Francesco Montefusco

Input-output finite-time stability of linear systems

In the recent paper “Input-output finite-time stabilization of linear systems,” (F. Amato ) a sufficient condition for input-output finite-time stability (IO-FTS), when the inputs of the system are L2 signals, has been provided; such condition requires the existence of a feasible solution to an optimization problem involving a certain differential linear matrix inequality (DLMI). Roughly speaking, a system is said to be input-output finite-time stable if, given a class of norm bounded input signals over a specified time interval of length T, the outputs of the system do not exceed an assigned threshold during such time interval. IO-FTS constraints permit to specify quantitative bounds on the controlled variables to be fulfilled during the transient response. In this context, this paper presents several novel contributions. First, by using an approach based on the reachability Gramian theory, we show that the main theorem of F. Amato is actually also a necessary condition for IO-FTS; at the same time we provide an alternative-still necessary and sufficient-condition for IO-FTS, in this case based on the existence of a suitable solution to a differential Lyapunov equality (DLE). We show that the last condition is computationally more efficient; however, the formulation via DLMI allows to solve the problem of the IO finite-time stabilization via output feedback. The effectiveness and computational issues of the two approaches for the analysis and the synthesis, respectively, are discussed in two examples; in particular, our methodology is used in the second example to minimize the maximum displacement and velocity of a building subject to an earthquake of given magnitude.

CORE-Net: exploiting prior knowledge and preferential attachment to infer biological interaction networks

The problem of reverse-engineering the topology of interaction networks from time-course experimental data has received a considerable attention in the literature, due to the potential applications in the most diverse fields, comprising engineering, biology, economics and social sciences. An important insight was brought by the introduction of the concept of scale-free topology, whose implications have been widely discussed in literature over the last decade. The aim of this work is to investigate whether it is possible to improve the performances of an inference technique, based on dynamical linear systems and LMI-based optimization, by exploiting the same mechanisms that underpin scale-free networks generation, i.e. growth and preferential attachment (PA). The work is prominently concerned with applications in the biological domain, though the algorithm can be in principle adapted also to other frameworks. A statistical evaluation is performed, by using numerically simulated networks, showing that the growth and PA mechanisms actually improve the inference power of the considered technique. Finally the method is applied to a biological case-study, validating the results against experimental data available in literature.

Implementing Nonlinear Feedback Controllers Using DNA Strand Displacement Reactions

We show how an important class of nonlinear feedback controllers can be designed using idealized abstract chemical reactions and implemented via DNA strand displacement (DSD) reactions. Exploiting chemical reaction networks (CRNs) as a programming language for the design of complex circuits and networks, we show how a set of unimolecular and bimolecular reactions can be used to realize input-output dynamics that produce a nonlinear quasi sliding mode (QSM) feedback controller. The kinetics of the required chemical reactions can then be implemented as enzyme-free, enthalpy/entropy driven DNA reactions using a toehold mediated strand displacement mechanism via Watson-Crick base pairing and branch migration. We demonstrate that the closed loop response of the nonlinear QSM controller outperforms a traditional linear controller by facilitating much faster tracking response dynamics without introducing overshoots in the transient response. The resulting controller is highly modular and is less affected by retroactivity effects than standard linear designs.

Mathematical modelling of local calcium and regulated exocytosis during inhibition and stimulation of glucagon secretion from pancreatic alpha‐cells

The control of glucagon secretion from pancreatic alpha‐cells is still unclear and, when defective, is involved in the development of diabetes. We propose a mathematical model of Ca2+ dynamics and exocytosis to understand better the intracellular mechanisms downstream of electrical activity that control glucagon secretion. The model exploits compartmental modelling of Ca2+ levels near open and closed high voltage‐activated Ca2+ channels involved in exocytosis, in the sub‐membrane Ca2+ compartment, in the bulk cytosol and in the endoplasmic reticulum. The model reproduces the effects of glucose, glucagon‐like peptide 1 (GLP‐1) and adrenaline, providing insight into the relative contributions of the various subcellular Ca2+ compartments in the control of glucagon secretion. Our results highlight that the number of open Ca2+ channels is a dominant factor in glucagon release, and clarify why cytosolic Ca2+ is a poor read‐out of alpha‐cell secretion.

Biomolecular implementation of a quasi sliding mode feedback controller based on DNA strand displacement reactions

A fundamental aim of synthetic biology is to achieve the capability to design and implement robust embedded biomolecular feedback control circuits. An approach to realize this objective is to use abstract chemical reaction networks (CRNs) as a programming language for the design of complex circuits and networks. Here, we employ this approach to facilitate the implementation of a class of nonlinear feedback controllers based on sliding mode control theory. We show how a set of two-step irreversible reactions with ultrasensitive response dynamics can provide a biomolecular implementation of a nonlinear quasi sliding mode (QSM) controller. We implement our controller in closed-loop with a prototype of a biological pathway and demonstrate that the nonlinear QSM controller outperforms a traditional linear controller by facilitating faster tracking response dynamics without introducing overshoots in the transient response.

Ultrasensitive Negative Feedback Control: A Natural Approach for the Design of Synthetic Controllers

Many of the most important potential applications of Synthetic Biology will require the ability to design and implement high performance feedback control systems that can accurately regulate the dynamics of multiple molecular species within the cell. Here, we argue that the use of design strategies based on combining ultrasensitive response dynamics with negative feedback represents a natural approach to this problem that fully exploits the strongly nonlinear nature of cellular information processing. We propose that such feedback mechanisms can explain the adaptive responses observed in one of the most widely studied biomolecular feedback systems—the yeast osmoregulatory response network. Based on our analysis of such system, we identify strong links with a well-known branch of mathematical systems theory from the field of Control Engineering, known as Sliding Mode Control. These insights allow us to develop design guidelines that can inform the construction of feedback controllers for synthetic biological systems.

Concise Whole-Cell Modeling of BKCa-CaV Activity Controlled by Local Coupling and Stoichiometry

Large-conductance Ca2+-dependent K+ (BKCa) channels are important regulators of electrical activity. These channels colocalize and form ion channel complexes with voltage-dependent Ca2+ (CaV) channels. Recent stochastic simulations of the BKCa-CaV complex with 1:1 stoichiometry have given important insight into the local control of BKCa channels by fluctuating nanodomains of Ca2+. However, such Monte Carlo simulations are computationally expensive, and are therefore not suitable for large-scale simulations of cellular electrical activity. In this work we extend the stochastic model to more realistic BKCa-CaV complexes with 1:n stoichiometry, and analyze the single-complex model with Markov chain theory. From the description of a single BKCa-CaV complex, using arguments based on timescale analysis, we derive a concise model of whole-cell BKCa currents, which can readily be analyzed and inserted into models of cellular electrical activity. We illustrate the usefulness of our results by inserting our BKCa description into previously published whole-cell models, and perform simulations of electrical activity in various cell types, which show that BKCa-CaV stoichiometry can affect whole-cell behavior substantially. Our work provides a simple formulation for the whole-cell BKCa current that respects local interactions in BKCa-CaV complexes, and indicates how local-global coupling of ion channels may affect cell behavior.

Reverse-engineering biological interaction networks from noisy data using Regularized Least Squares and Instrumental Variables

The problem of reverse engineering the topology of a biological network from noisy time-series measurements is one of the most important challenges in the field of Systems Biology. In this work, we develop a new inference approach which combines the Regularized Least Squares (RLS) technique with a technique to avoid the introduction of bias and non-consistency due to measurement noise in the estimation of the parameters in the standard Least Squares (LS) formulation, the Instrumental Variables (IV) method. We test our approach on a set of nonlinear in silico networks and show that the combined exploitation of RLS and IV methods improves the predictions with respect to other standard approaches.

Reverse Engineering Partially-Known Interaction Networks from Noisy Data

Abstract One of the most difficult challenges associated with the problem of inferring functional interaction networks from experimental data is that of dealing with the effects of measurement noise in the data used for reverse engineering. A second important challenge is that of taking full advantage of prior knowledge about some elements of the network to improve the results of the reconstruction process. This paper introduces a new inference algorithm, PACTLS, which addresses both of the above issues. The algorithm combines methods to exploit mechanisms underpinning scale–free networks generation, i.e. network growth and preferential attachment (PA), with a technique to optimally reduce the effects of measurement noise in the data on the reliability of the inference results, i.e. the Constrained Total Least Squares (CTLS) algorithm. The technique is assessed through numerical tests on in silico random networks and is shown to consistently outperform approaches based on Bayesian networks.

Inferring scale-free networks via multiple linear regression and preferential attachment

The problem of reverse-engineering the topology of interaction networks from time-course experimental data has been the subject of a considerable research effort in the last years, due to the potential applications in the most diverse fields, comprising engineering, biology, economics and social sciences. An important insight into such topic was brought by the introduction of the concept of scale-free topology, whose implications have been widely discussed in literature over the last decade. The aim of this work is to investigate whether it is possible to improve the performances of an inference technique, based on dynamical linear systems and multiple linear regression, by exploiting the same mechanisms that underpin scale-free networks generation, i.e. growth and preferential attachment (PA). The work is prominently concerned with applications in the biological domain, though the algorithm can be in principle adapted also to other frameworks. A statistical evaluation is performed, by using numerically simulated networks, showing that the growth and PA mechanisms actually improve the inference power of the considered technique. Finally the method has been applied to a biological case-study, validating the results against experimental data available in literature.