# Elisa Tonello's research while affiliated with Freie Universität Berlin and other places

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## Publications (26)

To simplify the analysis of Boolean networks, a reduction in the number of components is often considered. A popular reduction method consists in eliminating components that are not autoregulated, using variable substitution. In this work, we show how this method can be extended, for asynchronous dynamics of Boolean networks, to the elimination of...

Control of Boolean networks enables important medical and biological applications. At the core of many approaches is value percolation, by virtue of its simplicity and ease of implementation. Methods based uniquely on percolation can however miss many control strategies. We previously introduced a new method which, using the network's trap spaces,...

The structure of the graph defined by the interactions in a Boolean network can determine properties of the asymptotic dynamics. For instance, considering the asynchronous dynamics, the absence of positive cycles guarantees the existence of a unique attractor, and the absence of negative cycles ensures that all attractors are fixed points. In prese...

Understanding control mechanisms in biological systems plays a crucial role in important applications, for instance in cell reprogramming. Boolean modeling allows the identification of possible efficient strategies, helping to reduce the usually high and time-consuming experimental efforts. Available approaches to control strategy identification us...

The study of control mechanisms of biological systems allows for interesting applications in bioengineering and medicine, for instance in cell reprogramming or drug target identification. A control strategy often consists of a set of interventions that, by fixing the values of some components, ensure that the long term dynamics of the controlled sy...

Boolean networks are popular tools for the exploration of qualitative dynamical properties of biological systems. Several dynamical interpretations have been proposed based on the same logical structure that captures the interactions between Boolean components. They reproduce, in different degrees, the behaviours emerging in more quantitative model...

Understanding control mechanisms in biological systems plays a crucial role in important applications, for instance in cell reprogramming. Boolean modeling allows the identification of possible efficient strategies, helping to reduce the usually high and time-consuming experimental efforts. Available approaches to control strategy identification us...

Motivated by the problem of identifying a mathematical framework for the formal definition of concepts such as weather, climate and connections between them, we discuss a question of convergence of short-time time averages for random nonautonomous dynamical systems depending on a parameter. The problem is formulated by means of Young measures. Usin...

The formation of spatial structures lies at the heart of developmental processes. However, many of the underlying gene regulatory and biochemical processes remain poorly understood. Turing patterns constitute a main candidate to explain such processes, but they appear sensitive to fluctuations and variations in kinetic parameters, raising the quest...

The formation of spatial structures lies at the heart of developmental processes. However, many of the underlying gene regulatory and biochemical processes remain poorly understood. Turing patterns constitute a main candidate to explain such processes, but they appear sensitive to fluctuations and variations in kinetic parameters, raising the quest...

The control of biological systems presents interesting applications such as cell reprogramming or drug target identification. A common type of control strategy consists in a set of interventions that, by fixing the values of some variables, force the system to evolve to a desired state. This work presents a new approach for finding control strategi...

We study Boolean networks which are simple spatial models of the highly conserved Delta–Notch system. The models assume the inhibition of Delta in each cell by Notch in the same cell, and the activation of Notch in presence of Delta in surrounding cells. We consider fully asynchronous dynamics over undirected graphs representing the neighbour relat...

The control of biological systems presents interesting applications such as cell reprogramming or drug target identification. A common type of control strategy consists in a set of interventions that, by fixing the values of some variables, force the system to evolve to a desired state. This work presents a new approach for finding control strategi...

The induced kinetic differential equations of a reaction network endowed with mass action type kinetics is a system of polynomial differential equations. The problem studied here is: Given a system of polynomial differential equations, is it possible to find a network which induces these equations; in other words: is it possible to find a kinetic r...

The induced kinetic differential equation of a reaction network endowed with mass action type kinetics is a system of polynomial differential equations. The problem studied here is: Given a polynomial differential equation, is it possible to find a network which induces the equation? If yes, can we find a network with some chemically relevant prope...

We study Boolean networks which are simple spatial models of the highly conserved Delta-Notch system. The models assume the inhibition of Delta in each cell by Notch in the same cell, and the activation of Notch in presence of Delta in surrounding cells. We consider fully asynchronous dynamics over undirected graphs representing the neighbour relat...

Results and tools on discrete interaction networks are often concerned with Boolean variables, whereas considering more than two levels is sometimes useful. Multivalued networks can be converted to partial Boolean maps, in a way that preserves the asynchronous dynamics. We investigate the problem of extending these maps to non-admissible states, i....

This thesis considers two modelling frameworks for interaction networks in biology. The first models the interacting species qualitatively as discrete variables, with the regulatory graphs expressing their mutual influence. Circuits in the regulatory structure are known to be indicative of some asymptotic behaviours. We investigate the relationship...

We consider the following question on the relationship between the asymptotic behaviours of Boolean networks and their regulatory structures: does the presence of a cyclic attractor imply the existence of a local negative circuit in the regulatory graph? When the number of model components $n$ verifies $n \geq 6$, the answer is known to be negative...

Network translation has recently be used to establish steady state properties of mass action systems by corresponding the given system to a generalized one which is either dynamically or steady state equivalent. In this work we further use network translation to identify network structures which give rise to the well-studied property of absolute co...

We consider the modeling approach introduced by R. Thomas for the qualitative study of gene regulatory networks. Tools and results on regulatory networks are often concerned only with the Boolean case of this formalism. However, multivalued approaches are sometimes more suited to model biological situations. Multivalued networks can be converted to...

Reaction networks can be simpliﬁed by eliminating linear intermediate species in partial steadystates. Inthispaper,westudythequestionwhetherthisrewriteprocedureisconﬂuent,so that for any given reaction network with kinetic constraints, a unique normal form will be obtained independently of the elimination order. We ﬁrst show that conﬂuence fails fo...

Reaction networks can be simplified by eliminating linear intermediate species in partial steady states. In this paper, we study the question whether this rewrite procedure is confluent, so that for any given reaction network, a unique normal form will be obtained independently of the elimination order. We first contribute a counter example which s...

We study the structural simplification of chemical reaction networks with partial steady state semantics assuming that the concentrations of some but not all species are constant. We present a simplification rule that can eliminate intermediate species that are in partial steady state, while preserving the dynamics of all other species. Our simplif...

## Citations

... We significantly broaden the theoretical and computational framework to include edge control, reworking the original material to obtain a consistent, comprehensive and flexible approach. For efficient implementation, we use a logical programing approach, namely Answer Set Programming (ASP), extending the works from [9] and [4]. Finally, building on a case study from [3], we show the applicability of the method and illustrate the potential inherent in comprehensive analysis using both node and edge control. ...

... Under these conditions, model analyses that investigate reachability of attractors or existence of control strategies (see e.g. [10]) can be greatly facilitated. Of particular interest are structural conditions on the interaction graph that can guarantee these properties. ...

... Model comparison methods, including model selection, multi-model averaging, and topological sensitivity analysis can be used to group models that provide comparable descriptions of a certain type of biological behaviour, henceforth denoted by Q. For biological systems, instances of a behaviour Q could be oscillations, switch-like characteristics [31], signal filtering [32], robust perfect adaptation [33,34], or Turing pattern behaviour [35,36]. ...

Reference: Open Problems in Mathematical Biology

... Such an analysis that compares different modelling frameworks requires careful identification of equivalent model features. A large scale analysis that compared lattice gas cellular automaton models of TPs with continuous models [20] has recently confirmed that only a small number of network architectures are capable of generating stable spatial patterns. This means that design principles are robust with respect to a change in the modelling formalism employed. ...

... From this perspective, BNs offer a formal framework for predicting perturbations that destabilize the system and drive it towards a desired new stable behavior. BN control or BN reprogramming, in reference to cellular reprogramming which aims at converting cell types, is thus receiving a lot of interest from the computational systems biology community (Biane and Delaplace, 2019;Fontanals, Tonello, and Siebert, 2020;Mandon, Su, Haar, Pang, and Paulevé, 2019;Rozum, Deritei, Park, Jorge Gómez Tejeda Zañudo, and Albert, 2021;Su and Pang, 2020;Yang, Jorge Gómez Tejeda Zañudo, and Albert, 2018; Jorge G. T. Zañudo and Albert, 2015). ...

... The author applies the notion of autopoiesis to the comparably compact setup of the cellular automaton to investigate its consequences, implications, and shortcomings. While these works tackle large-scale questions in the emergence of life and cognition, the work of Tonello and Siebert (2019) considers the small-scale question of inhibition-models in the context of cell-to-cell communication. Similar to the activator-inhibitor approach presented in Section 3.2, their model assumes differentiated and undifferentiated cells, characterized by delta and notch. ...

... Chemical reaction networks (CRNs) are often modelled by reaction rate equations, which are systems of first-order, autonomous, ordinary differential equations (ODEs) describing the time evolution of the concentrations of chemical species involved. Considering CRNs which are subject to the law of mass action, their reaction rate equations have polynomials on their right-hand sides [1,2]. The mathematical investigation of ODEs with polynomial right-hand sides has a long history and includes important question is how small the CRN can be so that it has K limit cycles. ...

Reference: Chemical systems with limit cycles

... Because the majority of tools and theorems available for the analysis of logical networks are restricted to the Boolean case, binarization methods for converting systems with multi-valued elements into Boolean models have been developed as a way to extend the utility of the available methods [5,[11][12][13]. However, these binarization approaches mainly focus on maintaining a model's asymptotic dynamics, rather than preserving the causal structure of the original non-binary system. ...

... Ruet's counter example is built with another technic. Recently, Tonello, Chaouiya and Farcot [69] proved, using a SAT solver, that there is no counter example with n ≤ 5. We have seen that if G(f ) has no negative cycle, then all asynchronous attractors are fixed points. Can these fixed points be reached quickly? ...

... (For a reaction 1X + 1Y → Z, the rate is not ∼ x 1 y 1 , but ∼ x α y β with arbitrary, not necessarily integer α, β.) Besides the limited validity of the mass-action "law", a CRN with MAK may not have zero deficiency and may not be weakly reversible, but there may be a dynamically equivalent, "translated" CRN with GMAK that has the desired properties [25,26,40,27]. ...