Many cell functions are accomplished thanks to intracellular transport mechanisms of macromolecules along filaments. Molecular motors such as dynein or kinesin are proteins playing a primary role in these processes. The behavior of such proteins is q
uite well understood when there is only one of them moving a cargo particle. Indeed, numerous in vitro experiments have been performed to derive accurate models for a single molecular motor. However, in vivo macromolecules are often carried by multiple motors. The main focus of this paper is to provide an analysis of the behavior of more molecular motors interacting together in order to improve the understanding of their actual physiological behavior. Previous studies provide analyses based on results obtained from Monte Carlo simulations. Different from these studies, we derive an equipollent probabilistic model to describe the dynamics of multiple proteins coupled together and provide an exact theoretical analysis. We are capable of obtaining the probability density function of the motor protein configurations, thus enabling a deeper understanding of their behavior.
The interest for networks of dynamical systems has been increasing in the past years, especially because of their capability of modeling and describing a large variety of phenomena and behaviors. We propose a technique, based on Wiener filtering, whi
ch provides general theoretical guarantees for the detection of links in a network of dynamical systems. For a large class of network that we name self-kin sufficient conditions for a correct detection of a link are formulated. For networks not belonging to this class we give conditions for correct detection of links belonging to the smallest self-kin network containing the actual one.
