Adam L. MacLean

The ecology in the hematopoietic stem cell niche determines the clinical outcome in chronic myeloid leukemia

Significance Three contrasting models of the ecological interactions in the hematopoietic stem cell niche explain clinical progression of chronic myeloid leukemia equally well, but do so in different ways. We identify key differences between models and find that we can conclusively rule out those that fail to take competition between healthy and leukemic lineages explicitly into account. Detailed analysis of population dynamics within the bone marrow niche allows us to ascribe mechanisms to distinct disease outcomes and suggests experiments to distinguish between these mechanisms. Chronic myeloid leukemia (CML) is a blood disease that disrupts normal function of the hematopoietic system. Despite the great progress made in terms of molecular therapies for CML, there remain large gaps in our understanding. By comparing mathematical models that describe CML progression and etiology we sought to identify those models that provide the best description of disease dynamics and their underlying mechanisms. Data for two clinical outcomes—disease remission or relapse—are considered, and we investigate these using Bayesian inference techniques throughout. We find that it is not possible to choose between the models based on fits to the data alone; however, by studying model predictions we can discard models that fail to take niche effects into account. More detailed analysis of the remaining models reveals mechanistic differences: for one model, leukemia stem cell dynamics determine the disease outcome; and for the other model disease progression is determined at the stage of progenitor cells, in particular by differences in progenitor death rates. This analysis also reveals distinct transient dynamics that will be experimentally accessible, but are currently at the limits of what is possible to measure. To resolve these differences we need to be able to probe the hematopoietic stem cell niche directly. Our analysis highlights the importance of further mapping of the bone marrow hematopoietic niche microenvironment as the “ecological” interactions between cells in this niche appear to be intricately linked to disease outcome.

Parameter-free methods distinguish Wnt pathway models and guide design of experiments

Significance The canonical Wnt/β-catenin signaling pathway is important for essential cellular functions and is implicated in many diseases. We introduce a new mathematical model that focuses on β-catenin degradation and protein shuttling between cellular compartments. We compare our model to others and show that all fit to time-dependent experimental data. To evade this parameter problem, we use algebraic methods and characterize model features that are independent of the choice of parameter values. We find that multiple responses to Wnt are feasible under certain conditions for the new model, but not for the others; moreover, we provide dependencies between species (variables) that inform future experiments and model discrimination. We also highlight the wide applicability of these tools across problems in systems biology. The canonical Wnt signaling pathway, mediated by β-catenin, is crucially involved in development, adult stem cell tissue maintenance, and a host of diseases including cancer. We analyze existing mathematical models of Wnt and compare them to a new Wnt signaling model that targets spatial localization; our aim is to distinguish between the models and distill biological insight from them. Using Bayesian methods we infer parameters for each model from mammalian Wnt signaling data and find that all models can fit this time course. We appeal to algebraic methods (concepts from chemical reaction network theory and matroid theory) to analyze the models without recourse to specific parameter values. These approaches provide insight into aspects of Wnt regulation: the new model, via control of shuttling and degradation parameters, permits multiple stable steady states corresponding to stem-like vs. committed cell states in the differentiation hierarchy. Our analysis also identifies groups of variables that should be measured to fully characterize and discriminate between competing models, and thus serves as a guide for performing minimal experiments for model comparison.

Population dynamics of normal and leukaemia stem cells in the haematopoietic stem cell niche show distinct regimes where leukaemia will be controlled

Haematopoietic stem cells (HSCs) are responsible for maintaining immune cells, red blood cells and platelets throughout life. HSCs must be located in their ecological niche (the bone marrow) to function correctly, that is, to regenerate themselves and their progeny; the latter eventually exit the bone marrow and enter circulation. We propose that cells with oncogenic potential—cancer/leukaemia stem cells (LSC)—and their progeny will also occupy this niche. Mathematical models, which describe the dynamics of HSCs, LSCs and their progeny allow investigation into the conditions necessary for defeating a malignant invasion of the niche. Two such models are developed and analysed here. To characterize their behaviour, we use an inferential framework that allows us to study regions in parameter space that give rise to desired behaviour together with an assessment of the robustness of the dynamics. Using this approach, we map out conditions under which HSCs can outcompete LSCs. In therapeutic applications, we clearly want to drive haematopoiesis into such regimes and the current analysis provide some guidance as to how we can identify new therapeutic targets. Our results suggest that maintaining a viable population of HSCs and their progenies in the niche may often already be nearly sufficient to eradicate LSCs from the system.

Feedback mechanisms control coexistence in a stem cell model of acute myeloid leukaemia

Haematopoietic stem cell dynamics regulate healthy blood cell production and are disrupted during leukaemia. Competition models of cellular species help to elucidate stem cell dynamics in the bone marrow microenvironment (or niche), and to determine how these dynamics impact leukaemia progression. Here we develop two models that target acute myeloid leukaemia with particular focus on the mechanisms that control proliferation via feedback signalling. It is within regions of parameter space permissive of coexistence that the effects of competition are most subtle and the clinical outcome least certain. Steady state and linear stability analyses identify parameter regions that allow for coexistence to occur, and allow us to characterise behaviour near critical points. Where analytical expressions are no longer informative, we proceed statistically and sample parameter space over a coexistence region. We find that the rates of proliferation and differentiation of healthy progenitors exert key control over coexistence. We also show that inclusion of a regulatory feedback onto progenitor cells promotes healthy haematopoiesis at the expense of leukaemia, and that – somewhat paradoxically – within the coexistence region feedback increases the sensitivity of the system to dominance by one lineage over another.

Mathematical and Statistical Techniques for Systems Medicine: The Wnt Signaling Pathway as a Case Study.

The last decade has seen an explosion in models that describe phenomena in systems medicine. Such models are especially useful for studying signaling pathways, such as the Wnt pathway. In this chapter we use the Wnt pathway to showcase current mathematical and statistical techniques that enable modelers to gain insight into (models of) gene regulation and generate testable predictions. We introduce a range of modeling frameworks, but focus on ordinary differential equation (ODE) models since they remain the most widely used approach in systems biology and medicine and continue to offer great potential. We present methods for the analysis of a single model, comprising applications of standard dynamical systems approaches such as nondimensionalization, steady state, asymptotic and sensitivity analysis, and more recent statistical and algebraic approaches to compare models with data. We present parameter estimation and model comparison techniques, focusing on Bayesian analysis and coplanarity via algebraic geometry. Our intention is that this (non-exhaustive) review may serve as a useful starting point for the analysis of models in systems medicine.

Conditional random matrix ensembles and the stability of dynamical systems

Random matrix theory (RMT) has found applications throughout physics and applied mathematics, in subject areas as diverse as communications networks, population dynamics, neuroscience, and models of the banking system. Many of these analyses exploit elegant analytical results, particularly the circular law and its extensions. In order to apply these results, assumptions must be made about the distribution of matrix elements. Here we demonstrate that the choice of matrix distribution is crucial. In particular, adopting an unrealistic matrix distribution for the sake of analytical tractability is liable to lead to misleading conclusions. We focus on the application of RMT to the long-standing, and at times fractious, ?diversity-stability debate?, which is concerned with establishing whether large complex systems are likely to be stable. Early work (and subsequent elaborations) brought RMT to bear on the debate by modelling the entries of a system?s Jacobian matrix as independent and identically distributed (i.i.d.) random variables. These analyses were successful in yielding general results that were not tied to any specific system, but relied upon a restrictive i.i.d. assumption. Other studies took an opposing approach, seeking to elucidate general principles of stability through the analysis of specific systems. Here we develop a statistical framework that reconciles these two contrasting approaches. We use a range of illustrative dynamical systems examples to demonstrate that: (i) stability probability cannot be summarily deduced from any single property of the system (e.g. its diversity); and (ii) our assessment of stability depends on adequately capturing the details of the systems analysed. Failing to condition on the structure of dynamical systems will skew our analysis and can, even for very small systems, result in an unnecessarily pessimistic diagnosis of their stability.

Cellular population dynamics control the robustness of the stem cell niche

ABSTRACT Within populations of cells, fate decisions are controlled by an indeterminate combination of cell-intrinsic and cell-extrinsic factors. In the case of stem cells, the stem cell niche is believed to maintain ‘stemness’ through communication and interactions between the stem cells and one or more other cell-types that contribute to the niche conditions. To investigate the robustness of cell fate decisions in the stem cell hierarchy and the role that the niche plays, we introduce simple mathematical models of stem and progenitor cells, their progeny and their interplay in the niche. These models capture the fundamental processes of proliferation and differentiation and allow us to consider alternative possibilities regarding how niche-mediated signalling feedback regulates the niche dynamics. Generalised stability analysis of these stem cell niche systems enables us to describe the stability properties of each model. We find that although the number of feasible states depends on the model, their probabilities of stability in general do not: stem cell–niche models are stable across a wide range of parameters. We demonstrate that niche-mediated feedback increases the number of stable steady states, and show how distinct cell states have distinct branching characteristics. The ecological feedback and interactions mediated by the stem cell niche thus lend (surprisingly) high levels of robustness to the stem and progenitor cell population dynamics. Furthermore, cell–cell interactions are sufficient for populations of stem cells and their progeny to achieve stability and maintain homeostasis. We show that the robustness of the niche – and hence of the stem cell pool in the niche – depends only weakly, if at all, on the complexity of the niche make-up: simple as well as complicated niche systems are capable of supporting robust and stable stem cell dynamics. Summary: Stem cell niche dynamics are very robust to external and physiological perturbations because proliferation and differentiation are naturally balanced and controlled by the reliance on a shared niche environment.

Systematic tracking of altered haematopoiesis during sporozoite-mediated malaria development reveals multiple response points

Haematopoiesis is the complex developmental process that maintains the turnover of all blood cell lineages. It critically depends on the correct functioning of rare, quiescent haematopoietic stem cells (HSCs) and more numerous, HSC-derived, highly proliferative and differentiating haematopoietic progenitor cells (HPCs). Infection is known to affect HSCs, with severe and chronic inflammatory stimuli leading to stem cell pool depletion, while acute, non-lethal infections exert transient and even potentiating effects. Both whether this paradigm applies to all infections and whether the HSC response is the dominant driver of the changes observed during stressed haematopoiesis remain open questions. We use a mouse model of malaria, based on natural, sporozoite-driven Plasmodium berghei infection, as an experimental platform to gain a global view of haematopoietic perturbations during infection progression. We observe coordinated responses by the most primitive HSCs and multiple HPCs, some starting before blood parasitaemia is detected. We show that, despite highly variable inter-host responses, primitive HSCs become highly proliferative, but mathematical modelling suggests that this alone is not sufficient to significantly impact the whole haematopoietic cascade. We observe that the dramatic expansion of Sca-1+ progenitors results from combined proliferation of direct HSC progeny and phenotypic changes in downstream populations. We observe that the simultaneous perturbation of HSC/HPC population dynamics is coupled with early signs of anaemia onset. Our data uncover a complex relationship between Plasmodium and its hosts haematopoiesis and raise the question whether the variable responses observed may affect the outcome of the infection itself and its long-term consequences on the host.

A mathematical model of mechanotransduction reveals how mechanical memory regulates mesenchymal stem cell fate decisions

BackgroundMechanical and biophysical properties of the cellular microenvironment regulate cell fate decisions. Mesenchymal stem cell (MSC) fate is influenced by past mechanical dosing (memory), but the mechanisms underlying this process have not yet been well defined. We have yet to understand how memory affects specific cell fate decisions, such as the differentiation of MSCs into neurons, adipocytes, myocytes, and osteoblasts.ResultsWe study a minimal gene regulatory network permissive of multi-lineage MSC differentiation into four cell fates. We present a continuous model that is able to describe the cell fate transitions that occur during differentiation, and analyze its dynamics with tools from multistability, bifurcation, and cell fate landscape analysis, and via stochastic simulation. Whereas experimentally, memory has only been observed during osteogenic differentiation, this model predicts that memory regions can exist for each of the four MSC-derived cell lineages. We can predict the substrate stiffness ranges over which memory drives differentiation; these are directly testable in an experimental setting. Furthermore, we quantitatively predict how substrate stiffness and culture duration co-regulate the fate of a stem cell, and we find that the feedbacks from the differentiating MSC onto its substrate are critical to preserve mechanical memory. Strikingly, we show that re-seeding MSCs onto a sufficiently soft substrate increases the number of cell fates accessible.ConclusionsControl of MSC differentiation is crucial for the success of much-lauded regenerative therapies based on MSCs. We have predicted new memory regions that will directly impact this control, and have quantified the size of the memory region for osteoblasts, as well as the co-regulatory effects on cell fates of substrate stiffness and culture duration. Taken together, these results can be used to develop novel strategies to better control the fates of MSCs in vitro and following transplantation.

Exploring intermediate cell states through the lens of single cells

As our catalog of cell states expands, appropriate characterization of these states and the transitions between them is crucial. Here we discuss the roles of intermediate cell states (ICSs) in this growing collection. We begin with definitions and discuss evidence for the existence of ICSs and their relevance in various tissues. We then provide a list of possible functions for ICSs with examples. Finally, we describe means by which ICSs and their functional roles can be identified from single-cell data or predicted from models.