Les réactions non-linéaires peuvent donner naissance à des phénomènes coopératifs nouveaux dans des systèmes microstructurés en fonction de la taille des éléments actifs et du couplage entre eux. Nous avons étudié la dynamique de l'électrooxydation de CO, une réaction bistable présentant une branche de résistance différentielle négative en forme de S, sur une microélectrode de platine et des réseaux. Au voisinage d'une instabilité spatiale, une amplification du bruit moléculaire a été observée à cause de l'interaction avec la bifurcation spatiale. Le comportement dynamique est fortement affecté par la concentration en acide sulfurique et par la présence d'une faible quantité de chlorures dans la solution. Quand plusieurs microélectrodes sont couplées globalement, des comportements coopératifs nouveaux ont été mis en évidence comme l'émergence d'oscillations cohérentes et la présence d'un régime d'échange dynamique complexe faisant intervenir des processus inter et intra électrodes. / Nonlinear reactions may give rise to new cooperative phenomena when they occur in microstructured systems depending on the size of the active elements and on the coupling between them. We have studied the dynamics of CO electrooxidation, a bistable electrochemical reaction With an S-shaped negative differential resistance on single Pt microelectrode and on their array. For microelectrodes, close to a spatial instability threshold, strong enhancement of the molecular noise was observed due to its interaction With the spatial bifurcation. The dynamic behaviour of the reaction was shown to be strongly affected by the sulfuric acid concentration and by the presence of a small amount of chlorides in solution. When several microelectrodes are globally coupled, the emergence of new cooperative behaviour could be evidenced such as the emergence of coherent oscillations and the presence of a complex dynamic switching regime involving the interplay of inter and intra electrode processes.

The interconnection of molecular machines with different functionalities to form molecular communication systems can increase the number of design possibilities and overcome the limited reliability of the individual molecular machines. Artificial information exchange using molecular signals would also expand the capabilities of single engineered cell populations by providing them a way to cooperate across heterogeneous cell populations for the applications of synthetic biology and lab-on-a-chip systems. The realization of molecular communication systems necessitates analysis and design of the communication channel, where the information carrying molecular signal is transported from the transmitter to the receiver. In this thesis, significant progress towards the use of microfluidic channels to interconnect molecular transmitter and receiver pairs is presented. System-theoretic analysis of the microfluidic channels are performed, and a finite-impulse response filter is designed using microfluidic channels. The spectral density of the propagation noise is studied and the additive white Gaussian noise channel model is developed. Memory due to inter-diffusion of the transmitted molecular signals is also modeled. Furthermore, the interference modeling is performed for multiple transmitters and its impact on the communication capacity is shown. Finally, the efficient sampling of the signal transduction by engineered bacterial receivers connected to a microfluidic channel is investigated for the detection of the pulse-amplitude modulated molecular signals. This work lays the foundation for molecular communication over microfluidic channels that will enable interconnection of engineered molecular machines.

Living cells are made up of networks of interacting genes, proteins and other bio-molecules. Simple interactions between network components in forms of feedback regulations can lead to complex collective dynamics. A key task in cell biology is to gain a thorough understanding of the dynamics of intracellular systems and processes. In this thesis, a combined approach of mathematical modelling, computational simulation and analytical techniques, has been used to obtain a deeper insight into the dynamical aspects of a variety of feedback systems commonly encountered in cells. These systems range from model system with detailed available molecular knowledge to general regulatory motifs with varying network structures. Deterministic as well as stochastic modelling techniques have been employed, depending primarily on the specific questions asked. The first part of the thesis focuses on dissecting the principles behind the regulatory design of the Tryptophan Operon system in Escherichia coli. It has evolved three negative feedback loops, namely repression, attenuation and enzyme inhibition, as core regulator mechanisms to control the intracellular level of tryptophan amino acid, which is taken up for protein synthesis. Despite extensive experimental knowledge, the roles of these seemingly redundant loops remain unclear from a dynamical point of view. We aim to understand why three loops, rather than one, have evolved. Using a large-scale perturbation/response analysis through modelling and simulations and novel metrics for transient dynamics quantification, it has been revealed that the multiple negative feedback loops employed by the tryptophan operon are not redundant. In fact, they have evolved to concertedly give rise to a much more efficient, adaptive and stable system, than any single mechanism would provide. Since even the full topology of feedback interactions within a network is insufficient to determine its behavioural dynamics, other factors underlying feedback loops must be characterised to better predict system dynamics. In the second part of the thesis, we aim to derive these factors and explore how they shape system dynamics. We develop an analytical approach for stability and bifurcation analysis and apply it to class of feedback systems commonly encountered in cells. Our analysis showed that the strength and the Hill coefficient of a feedback loop play key role in determining the dynamics of the system carrying the loop. Not only that, the position of the loop was also found to be crucial in this decision. The analytical method we developed also facilitates parameter sensitivity analysis in which we investigate how the production and degradation rates affect system dynamics. We find that these rates are quite different in the way they shape up system behaviour, with the degradation rates exhibiting a more intricate manner. We demonstrated that coupled-loop systems display greater complexity and a richer repertoire of behaviours in comparison with single-loop ones. Different combinations of the feedback strengths of individual loops give rise to different dynamical regimes. The final part of the thesis aims to understand the effects of molecular noise on dynamics of specific systems, in this case the Tryptophan Operon. We developed two stochastic models for the system and compared their predictions to those given by the deterministic model. By means of simulations, we have shown that noise can induce oscillatory behaviour. On the other hand, incorporating noise in an oscillatory system can alter the characteristics of oscillation by shifting the bifurcation point of certain parameters by a substantial amount. Measurement of fluctuations reveals that that noise at the transcript level is most significant while noise at the enzyme level is smallest. This study highlights that noise should not be neglected if we want to obtain a complete understanding of the dynamic behaviour of cells.