Structurally robust biological networks

Background: The molecular circuitry of living organisms performs remarkably robust regulatory tasks, despite the often intrinsic variability of its components. A large body of research has in fact highlighted that robustness is often a structural property of biological systems. However, there are few systematic methods to mathematically model and describe structural robustness. With a few exceptions, numerical studies are often the preferred approach to this type of investigation. Results: In this paper, we propose a framework to analyze robust stability of equilibria in biological networks. We employ Lyapunov and invariant sets theory, focusing on the structure of ordinary differential equation models. Without resorting to extensive numerical simulations, often necessary to explore the behavior of a model in its parameter space, we provide rigorous proofs of robust stability of known bio-molecular networks. Our results are in line with existing literature. Conclusions: The impact of our results is twofold: on the one hand, we highlight that classical and simple control theory methods are extremely useful to characterize the behavior of biological networks analytically. On the other hand, we are able to demonstrate that some biological networks are robust thanks to their structure and some qualitative properties of the interactions, regardless of the specific values of their parameters

Steady state and (bi-) stability evaluation of simple protease signalling networks

Signal transduction networks are complex, as are their mathematical models. Gaining a deeper understanding requires a system analysis. Important aspects are the number, location and stability of steady states. In particular, bistability has been recognised as an important feature to achieve molecular switching. This paper compares different model structures and analysis methods particularly useful for bistability analysis. The biological applications include proteolytic cascades as, for example, encountered in the apoptotic signalling pathway or in the blood clotting system. We compare three model structures containing zero-order, inhibitor and cooperative ultrasensitive reactions, all known to achieve bistability. The combination of phase plane and bifurcation analysis provides an illustrative and comprehensive understanding of how bistability can be achieved and indicates how robust this behaviour is. Experimentally, some so-called “inactive” components were shown to have a residual activity. This has been mostly ignored in mathematical models. Our analysis reveals that bistability is only mildly affected in the case of zero-order or inhibitor ultrasensitivity. However, the case where bistability is achieved by cooperative ultrasensitivity is severely affected by this perturbation

Interplay of Extrinsic and Intrinsic Cues in Cell-Fate Decisions

A cell’s decision making process is coordinated by dynamic interplay between its extracellular environment and its intracellular milieu. For example, during stem cell differentiation, fate decisions are believed to be ultimately controlled by differential expression of lineage-specific transcription factors, but cytokine receptor signals also play a crucial instructive role in addition to providing permissive proliferation and survival cues. Here, we present a minimal computational framework that integrates the intrinsic and extrinsic regulatory elements implicated in the commitment of hematopoietic progenitor cells to mature red blood cells (Chapter 2). Our model highlights the importance of bidirectional interactions between cytokine receptors and transcription factors in conferring properties such as ultrasensitivity and bistability to differentiating cells. These system-level properties can induce a switch-like characteristic during differentiation and provide robustness to the mature state. We then experimentally test predictions from this lineage commitment model in a model system for studying erythropoiesis (Chapter 3). Our experiments show that hemoglobin synthesis is highly switch-like in response to cytokine and cells undergoing lineage commitment possess memory of earlier cytokine signals. We show that erythrocyte-specific receptor and transcription factor are indeed synchronously co-upregulated and the heterogeneity in their expression is positively correlated during differentiation, confirming the presence of autofeedback and receptor-mediated positive feedback loops. To evaluate the possibility of employing this minimal topology as a synthetic “memory module” for cell engineering applications, we constructed this topology synthetically in Saccharomyces cerevisiae by integrating Arabidopsis thaliana signaling components with an endogenous yeast pathway (Chapter 4). Our experiments show that any graded and unimodal signaling pathway can be rationally rewired to achieve our desired topology and the resulting network immediately attains high ultrasensitivity and bimodality without tweaking. We further show that this topology can be tuned to regulate system dynamics such as activation/deactivation kinetics, signal amplitude, switching threshold and sensitivity. We conclude with a computational study to explore the generality of this interplay between extrinsic and intrinsic cues in hematopoiesis. We extend our minimal model analysis in Chapter 2 to examine the more complex fate decisions in bipotent and multipotent progenitors, particularly how these cells can make robust decisions in the presence of multiple extrinsic cues and intrinsic noise (Chapter 5). Our model provides support to both the instructive and stochastic theories of commitment: cell fates are ultimately driven by lineage-specific transcription factors, but cytokine signaling can strongly bias lineage commitment by regulating these inherently noisy cell-fate decisions with complex, pertinent behaviors such as ligand-mediated ultrasensitivity and robust multistability. The simulations further suggest that the kinetics of differentiation to a mature cell state can depend on the starting progenitor state as well as on the route of commitment that is chosen. Lastly, our model shows good agreement with lineage-specific receptor expression kinetics from microarray experiments and provides a computational framework that can integrate both classical and alternative commitment paths in hematopoiesis that have been observed experimentally

Robustness and timing of cellular differentiation through population-based symmetry breaking

During mammalian development, cell types expressing mutually exclusive genetic markers are differentiated from a multilineage primed state. These observations have invoked single-cell multistability view as the dynamical basis of differentiation. However, the robust regulative nature of mammalian development is not captured therein. Considering the well-established role of cell-cell communication in this process, we propose a fundamentally different dynamical treatment in which cellular identities emerge and are maintained on population level, as a novel unique solution of the coupled system. Subcritical system’s organization here enables symmetry-breaking to be triggered by cell number increase in a timed, self-organized manner. Robust cell type proportions are thereby an inherent feature of the resulting inhomogeneous solution. This framework is generic, as exemplified for early embryogenesis and neurogenesis cases. Distinct from mechanisms that rely on pre-existing asymmetries, we thus demonstrate that robustness and accuracy necessarily emerge from the cooperative behaviour of growing cell populations during development

Bistability and Oscillations in the Huang-Ferrell Model of MAPK Signaling

Physicochemical models of signaling pathways are characterized by high levels of structural and parametric uncertainty, reflecting both incomplete knowledge about signal transduction and the intrinsic variability of cellular processes. As a result, these models try to predict the dynamics of systems with tens or even hundreds of free parameters. At this level of uncertainty, model analysis should emphasize statistics of systems-level properties, rather than the detailed structure of solutions or boundaries separating different dynamic regimes. Based on the combination of random parameter search and continuation algorithms, we developed a methodology for the statistical analysis of mechanistic signaling models. In applying it to the well-studied MAPK cascade model, we discovered a large region of oscillations and explained their emergence from single-stage bistability. The surprising abundance of strongly nonlinear (oscillatory and bistable) input/output maps revealed by our analysis may be one of the reasons why the MAPK cascade in vivo is embedded in more complex regulatory structures. We argue that this type of analysis should accompany nonlinear multiparameter studies of stationary as well as transient features in network dynamics

A Dynamical Model of Oocyte Maturation Unveils Precisely Orchestrated Meiotic Decisions

Maturation of vertebrate oocytes into haploid gametes relies on two consecutive meioses without intervening DNA replication. The temporal sequence of cellular transitions driving eggs from G2 arrest to meiosis I (MI) and then to meiosis II (MII) is controlled by the interplay between cyclin-dependent and mitogen-activated protein kinases. In this paper, we propose a dynamical model of the molecular network that orchestrates maturation of Xenopus laevis oocytes. Our model reproduces the core features of maturation progression, including the characteristic non-monotonous time course of cyclin-Cdks, and unveils the network design principles underlying a precise sequence of meiotic decisions, as captured by bifurcation and sensitivity analyses. Firstly, a coherent and sharp meiotic resumption is triggered by the concerted action of positive feedback loops post-translationally activating cyclin-Cdks. Secondly, meiotic transition is driven by the dynamic antagonism between positive and negative feedback loops controlling cyclin turnover. Our findings reveal a highly modular network in which the coordination of distinct regulatory schemes ensures both reliable and flexible cell-cycle decisions