We present a brief review of molecular biological basis and mathematical modelling of circadian rhythms in Drosophila. We discuss pertinent aspects of a new modelthat incorporates the transcriptional feedback loops revealed so far in the network of thecircadian clock (PER/TIM and VRI/PDP1 loops). Conventional Hill functions are not usedto describe the regulation of genes, instead the explicit reactions of binding and unbindingprocesses of transcription factors to promoters are probabilistically modelled. The modelis described by a set of ordinary differential equations, and the parameters are estimatedfrom the in vitro experimental data of the clocks' components. The model is robust over awide range of parameter variations. Through the sensitivity analysis of the model, roles ofVRI and PDP1 feedback loops are investigated, and it is proposed that they increase therobustness of the clock.

Studying the evolutive and adaptative machanisms of prokayotes is a complicated task.As these machanisms cannot be easily studied "in vivo", it is necessary to consider other methods.We have therefore developed the RAevol model, a model designed to study the evolution of bacteria and their adaptationto the environment.Our model simulates the evolution of a population of artificial bacteria in a changing environment, providing us with an insight into the strategies that digital organisms develop to adapt to new conditions.In this paper we describe the principle and architecture of the model, focusing on the mechanisms of the regulatory networks of artificial organisms.Experiments were conducted on populations of artificial bacteria under conditions of stress.We study the ways in which organisms adapt to environmental changes and examine the strategies they adopt.An analysis of these adaptation strategies is presented and a brief overview was proposed concerning the patterns and topological characteristics of the evolved regulatory networks.

No other concepts have shaken so deeply the bases of engineering like those of positiveand negative feedback. They have played a most prominent role in engineering since the beginningof the previous century. The birth certificate of positive feedback can be traced back to a pair ofpatents by Edwin H. Armstrong in 1914 and 1922, whereas that of negative feedback is alreadylost in time. We present in this paper a short review on the feedback's origins in the fields ofengineering and biology. Besides, we compare the main feedback's ideas in control theory andsystem biology in order to get a better understanding of the lactose and tryptophan operons' regulatorysystems (control systems). It is obvious that we need to know the genome of an organismin order to understand how it works, but that is only half of the puzzle, for we also need to knowhow the underlying genetic regulatory systems work in order to get a complete picture of the cell'sdynamics.

Hill functions follow from the equilibrium state of the reaction in which n ligands simultaneouslybind a single receptor. This result if often employed to interpret the Hill coefficient asthe number of ligand binding sites in all kinds of reaction schemes. Here, we study the equilibriumstates of the reactions in which n ligand bind a receptor sequentially, both non-cooperatively andin a cooperative fashion. The main outcomes of such analysis are that: n is not a good estimate,but only an upper bound, for the Hill coefficient; while the Hill coefficient depends quite stronglyon the cooperativity level among ligands. We finally use these results to discuss the feasibilityand constrains of using Hill functions to model the regulatory functions in mathematical models ofgene regulatory networks.