Master Equation: Biological Applications and Thermodynamic Description

It is well known that many realistic mathematical models of biological systems, such as cell growth, cellular development and differentiation, gene expression, gene regulatory networks, enzyme cascades, synaptic plasticity, aging and population growth need to include stochasticity. These systems are not isolated, but rather subject to intrinsic and extrinsic fluctuations, which leads to a quasi equilibrium state (homeostasis). The natural framework is provided by Markov processes and the Master equation (ME) describes the temporal evolution of the probability of each state, specified by the number of units of each species. The ME is a relevant tool for modeling realistic biological systems and allow also to explore the behavior of open systems. These systems may exhibit not only the classical thermodynamic equilibrium states but also the nonequilibrium steady states (NESS). This thesis deals with biological problems that can be treat with the Master equation and also with its thermodynamic consequences. It is organized into six chapters with four new scientific works, which are grouped in two parts: (1) Biological applications of the Master equation: deals with the stochastic properties of a toggle switch, involving a protein compound and a miRNA cluster, known to control the eukaryotic cell cycle and possibly involved in oncogenesis and with the propose of a one parameter family of master equations for the evolution of a population having the logistic equation as mean field limit. (2) Nonequilibrium thermodynamics in terms of the Master equation: where we study the dynamical role of chemical fluxes that characterize the NESS of a chemical network and we propose a one parameter parametrization of BCM learning, that was originally proposed to describe plasticity processes, to study the differences between systems in DB and NESS.

Photoactive nanodevices for potential biological applications

Biological systems are complex and highly organized architectures governed by noncovalent interactions, which are responsible for molecular recognition, self-assembly, self-organization, adaptation and evolution processes. These systems provided the inspiration for the development of supramolecular chemistry, that aimed at the design of artificial multicomponent molecular assemblies, namely supramolecular systems, properly designed to perform different operations: each constituting unit performs a single act, whereas the entire supramolecular system is able to execute a more complex function, resulting from the cooperation of the constituting components. Supramolecular chemistry deals with the development of molecular systems able to mimic naturally occurring events, for example complexation and self-assembly through the establishment of noncovalent interactions. Moreover, the application of external stimuli, such as light, allows to perform these operations in a time- and space-controlled manner. These systems can interact with biological systems and, thus, can be applied for bioimaging, therapeutic and drug delivery purposes. In this work the study of biocompatible supramolecular species able to interact with light is presented. The first part deals with the photophysical, photochemical and electrochemical characterization of water-soluble blue emitting triazoloquinolinium and triazolopyridinium salts. Moreover, their interaction with DNA has been explored, in the perspective of developing water-soluble systems for bioimaging applications. In the second part, the effect exerted by the presence of azobenzene-bearing supramolecular species in liposomes, inserted both in the phospholipid bilayer and in the in the aqueous core of vesicles has been studied, in order to develop systems able to deliver small molecules and ions in a photocontrolled manner. Moreover, the versatility of azobenzene and its broad range of applications have been highlighted, since conjugated oligoazobenzene derivatives proved not to be adequate to be inserted in the phospholipid bilayer of liposomes, but their electrochemical properties made them interesting candidates as electron acceptor materials for photovoltaic applications.