Intercepting Cyclic Dinucleotide Signaling with Small Molecules

Bacterial infections, especially the ones that are caused by multidrug-resistant strains, are becoming increasingly difficult to treat and put enormous stress on healthcare systems. Recently President Obama announced a new initiative to combat the growing problem of antibiotic resistance. New types of antibiotic drugs are always in need to catch up with the rapid speed of bacterial drug-resistance acquisition. Bacterial second messengers, cyclic dinucleotides, play important roles in signal transduction and therefore are currently generating great buzz in the microbiology community because it is believed that small molecules that inhibit cyclic dinucleotide signaling could become next-generation antibacterial agents. The first identified cyclic dinucleotide, c-di-GMP, has now been shown to regulate a large number of processes, such as virulence, biofilm formation, cell cycle, quorum sensing, etc. Recently, another cyclic dinucleotide, c-di-AMP, has emerged as a regulator of key processes in Gram-positive and mycobacteria. C-di-AMP is now known to regulate DNA damage sensing, fatty acid synthesis, potassium ion transport, cell wall homeostasis and host type I interferon response induction. Due to the central roles that cyclic dinucleotides play in bacteria, we are interested in small molecules that intercept cyclic dinucleotide signaling with the hope that these molecules would help us learn more details about cyclic dinucleotide signaling or could be used to inhibit bacterial viability or virulence. This dissertation documents the development of several small molecule inhibitors of a cyclic dinucleotide synthase (DisA from B. subtilis) and phosphodiesterases (RocR from P. aeruginosa and CdnP from M. tuberculosis). We also demonstrate that an inhibitor of RocR PDE can inhibit bacterial swarming motility, which is a virulence factor.

Cyclic Pursuit: Symmetry, Reduction and Nonlinear Dynamics

In this dissertation, we explore the use of pursuit interactions as a building block for collective behavior, primarily in the context of constant bearing (CB) cyclic pursuit. Pursuit phenomena are observed throughout the natural environment and also play an important role in technological contexts, such as missile-aircraft encounters and interactions between unmanned vehicles. While pursuit is typically regarded as adversarial, we demonstrate that pursuit interactions within a cyclic pursuit framework give rise to seemingly coordinated group maneuvers. We model a system of agents (e.g. birds, vehicles) as particles tracing out curves in the plane, and illustrate reduction to the shape space of relative positions and velocities. Introducing the CB pursuit strategy and associated pursuit law, we consider the case for which agent i pursues agent i+1 (modulo n) with the CB pursuit law. After deriving closed-loop cyclic pursuit dynamics, we demonstrate asymptotic convergence to an invariant submanifold (corresponding to each agent attaining the CB pursuit strategy), and proceed by analysis of the reduced dynamics restricted to the submanifold. For the general setting, we derive existence conditions for relative equilibria (circling and rectilinear) as well as for system trajectories which preserve the shape of the collective (up to similarity), which we refer to as pure shape equilibria. For two illustrative low-dimensional cases, we provide a more comprehensive analysis, deriving explicit trajectory solutions for the two-particle "mutual pursuit" case, and detailing the stability properties of three-particle relative equilibria and pure shape equilibria. For the three-particle case, we show that a particular choice of CB pursuit parameters gives rise to remarkable almost-periodic trajectories in the physical space. We also extend our study to consider CB pursuit in three dimensions, deriving a feedback law for executing the CB pursuit strategy, and providing a detailed analysis of the two-particle mutual pursuit case. We complete the work by considering evasive strategies to counter the motion camouflage (MC) pursuit law. After demonstrating that a stochastically steering evader is unable to thwart the MC pursuit strategy, we propose a (deterministic) feedback law for the evader and demonstrate the existence of circling equilibria for the closed-loop pursuer-evader dynamics.