Ubiquitin chain specific auto-ubiquitination triggers sustained oscillation, bistable switches and excitable firing

A nested bistable module within a negative feedback loop ensures different types of oscillations in signaling systems

In this article, we consider a double phosphorylation cycle, a ubiquitous signaling component, having the ability to display bistability, a behavior strongly related to the existence of positive feedback loops. If this component is connected to other signaling elements, it very likely undergoes some sort of protein-protein interaction. In several cases, these interactions result in a non-explicit negative feedback effect, leading to interlinked positive and negative feedbacks. This combination was studied in the literature as a way to generate relaxation-type oscillations. Here, we show that the two feedbacks together ensure two types of oscillations, the relaxation-type ones and a smoother type of oscillations functioning in a very narrow range of frequencies, in such a way that outside that range, the amplitude of the oscillations is severely compromised. Even more, we show that the two feedbacks are essential for both oscillatory types to emerge, and it is their hierarchy what determines the type of oscillation at work. We used bifurcation analyses and amplitude vs. frequency curves to characterize and classify the oscillations. We also applied the same ideas to another simple model, with the goal of generalizing what we learned from signaling models. The results obtained display the wealth of oscillatory dynamics that exists in a system with a bistable module nested within a negative feedback loop, showing how to transition between different types of oscillations and other dynamical behaviors such as excitability. Our work provides a framework for the study of other oscillatory systems based on bistable modules, from simple two-component models to more complex examples like the MAPK cascade and experimental cases like cell cycle oscillators.

Multi-Dimensional Analysis of Biochemical Network Dynamics Using pyDYVIPAC

Biochemical networks are dynamic, nonlinear, and high-dimensional systems. Realistic kinetic models of biochemical networks often comprise a multitude of kinetic parameters and state variables. Depending on the specific parameter values, a network can display one of a variety of possible dynamic behaviors such as monostable fixed point, damped oscillation, sustained oscillation, and/or bistability. Understanding how a network behaves under a particular parametric condition, and how its behavior changes as the model parameters are varied within the multidimensional parameter space are imperative for gaining a holistic understanding of the network dynamics. Such knowledge helps elucidate the parameter-to-dynamics mapping, uncover how cells make decisions under various pathophysiological contexts, and inform the design of biological circuits with desired behavior, where the latter is critical to the field of synthetic biology. In this chapter, we will present a practical guide to the multidimensional exploration, analysis, and visualization of network dynamics using pyDYVIPAC, which is a tool ideally suited to these purposes implemented in Python. The utility of pyDYVIPAC will be demonstrated using specific examples of biochemical networks with differing structures and dynamic properties via the interactive Jupyter Notebook environment.

Development and characterisation of SMURF2-targeting modifiers

The C2-WW-HECT-domain E3 ubiquitin ligase SMURF2 emerges as an important regulator of diverse cellular processes. To date, SMURF2-specific modulators were not developed. Here, we generated and investigated a set of SMURF2-targeting synthetic peptides and peptidomimetics designed to stimulate SMURF2’s autoubiquitination and turnover via a disruption of the inhibitory intramolecular interaction between its C2 and HECT domains. The results revealed the effects of these molecules both in vitro and in cellulo at the nanomolar concentration range. Moreover, the data showed that targeting of SMURF2 with either these modifiers or SMURF2-specific shRNAs could accelerate cell growth in a cell-context-dependent manner. Intriguingly, a concomitant cell treatment with a selected SMURF2-targeting compound and the DNA-damaging drug etoposide markedly increased the cytotoxicity produced by this drug in growing cells. Altogether, these findings demonstrate that SMURF2 can be druggable through its self-destructive autoubiquitination, and inactivation of SMURF2 might be used to affect cell sensitivity to certain anticancer drugs.

Dynamic modelling of the mTOR signalling network reveals complex emergent behaviours conferred by DEPTOR

The mechanistic Target of Rapamycin (mTOR) signalling network is an evolutionarily conserved network that controls key cellular processes, including cell growth and metabolism. Consisting of the major kinase complexes mTOR Complex 1 and 2 (mTORC1/2), the mTOR network harbours complex interactions and feedback loops. The DEP domain-containing mTOR-interacting protein (DEPTOR) was recently identified as an endogenous inhibitor of both mTORC1 and 2 through direct interactions, and is in turn degraded by mTORC1/2, adding an extra layer of complexity to the mTOR network. Yet, the dynamic properties of the DEPTOR-mTOR network and the roles of DEPTOR in coordinating mTORC1/2 activation dynamics have not been characterised. Using computational modelling, systems analysis and dynamic simulations we show that DEPTOR confers remarkably rich and complex dynamic behaviours to mTOR signalling, including abrupt, bistable switches, oscillations and co-existing bistable/oscillatory responses. Transitions between these distinct modes of behaviour are enabled by modulating DEPTOR expression alone. We characterise the governing conditions for the observed dynamics by elucidating the network in its vast multi-dimensional parameter space, and develop strategies to identify core network design motifs underlying these dynamics. Our findings provide new systems-level insights into the complexity of mTOR signalling contributed by DEPTOR.

Protein-protein interactions generate hidden feedback and feed-forward loops to trigger bistable switches, oscillations and biphasic dose-responses

Protein-protein interactions (PPIs) defined as reversible association of two proteins to form a complex, are undoubtedly among the most common interaction motifs featured in cells. Recent large-scale proteomic studies have revealed an enormously complex interactome of the cell, consisting of tens of thousands of PPIs with numerous signalling hubs. PPIs have functional roles in regulating a wide range of cellular processes including signal transduction and post-translational modifications, and de-regulation of PPIs is implicated in many diseases including cancers and neuro-degenerative disorders. Despite the ubiquitous appearance and physiological significance of PPIs, our understanding of the dynamic and functional consequences of these simple motifs remains incomplete, particularly when PPIs occur within large biochemical networks. We employ quantitative, dynamic modelling to computationally analyse salient dynamic features of the PPI motifs and PPI-containing signalling networks varying in topological architecture. Our analyses surprisingly reveal that simple reversible PPI motifs, when being embedded into signalling cascades, could give rise to extremely rich and complex regulatory dynamics in the absence of explicit positive and negative feedback loops. Our work represents a systematic investigation of the dynamic properties of PPIs in signalling networks, and the results shed light on how this simple event may potentiate diverse and intricate behaviours in vivo.

Competing to coordinate cell fate decisions: the MST2-Raf-1 signaling device

How do biochemical signaling pathways generate biological specificity? This question is fundamental to modern biology, and its enigma has been accentuated by the discovery that most proteins in signaling networks serve multifunctional roles. An answer to this question may lie in analyzing network properties rather than individual traits of proteins in order to elucidate design principles of biochemical networks that enable biological decision-making. We discuss how this is achieved in the MST2/Hippo-Raf-1 signaling network with the help of mathematical modeling and model-based analysis, which showed that competing protein interactions with affinities controlled by dynamic protein modifications can function as Boolean computing devices that determine cell fate decisions. In addition, we discuss areas of interest for future research and highlight how systems approaches would be of benefit.

DYVIPAC: an integrated analysis and visualisation framework to probe multi-dimensional biological networks

Biochemical networks are dynamic and multi-dimensional systems, consisting of tens or hundreds of molecular components. Diseases such as cancer commonly arise due to changes in the dynamics of signalling and gene regulatory networks caused by genetic alternations. Elucidating the network dynamics in health and disease is crucial to better understand the disease mechanisms and derive effective therapeutic strategies. However, current approaches to analyse and visualise systems dynamics can often provide only low-dimensional projections of the network dynamics, which often does not present the multi-dimensional picture of the system behaviour. More efficient and reliable methods for multi-dimensional systems analysis and visualisation are thus required. To address this issue, we here present an integrated analysis and visualisation framework for high-dimensional network behaviour which exploits the advantages provided by parallel coordinates graphs. We demonstrate the applicability of the framework, named "Dynamics Visualisation based on Parallel Coordinates" (DYVIPAC), to a variety of signalling networks ranging in topological wirings and dynamic properties. The framework was proved useful in acquiring an integrated understanding of systems behaviour.