Bounded noises as a natural tool to model extrinsic fluctuations in biomolecular networks

In the first part of this invited paper we review the role of both extrinsic and intrinsic stochasticity in shaping the dynamics of biomolecular networks. In particular, we stress the use of bounded stochastic processes as a model of extrinsic random perturbations. In the second part, we propose three examples of molecular circuits under the influence of external fluctuations modeled by means of bounded noises. The first two examples involve the linear decay of a protein with, respectively, large or low number of molecules, so to stress different modeling approaches. The third example concerns the spatio-temporal dynamics of proteins determining the chemotaxis-driven polarization of a cell. In these examples one can observe phenomena that are dependent on the specific class of employed bounded noise.