arXiv subjects

Elisa Tonello

Publications and source records attributed to Elisa Tonello.

12 recordsLinked to original sources

arXiv2024

Phenotype control and elimination of variables in Boolean networks

We investigate how elimination of variables can affect the asymptotic dynamics and phenotype control of Boolean networks. In particular, we look at the impact on minimal trap spaces, and identify a structural condition that guarantees their preservation. We examine the possible effects of variable elimination under three of the most popular approaches to control (attractor-based control, value propagation and control of minimal trap spaces), and under different update schemes (synchronous, asynchronous, generalized asynchronous). We provide some insights on the application of reduction, and an ample inventory of examples and counterexamples.

cs.DM↗

arXiv2024

Reduction for asynchronous Boolean networks: elimination of negatively autoregulated components

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 vertices that have a negative autoregulation, and study the effects on the dynamics and interaction structure. For elimination of non-autoregulated variables, the preservation of attractors is in general guaranteed only for fixed points. Here we give sufficient conditions for the preservation of complex attractors. The removal of so called mediator nodes (i.e. vertices with indegree and outdegree one) is often considered, and frequently does not affect the attractor landscape. We clarify that this is not always the case, and in some situations even subtle changes in the interaction structure can lead to a different asymptotic behaviour. Finally, we use properties of the more general elimination method introduced here to give an alternative proof for a bound on the number of attractors of asynchronous Boolean networks in terms of the cardinality of positive feedback vertex sets of the interaction graph.

cs.DM↗

arXiv2023

Attractor identification in asynchronous Boolean dynamics with network reduction

Identification of attractors, that is, stable states and sustained oscillations, is an important step in the analysis of Boolean models and exploration of potential variants. We describe an approach to the search for asynchronous cyclic attractors of Boolean networks that exploits, in a novel way, the established technique of elimination of components. Computation of attractors of simplified networks allows the identification of a limited number of candidate attractor states, which are then screened with techniques of reachability analysis combined with trap space computation. An implementation that brings together recently developed Boolean network analysis tools, tested on biological models and random benchmark networks, shows the potential to significantly reduce running times.

cs.DM↗

arXiv2022

Attractor separation and signed cycles in asynchronous Boolean networks

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 presence of multiple attractors, one might be interested in properties that ensure that attractors are sufficiently "isolated", that is, they can be found in separate subspaces or even trap spaces, subspaces that are closed with respect to the dynamics. Here we introduce notions of separability for attractors and identify corresponding necessary conditions on the interaction graph. In particular, we show that if the interaction graph has at most one positive cycle, or at most one negative cycle, or if no positive cycle intersects a negative cycle, then the attractors can be separated by subspaces. If the interaction graph has no path from a negative to a positive cycle, then the attractors can be separated by trap spaces. Furthermore, we study networks with interaction graphs admitting two vertices that intersect all cycles, and show that if their attractors cannot be separated by subspaces, then their interaction graph must contain a copy of the complete signed digraph on two vertices, deprived of a negative loop. We thus establish a connection between a dynamical property and a complex network motif. The topic is far from exhausted and we conclude by stating some open questions.

cs.DM↗

arXiv2022

Node and edge control strategy identification via trap spaces in Boolean networks

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 system is in a desired state. A common approach to control in the Boolean framework consists in checking how the fixed values propagate through the network, to establish whether the effect of percolating the interventions is sufficient to induce the target state. Although methods based uniquely on value percolation allow for efficient computation, they can miss many control strategies. Exhaustive methods for control strategy identification, on the other hand, often entail high computational costs. In order to increase the number of control strategies identified while still benefiting from an efficient implementation, we introduce a method based on value percolation that uses trap spaces, subspaces of the state space that are closed with respect to the dynamics, and that can usually be easily computed in biological networks. The approach allows for node interventions, which fix the value of certain components, and edge interventions, which fix the effect that one component has on another. The method is implemented using Answer Set Programming, extending an existing efficient implementation of value percolation to allow for the use of trap spaces and edge control. The applicability of the approach is studied for different control targets in a biological case study, identifying in all cases new control strategies that would escape usual percolation-based methods.

q-bio.MN↗

arXiv2022

Linear cuts in Boolean networks

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 models. In particular, regulatory conflicts can prevent the standard asynchronous dynamics from reproducing some trajectories that might be expected upon inspection of more detailed models. We introduce and study the class of networks with linear cuts, where linear components -- intermediates with a single regulator and a single target -- eliminate the aforementioned regulatory conflicts. The interaction graph of a Boolean network admits a linear cut when a linear component occurs in each cycle and in each path from components with multiple targets to components with multiple regulators. Under this structural condition the attractors are in one-to-one correspondence with the minimal trap spaces, and the reachability of attractors can also be easily characterized. Linear cuts provide the base for a new interpretation of the Boolean semantics that captures all behaviours of multi-valued refinements with regulatory thresholds that are uniquely defined for each interaction, and contribute a new approach for the investigation of behaviour of logical models.

cs.DM↗

arXiv2021

Control in Boolean networks with model checking

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 usually focus either on attractor or phenotype control, and are unable to deal with more complex control problems, for instance phenotype avoidance. They also fail to capture, in many situations, all possible minimal strategies, finding instead only sub-optimal solutions. In order to fill these gaps, we present a novel approach to control strategy identification in Boolean networks based on model checking. The method is guaranteed to identify all minimal control strategies, and provides maximal flexibility in the definition of the control target. We investigate the applicability of the approach by considering a range of control problems for different biological systems, comparing the results, where possible, to those obtained by alternative control methods.

q-bio.MN↗

arXiv2020

Boolean analysis of lateral inhibition

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 relation between cells. In this framework, one can show that all attractors are fixed points for the system, independently of the neighbour relation, for instance by using known properties of simplified versions of the models, where only one species per cell is defined. The fixed points correspond to the so-called fine-grained "patterns" that emerge in discrete and continuous modelling of lateral inhibition. We study the reachability of fixed points, giving a characterisation of the trap spaces and the basins of attraction for both the full and the simplified models. In addition, we use a characterisation of the trap spaces to investigate the robustness of patterns to perturbations. The results of this qualitative analysis can complement and guide simulation-based approaches, and serve as a basis for the investigation of more complex mechanisms.

cs.DM↗

arXiv2020

Control Strategy Identification via Trap Spaces in Boolean Networks

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 strategies in biological systems modeled by Boolean networks. In this context, we explore the properties of trap spaces, subspaces of the state space which the dynamics cannot leave. Trap spaces for biological networks can often be efficiently computed, and provide useful approximations of attraction basins. Our approach provides control strategies for a target phenotype that are based on interventions that allow the control to be eventually released. Moreover, our method can incorporate information about the attractors to find new control strategies that would escape usual percolation-based methods. We show the applicability of our approach to two cell fate decision models.

q-bio.MN↗

arXiv2018

On the conversion of multivalued to Boolean dynamics

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.e. states that do not have a multivalued counterpart. We observe that attractors are preserved if a stepwise version of the original function is considered for conversion. Different extensions of the Boolean conversion affect the structure of the interaction graphs in different ways. A particular technique for extending the partial Boolean conversion is identified, that ensures that feedback cycles are preserved. This property, combined with the conservation of the asymptotic behaviour, can prove useful for the application of results and analyses defined in the Boolean setting to multivalued networks, and vice versa. As a first application, by considering the conversion of a known example for the discrete multivalued case, we create a Boolean map showing that the existence of a cyclic attractor and the absence of fixed points are compatible with the absence of local negative cycles. We then state a multivalued version of a result connecting mirror states and local feedback cycles.

cs.DM↗

arXiv2018

Local negative circuits and cyclic attractors in Boolean networks with at most five components

We consider the following question on the relationship between the asymptotic behaviours of asynchronous dynamics 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. We show that the question can be translated into a Boolean satisfiability problem on $n \cdot 2^n$ variables. A Boolean formula expressing the absence of local negative circuits and a necessary condition for the existence of cyclic attractors is found unsatisfiable for $n \leq 5$. In other words, for Boolean networks with up to $5$ components, the presence of a cyclic attractor requires the existence of a local negative circuit.

cs.DM↗

arXiv2018

Network translation and steady state properties of chemical reaction systems

Network translation has recently been 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 concentration robustness in the corresponding mass action systems. In addition to establishing the capacity for absolute concentration robustness, we show that network translation can often provide a method for deriving the steady state value of the robust species. We furthermore present a MILP algorithm for the identification of translated chemical reaction networks that improves on previous approaches, allowing for easier application of the theory.

math.DS↗