Elisabetta De Maria

Design, optimization and predictions of a coupled model of the cell cycle, circadian clock, DNA repair system, irinotecan metabolism and exposure control under temporal logic constraints

In systems biology, the number of available models of cellular processes has increased rapidly, but re-using models in different contexts or for different questions remains a challenging issue. In this paper, we study the coupling of different models playing a role in the mammalian cell cycle and in cancer therapies. We show how the formalization of experimental observations in temporal logic with numerical constraints can be used to compute the unknown coupling kinetics parameter values agreeing with experimental data. This constraint-based approach to computing with partial information is illustrated through the design of a complex model of the mammalian cell cycle, the circadian clock, the p53/Mdm2 DNA-damage repair system, the metabolism of irinotecan and the control of cell exposure to it. We discuss the use of this model for cancer chronotherapies and evaluate its predictive power with respect to circadian core gene knock-outs.

On Coupling Models Using Model-Checking: Effects of Irinotecan Injections on the Mammalian Cell Cycle

In systems biology, the number of models of cellular processes increases rapidly, but re-using models in different contexts or for different questions remains a challenging issue. In this paper, we show how the validation of a coupled model and the optimization of its parameters with respect to biological properties formalized in temporal logics, can be done automatically by model-checking. More specifically, we illustrate this approach with the coupling of existing models of the mammalian cell cycle, the p53-based DNA-damage repair network, and irinotecan metabolism, with respect to the biological properties of this anticancer drug.

A Logical Framework for Systems Biology

We propose a novel approach for the formal verification of biological systems based on the use of a modal linear logic. We show how such a logic can be used, with worlds as instants of time, as an unified framework to encode both biological systems and temporal properties of their dynamic behaviour. To illustrate our methodology, we consider a model of the P53/Mdm2 DNA-damage repair mechanism. We prove several properties that are important for such a model to satisfy and serve to illustrate the promise of our approach. We formalize the proofs of these properties in the Coq Proof Assistant, with the help of a Lambda Prolog prover for partial automation of the proofs.

Verification of Temporal Properties of Neuronal Archetypes Modeled as Synchronous Reactive Systems

There exists many ways to connect two, three or more neurons together to form different graphs. We call archetypes only the graphs whose properties can be associated with specific classes of biologically relevant structures and behaviors. These archetypes are supposed to be the basis of typical instances of neuronal information processing. To model different representative archetypes and express their temporal properties, we use a synchronous programming language dedicated to reactive systems (Lustre). The properties are then automatically validated thanks to several model checkers supporting data types. The respective results are compared and depend on their underlying abstraction methods.

Parameter Learning for Spiking Neural Networks Modelled as Timed Automata

In this paper we present a novel approach to automatically infer parameters of spiking neural networks. Neurons are modelled as timed automata waiting for inputs on a number of different channels (synapses), for a given amount of time (the accumulation period). When this period is over, the current potential value is computed considering current and past inputs. If this potential overcomes a given threshold, the automaton emits a broadcast signal over its output channel, otherwise it restarts another accumulation period. After each emission, the automaton remains inactive for a fixed refractory period. Spiking neural networks are formalised as sets of automata, one for each neuron, running in parallel and sharing channels according to the network structure. This encoding is exploited to find an assignment for the synaptical weights of neural networks such that they can reproduce a given behaviour. The core of this approach consists in identifying some correcting actions adjusting synaptical weights and back-propagating them until the expected behaviour is displayed. A concrete case study is discussed.

Formal Validation of Neural Networks as Timed Automata

We propose a formalisation of spiking neural networks based on timed automata networks. Neurons are modelled as timed automata waiting for inputs on a number of different channels (synapses), for a given amount of time (the accumulation period). When this period is over, the current potential value is computed taking into account the current inputs and the previous decayed potential value. If the current potential overcomes a given threshold, the automaton emits a broadcast signal over its output channel, otherwise it restarts another accumulation period. After each emission, the automaton is constrained to remain inactive for a fixed refractory period. Spiking neural networks are formalised as sets of automata, one for each neuron, running in parallel and sharing channels according to the structure of the network. The model is then validated against some crucial properties defined via proper temporal logic formulae.

Modelling and Formal Verification of Neuronal Archetypes Coupling

In the literature, neuronal networks are often represented as graphs where each node symbolizes a neuron and each arc stands for a synaptic connection. Some specific neuronal graphs have biologically relevant structures and behaviors and we call them archetypes. Six of them have already been characterized and validated using formal methods. In this work, we tackle the next logical step and proceed to the study of the properties of their couplings. For this purpose, we rely on Leaky Integrate and Fire neuron modeling and we use the synchronous programming language Lustre to implement the neuronal archetypes and to formalize their expected properties. Then, we exploit an associated model checker called kind2 to automatically validate these behaviors. We show that, when the archetypes are coupled, either these behaviors are slightly modulated or they give way to a brand new behavior. We can also observe that different archetype couplings can give rise to strictly identical behaviors. Our results show that time coding modeling is more suited than rate coding modeling for this kind of studies.