications in studies of the dynamics of cell populations. In this paper, we focus on the subcritical case and examine asymptotic properties of the process. We establish limit theorems, which generalize classical results due to Sevastyanov and others. Our key findings include novel LLN and CLT which emerge from the non-homogeneity of the immigration process.

Quantifying T lymphocyte turnover

Peripheral T cell populations are maintained by production of naive T cells in the thymus, clonal expansion of activated cells, cellular self-renewal (or homeostatic proliferation), and density dependent cell life spans. A variety of experimental techniques have been employed to quantify the relative contributions of these processes. In modern studies lymphocytes are typically labeled with 5-bromo-2'-deoxyuridine (BrdU), deuterium, or the fluorescent dye carboxy-fluorescein diacetate succinimidyl ester (CFSE), their division history has been studied by monitoring telomere shortening and the dilution of T cell receptor excision circles (TRECs) or the dye CFSE, and clonal expansion has been documented by recording changes in the population densities of antigen specific cells. Proper interpretation of such data in terms of the underlying rates of T cell production, division, and death has proven to be notoriously difficult and involves mathematical modeling. We review the various models that have been developed for each of these techniques, discuss which models seem most appropriate for what type of data, reveal open problems that require better models, and pinpoint how the assumptions underlying a mathematical model may influence the interpretation of data. Elaborating various successful cases where modeling has delivered new insights in T cell population dynamics, this review provides quantitative estimates of several processes involved in the maintenance of naive and memory, CD4(+) and CD8(+) T cell pools in mice and men.

Asymptotic behavior of cell populations described by two-type reducible age-dependent branching processes with non-homogeneous immigration()

Stem and precursor cells play a critical role in tissue development, maintenance, and repair throughout the life. Often, experimental limitations prevent direct observation of the stem cell compartment, thereby posing substantial challenges to the analysis of such cellular systems. Two-type age-dependent branching processes with immigration are proposed to model populations of progenitor cells and their differentiated progenies. Immigration of cells into the pool of progenitor cells is formulated as a non-homogeneous Poisson process. The asymptotic behavior of the process is governed by the largest of two Malthusian parameters associated with embedded Bellman-Harris processes. Asymptotic approximations to the expectations of the total cell counts are improved by Markov compensators.

Quasi- and pseudo-maximum likelihood estimators for discretely observed continuous-time Markov branching processes

This article deals with quasi- and pseudo-likelihood estimation in a class of continuous-time multi-type Markov branching processes observed at discrete points in time. "Conventional" and conditional estimation are discussed for both approaches. We compare their properties and identify situations where they lead to asymptotically equivalent estimators. Both approaches possess robustness properties, and coincide with maximum likelihood estimation in some cases. Quasi-likelihood functions involving only linear combinations of the data may be unable to estimate all model parameters. Remedial measures exist, including the resort either to non-linear functions of the data or to conditioning the moments on appropriate sigma-algebras. The method of pseudo-likelihood may also resolve this issue. We investigate the properties of these approaches in three examples: the pure birth process, the linear birth-and-death process, and a two-type process that generalizes the previous two examples. Simulations studies are conducted to evaluate performance in finite samples.

Two-Type Age-Dependent Branching Processes with Inhomogeneous Immigration as Models of Renewing Cell Populations

Two-type reducible age-dependent branching processes with inhomogeneous immigration are considered to describe the kinetics of renewing cell populations. This class of processes can be used to model the generation of oligodendrocytes in the central nervous system in vivo or the kinetics of leukemia cells. The asymptotic behavior of the first and second moments, including the correlation, of the process is investigated.

An age-dependent branching process model for the analysis of CFSE-labeling experiments

BACKGROUND

Over the past decade, flow cytometric CFSE-labeling experiments have gained considerable popularity among experimentalists, especially immunologists and hematologists, for studying the processes of cell proliferation and cell death. Several mathematical models have been presented in the literature to describe cell kinetics during these experiments.

RESULTS

We propose a multi-type age-dependent branching process to model the temporal development of populations of cells subject to division and death during CFSE-labeling experiments. We discuss practical implementation of the proposed model; we investigate a competing risk version of the process; and we identify the classes of cellular dependencies that may influence the expectation of the process and those that do not. An application is presented where we study the proliferation of human CD8+ T lymphocytes using our model and a competing risk branching process.

CONCLUSIONS

The proposed model offers a widely applicable approach to the analysis of CFSE-labeling experiments. The model fitted very well our experimental data. It provided reasonable estimates of cell kinetics parameters as well as meaningful insights into the processes of cell division and cell death. In contrast, the competing risk branching process could not describe the kinetics of CD8+ T cells. This suggested that the decision of cell division or cell death may be made early in the cell cycle if not in preceding generations. Also, we show that analyses based on the proposed model are robust with respect to cross-sectional dependencies and to dependencies between fates of linearly filiated cells.

REVIEWERS

This article was reviewed by Marek Kimmel, Wai-Yuan Tan and Peter Olofsson.