• Chemical Reaction Networks
• Monotonicity
• ODEs
• Robustness
• Simulations
• Systems Biology

Cells are very complex to analyze because they consist of many components that interact with each other, producing multiple sequences of chemical reactions, which regulate their behavior. Besides, several fluctuations can alter the cell functionalities, such as internal error propagation, and variations in the concentrations of chemical species.
Regarding this, a significant biological property is \textit{robustness}, defined as the observed capacity of the system to maintain its functionalities despite the presence of internal or external perturbations. In nature, different mechanisms ensure this property, such as redundancy, modularity, system control, and structural stability. Redundancy and modularity represent the architectural characteristics of a biological pathway, resulting in multiple copies of structures and compartments, which, having the same functions, avoid the possible presence of errors and failures. Conversely, system control and structural stability are dynamical properties, expressed as the capacity to adapt to environmental changes.
In this context, Computer Science can help research in Biology in many different ways. Through simulations, for instance, it is possible to mimic the internal dynamics of a natural system and to predict its functions. Moreover, model-based analysis techniques can be used to interpret some non-intuitive aspects of a biological system.
In this thesis, we propose a new definition to formally describe a specific notion of robustness, the \textit{initial concentration robustness}. This has the purpose of analyzing how perturbations in the initial concentrations of the involved chemical species (identified as inputs) can alter the system behavior at a steady state. Therefore, we developed a theoretical framework, based on Petri net formalism, and we applied it to different known biological networks available in the literature.
To understand the behavior of a biological system, we should simulate it considering all the possible combinations of the initial values, which implies a huge computational effort. To face this issue, we found a sufficient condition that allows knowing if the concentration of an output species is monotonic concerning the concentration of an input species (which is the perturbed substance). By monotonic, we mean that increasing (or decreasing) the concentration of the input, the concentration of the output, at each time step, increases (or decreases) consequently. If the sufficient condition is met, we can drastically reduce the number of simulations, testing the model only on the extreme values of the input concentration range.
Finally, we apply our theoretical framework to the case study of Becker-Döring equations, a model that describes the aggregation kinetics of particle clusters. In particular, we study the robustness of this model using the proposed robustness formalism as well as other analytical approaches.