Integrated Structural and Probabilistic Approaches for Biological and Epidemiological Systems

Project Information

INSPIRE

Grant agreement ID: 101076926

DOI

10.3030/101076926

EC signature date 30 November 2022

Start date 1 January 2023

End date 31 December 2027

Funded under

• European Research Council (ERC)

Total cost

€ 1 500 000,00

EU contribution

€ 1 500 000,00

Coordinated by

UNIVERSITA DEGLI STUDI DI TRENTO
Italy

Periodic Reporting for period 1 - INSPIRE (Integrated Structural and Probabilistic Approaches for Biological and Epidemiological Systems)

Reporting period: 2023-01-01 to 2025-06-30

Summary of the context and overall objectives of the project

The central question underlying the INSPIRE project is the ability of systems in nature to preserve their function, despite uncertainties, variability and perturbations. Studying the complex dynamics of systems in nature is fundamental to understand important phenomena, ranging from regulatory systems in the cells to the functioning of the brain, from the onset of diseases in our body to the contagion of infections among individuals, from the interactions of species in ecosystems to social dynamics. Qualitative behaviours of these systems are often preserved even with huge parameter variations, because they rely on the system interconnection structure.
INSPIRE aims at bridging the gap between parameter-dependent numerical simulations, which can predict the system behaviour case by case and require the exact knowledge of models and parameter values (which is typically not available), and parameter-free structural approaches to check whether a property is preserved for a whole family of uncertain systems exclusively due to its structure. When an expected property fails to hold structurally, novel approaches are needed to understand why, which system features prevent it, which key parameters must be finely tuned to enforce it, and to quantify the probability with which the property can be expected to hold.
To this aim, the overarching objective of INSPIRE is to develop a unifying framework to analyse and control families of uncertain dynamical systems, which for the first time integrates structural, robust and probabilistic methods, and tailors them to the peculiarities of natural systems.
New methodologies - and efficient algorithms aimed at mitigating computational complexity - will allow us to assess (practically) structural properties and unveil the mechanisms that enable/prevent a property, identifying the key parameters or motifs, and to quantitatively assess the system’s robustness and resilience. The achieved insight will be exploited to develop effective control strategies.
The expected project outcomes, a mathematical theory as well as algorithms to analyse and control complex uncertain systems in nature, will have a strong impact, e.g. on the analysis and design of biomolecular feedback systems with a desired behaviour, on the identification of therapeutic targets, on the prediction and control of epidemic phenomena.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

As a key effort of the project, we have started developing a unifying framework that integrates both structural and probabilistic, qualitative and quantitative methodologies for the study of systems in the life sciences, and beyond.
We have started developing a framework that integrates the concepts of robustness and resilience, associated with a system’s ability to preserve its functions despite uncertainties, fluctuations and perturbations, both intrinsic and extrinsic. Numerous competing definitions of these concepts coexist and often lack a rigorous control-theoretic formulation, which we have provided in a unified framework for the first time, demonstrating their effectiveness in capturing behaviours of widely used models in biology.
We have obtained rigorous structural results to assess the convergence to periodic orbits that exploit the system structure of strongly 2-cooperative systems, and we have applied our new theory to well-known models in biology, such as the Goodwin oscillator.
We have preliminarily developed novel probabilistic approaches tailored to the sensitivity analysis and the prediction of qualitative behaviours of complex large-scale systems; in particular, the methodologies have been applied to large-scale agent-based opinion formation models.
Moreover, we have started investigating computationally efficient approaches, based on surrogate models obtained through the theory of generalized polynomial chaos, to quantify probabilistic robustness for various types of models in neuroscience. We have also developed a methodology for the efficient and faithful reconstruction of dynamical attractors using homogeneous differentiators, with applications to complex systems also in neuroscience.
We have introduced the concept of qualitative “spiking” behaviour of systems in a structural framework and discussed its relevance in population-infection dynamics.
We have tailored advanced computationally efficient optimal control algorithms, for which we have proven theoretical convergence guarantees, to a general class of epidemiological models. We have investigated the modelling, controllability and optimal control of antimicrobial resistance. The structure of optimization problems in ecology has also been exploited for their efficient solution relying on stability guarantees and nonlinear programming.
We have developed novel approaches to deal with uncertainty and noise in reaction-diffusion dynamics.
As our main interdisciplinary contributions, we have employed structural and/or probabilistic approaches to study physiological systems and explain pathogenesis, to analyse the inherent properties of biomolecular systems and design novel biomolecular circuits with desired behaviours.
We have also developed and analysed new models for epidemics in the host and between hosts, and for the interplay of epidemics and behaviours in populations, as well as for the behaviour of multi-agent systems in nature.
As we had anticipated, structural methodologies can also be profitably applied to uncertain systems in engineering, which we have also considered (in AC circuits and robotics).

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

The INSPIRE project constitutes a first attempt to systematically integrate structural and probabilistic approaches for the analysis and the control of uncertain dynamic phenomena in the life sciences, including biology, ecology, neuroscience and epidemiology. The goal is to provide a novel methodological framework for the qualitative and quantitative assessment of the behaviour of systems affected by uncertainties that are both intrinsic (parameter variations and fluctuations) and extrinsic (disturbances and perturbations).
A first major result of the project is to provide an integrated theoretical framework for robustness and resilience. Within this framework, we aim to develop efficient computational pipelines to assess the robustness and resilience of systems in the life sciences and to effectively detect early warning signals that predict critical behaviours of the system.
The developed mathematical theory and algorithms will enable the effective analysis and control of complex uncertain systems in nature, supporting e.g. a better understanding of systems in biology and neuroscience, the design of biomolecular feedback systems with a desired behaviour, the identification of therapeutic targets in physiological systems, the prediction and control of epidemic phenomena.

Integrated Structural and Probabilistic Framework: new theory, and applications in the life sciences