Fibromyalgia (FM) is a central disorder characterized by chronic pain, fatigue, insomnia, depression, and other minor symptoms. Knowledge about pathogenesis is lacking, diagnosis difficult, clinical approach puzzling, and patient management disappointing. We conducted a theoretical study based on literature data and computational analysis, aimed at developing a comprehensive model of FM pathogenesis and addressing suitable therapeutic targets. We started from the evidence that FM must involve a dysregulation of central pain processing, is female prevalent, suggesting a role for the hypothalamus-pituitary-gonadal (HPG) axis, and is stress-related, suggesting a role for the HP-adrenocortical (HPA) axis. Central pathogenesis was supposed to involve a pain processing loop system including the thalamic ventroposterolateral nucleus (VPL), the primary somatosensory cortex (SSC), and the thalamic reticular nucleus (TRN). For decreasing GABAergic and/or increasing glutamatergic transmission, the loop system crosses a bifurcation point, switching from monostable to bistable, and converging on a high-firing-rate steady state supposed to be the pathogenic condition. Thereafter, we showed that GABAergic transmission is positively correlated with gonadal-hormone-derived neurosteroids, notably allopregnanolone, whereas glutamatergic transmission is positively correlated with stress-induced glucocorticoids, notably cortisol. Finally, we built a dynamic model describing a multistable, double-inhibitory loop between HPG and HPA axes. This system has a high-HPA/low-HPG steady state, allegedly reached in females under combined premenstrual/postpartum brain allopregnanolone withdrawal and stress condition, driving the thalamocortical loop to the high-firing-rate steady state, and explaining the connection between endocrine and neural mechanisms in FM pathogenesis. Our model accounts for FM female prevalence and stress correlation, suggesting the use of neurosteroid drugs as a possible solution to currently unsolved problems in the clinical treatment of the disease.

In this article, we propose a dynamic augmentation scheme for the asymptotic solution of the nonlinear algebraic loops arising in well-known input saturated feedbacks typically designed by solving linear matrix inequalities. We prove that the existing approach based on dynamic augmentation, which replaces the static loop by a dynamic one through the introduction of a sufficiently small time constant, works under some restrictive sufficient well-posedness conditions, requiring the existence of a diagonal Lyapunov matrix. However it can fail in general, even when the algebraic loop is well-posed. Then, we propose a novel approach whose effectiveness is guaranteed whenever well-posedness holds. We also show how this augmentation allows preserving the guaranteed region of attraction with Lyapunov-based designs, as long as a gain parameter is sufficiently large. We finally propose an adaptive version of the scheme where this parameter is adjusted online. Simulation results show the effectiveness of the proposed solutions.

Recombinases are site-specific proteins found in nature that are capable of rearranging DNA. This function has made them promising gene editing tools in synthetic biology, as well as key elements in complex artificial gene circuits implementing Boolean logic. However, since DNA rearrangement is irreversible, it is still unclear how to use recombinases to build dynamic circuits like oscillators. In addition, this goal is challenging because a few molecules of recombinase are enough for promoter inversion, generating inherent stochasticity at low copy number. Here, we propose six different circuit designs for recombinase-based oscillators operating at a single copy number. We model them in a stochastic setting, leveraging the Gillespie algorithm for extensive simulations, and show that they can yield coherent periodic behaviors. Our results support the experimental realization of recombinase-based oscillators and, more generally, the use of recombinases to generate dynamic behaviors in synthetic biology.

Mal de Debarquement Syndrome (MdDS) is a puzzling central vestibular disorder characterized by a long-lasting perception of oscillatory postural instability that may occur after sea travels or flights. We have postulated that MdDS originates from the post-disembarking persistence of an adaptive internal oscillator consisting of a loop system, involving the right and left vestibular nuclei, and the Purkinje cells of the right and left flocculonodular cerebellar cortex, connected by GABAergic and glutamatergic fibers. We have formulated here a mathematical model of the vestibulo-cerebellar loop system and carried out a computational analysis based on a set of differential equations describing the interactions among the loop elements and containing Hill functions that model input-output firing rates relationships among neurons. The analysis indicates that the system acquires a spontaneous and permanent oscillatory behavior for a decrease of threshold and an increase of sensitivity in neuronal input-output responses. These results suggest a role for synaptic plasticity in MdDS pathophysiology, thus reinforcing our previous hypothesis that MdDS may be the result of excessive synaptic plasticity acting on the vestibulo-cerebellar network during its entraining to an oscillatory environment. Hence, our study points to neuroendocrine pathways that lead to increased synaptic response as possible new therapeutic targets for the clinical treatment of the disorder.

Early detection of the emergence of a new variant of concern (VoC) is essential to develop strategies that contain epidemic outbreaks. For example, knowing in which region a VoC starts spreading enables prompt actions to circumscribe the geographical area where the new variant can spread, by containing it locally. This paper presents ‘funnel plots’ as a statistical process control method that, unlike tools whose purpose is to identify rises of the reproduction number (R_t), detects when a regional R_t departs from the national average and thus represents an anomaly. The name of the method refers to the funnel-like shape of the scatter plot that the data take on. Control limits with prescribed false alarm rate are derived from the observation that regional R_t's are normally distributed with variance inversely proportional to the number of infectious cases. The method is validated on public COVID-19 data demonstrating its efficacy in the early detection of SARS-CoV-2 variants in India, South Africa, England, and Italy, as well as of a malfunctioning episode of the diagnostic infrastructure in England, during which the Immensa lab in Wolverhampton gave 43,000 incorrect negative tests relative to South West and West Midlands territories.

The interaction of phase-separating systems with chemical reactions is of great interest in various contexts, from biology to material science. In biology, phase separation is thought to be the driving force behind the formation of biomolecular condensates, i.e., organelles without a membrane that are associated with cellular metabolism, stress response, and development. RNA, proteins, and small molecules participating in the formation of condensates are also involved in a variety of biochemical reactions: how do the chemical reaction dynamics influence the process of phase separation? Here we are interested in finding chemical reactions that can arrest the growth of condensates, generating stable spatial patterns of finite size (microphase separation), in contrast with the otherwise spontaneous (unstable) growth of condensates. We consider a classical continuum model for phase separation coupled to a chemical reaction network (CRN), and we seek conditions for the emergence of stable oscillations of the solution in space. Given reaction dynamics with uncertain rate constants, but known structure, we derive easily computable conditions to assess whether microphase separation is impossible, possible for some parameter values, or robustly guaranteed for all parameter values within given bounds. Our results establish a framework to evaluate which classes of CRNs favor the emergence of condensates with finite size, a question that is broadly relevant to understanding and engineering life.

We formulate a control problem for positive compartmental systems formed by nodes (buffers) and arcs (flows). Our main result is that, on a finite horizon, we can solve the Pontryagin equations in one shot without resorting to trial and error via shooting. As expected, the solution is bang–bang and the switching times can be easily determined. We are also able to find a cost-to-go-function, in an analytic form, by solving a simple nonlinear differential equation. On an infinite horizon, we consider the Hamilton–Jacobi–Bellman theory and we show that the HJB equation can be solved exactly. Moreover, we show that the optimal solution is constant and the cost-to-go function is linear and copositive. This function is the solution of a nonlinear equation. We propose an iterative scheme for solving this equation, which converges in finite time. We also show that an exact solution can be found if there is a positive external disturbance affecting the process and the problem is formulated in a minsup framework. We finally provide illustrative examples related to flood control and epidemiology.

In 2022, worldwide mpox outbreaks have called attention to mpox virus infection and treatment opportunities using the drugs cidofovir and tecovirimat, which target different stages of in-host viral proliferation, respectively production and shedding. We propose a new model of in-host viral infection dynamics that distinguishes between the two stages, so as to explore the distinct effects of the two drugs, and we analyse the model properties and behaviour. Reducing the model order via timescale separation is shown to lead to the classical target-cell limited model, with a lumped viral proliferation rate depending on both production and shedding. We explicitly introduce the effect of the two drugs and we exemplify how to formulate and solve an optimal control problem that leverages the model dynamics to schedule optimal combined treatments.

When agent-based models are developed to capture opinion formation in large-scale populations, the opinion update equations often need to embed several complex psychological traits. The resulting models are more realistic, but also challenging to assess analytically, and hence numerical analysis techniques have an increasing importance in their study. Here, we propose the Qualitative Outcome Likelihood (QOL) analysis, a novel probabilistic analysis technique aimed to unravel behavioural patterns and properties of agent-based opinion formation models, and to characterise possible outcomes when only limited information is available. The QOL analysis reveals which qualitative categories of opinion distributions a model can produce, brings to light their relation to model features such as initial conditions, agent parameters and underlying digraph, and allows us to compare the behaviour of different opinion formation models. We exemplify the proposed technique by applying it to four opinion formation models: the classical Friedkin-Johnsen model and Bounded Confidence model, as well as the recently proposed Backfire Effect and Biased Assimilation model and Classification-based model.

We consider a class of biological networks where the nodes are associated with first-order linear dynamics and their interactions, which can be either activating or inhibitory, are modelled by nonlinear Michaelis–Menten functions (i.e., Hill functions with unitary Hill coefficient), possibly in the presence of external constant inputs. We show that all the systems belonging to this class admit at most one strictly positive equilibrium, which is stable; this property is structural, i.e., it holds for any possible choice of the parameter values, and topology-independent, i.e., it holds for any possible topology of the interaction network. When the network is strongly connected, the strictly positive equilibrium is the only equilibrium of the system if and only if the network includes either at least one inhibiting function, or a strictly positive external input (otherwise, the zero vector is an equilibrium). The proposed stability results hold also for more general classes of interaction functions, and even in the presence of arbitrary delays in the interactions.

We proposed network-decentralized control strategies, in which each actuator can exclusively rely on local information, without knowing the network topology and the external input, ensuring that the flow asymptotically converges to the optimal one with respect to the p -norm. For 1 < p < ∞ , the flow converges to a unique constant optimal up∗. We show that the state converges to the optimal Lagrange multiplier of the optimization problem. Then, we consider networks where the flows are affected by unknown spontaneous dynamics and the buffers need to be driven exactly to a desired set-point. We propose a network-decentralized proportional-integral controller that achieves this goal along with asymptotic flow optimality; now it is the integral variable that converges to the optimal Lagrange multiplier. The extreme cases p=1 and p=∞ are of some interest since the former encourages sparsity of the solution while the latter promotes fairness. Unfortunately, for p=1 or p=∞ these strategies become discontinuous and lead to chattering of the flow, hence no optimality is achieved. We then show how to approximately achieve the goal as the limit for p 1 or p ∞.

Starting from a symmetric state-feedback solution ensuring α-exponential convergence in an ellipsoidal sublevel set, with asymmetric saturation and single-input linear plants, we propose a novel asymmetric scheduled extension preserving the original symmetric solution in that sublevel set and extending the guaranteed stability region to the union of all possible contractive ellipsoids centered at a shifted equilibrium. Our design being based on the solution of a parametric optimization problem, we prove Lipschitz properties of the ensuing feedback law and we compute its explicit state-feedback expression.

While there is widespread concern regarding the impact of pesticides on honey bees, well-replicated field experiments, to date, have failed to provide clear insights on pesticide effects. Here, we adopt a systems biology approach to gain insights into the web of interactions amongst the factors influencing honey bee health. We put the focus on the properties of the system that depend upon its architecture and not on the strength, often unknown, of each single interaction. Then we test in vivo, on caged honey bees, the predictions derived from this modelling analysis. We show that the impact of toxic compounds on honey bee health can be shaped by the concurrent stressors affecting bees. We demonstrate that the immune-suppressive capacity of the widespread pathogen of bees, deformed wing virus, can introduce a critical positive feed-back loop in the system causing bistability, i.e., two stable equilibria. Therefore, honey bees under similar initial conditions can experience different consequences when exposed to the same stressor, including prolonged survival or premature death. The latter can generate an increased vulnerability of the hive to dwindling and collapse. Our conclusions reconcile contrasting field-testing outcomes and have important implications for the application of field studies to complex systems.

We consider the problem of assessing the sensitivity of uncertain biochemical systems in the presence of input perturbations (either constant or periodic) around a stable steady state. In particular, we propose approaches for the robust sensitivity analysis of systems with uncertain parameters assumed to take values in a hyper-rectangle. We highlight vertex results, which allow us to check whether a property is satisfied for all parameter choices in the hyper-rectangle by simply checking whether it is satisfied for all parameter choices at the vertices of the hyper-rectangle. We show that, for a vast class of systems, including (bio)chemical reaction networks with mass-action kinetics, the system Jacobian has a totally multiaffine structure (namely, all minors of the Jacobian matrix are multiaffine functions of the uncertain parameters), which can be exploited to obtain several vertex results. We consider different problems: robust non-singularity; robust stability of the steady-state; robust steady-state sensitivity analysis, in the case of constant perturbations; robust frequency-response sensitivity analysis, in the presence of periodic perturbations; and robust adaptation analysis. The developed theory is then applied to gain insight into some examples of uncertain biochemical systems, including the incoherent feed-forward loop, the coherent feed-forward loop, the Brusselator oscillator and the Goldbeter oscillator.

When facing the global health threat posed by an infectious disease, predictive mathematical models are crucial not only to understand and forecast the epidemic evolution, but also to plan effective control strategies that contrast the disease and its spread in the population. This tutorial aims to give a broad overview of the fundamental developments enabled by systems-and-control methodologies in modelling and controlling epidemiological dynamics across scales, from infection dynamics within hosts to contagion dynamics between hosts. The first part is focused on modelling and control of infectious diseases in the host, capturing the dynamic interplay between pathogens and the immune system, and discussing control strategies to design tailored therapies and treatments to optimally clear the infection. The second part deals with the spread of contagion between hosts: epidemic dynamics are modelled resorting to networked systems where the nodes represent individuals and the links represent interactions that can lead to contagion, and a comparison to compartmental models is carried out. The third part surveys multi-scale models and multi-pronged approaches to contrast the spread of infectious diseases: a holistic perspective is adopted, including behavioural and socioeconomic aspects along with public health issues, to discuss optimal epidemic control across scales.

Given a class of (bio)Chemical Reaction Networks (CRNs) identified by a stoichiometric matrix S, we define as dual reaction network, CRN∗, the class of (bio)Chemical Reaction Networks identified by the transpose stoichiometric matrix S⊤. We consider both the dynamical systems describing the time evolution of the species concentrations and of the reaction rates. First, based on the analysis of the Jacobian matrix, we show that the structural (i.e., parameter-independent) local stability properties are equivalent for a CRN and its dual CRN ∗. We also assess the structural global stability properties of the two dual networks, analysing both concentration and rate representations. We prove that the existence of a polyhedral (or piecewise-linear) Lyapunov function in concentrations for a CRN is equivalent to the existence of a piecewise-linear in rates Lyapunov function for the dual CRN ∗; in fact, if V is a polyhedral Lyapunov function for a CRN, the dual polyhedral function V∗ is a piecewise-linear in rates Lyapunov function for the dual network. We finally show how duality can be exploited to gain additional insight into biochemical reaction networks.