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.

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.

A SUBSET OF 3´ TO 5´ EXORIBONUCLEASES ARE THE PRIMARY ENZYMES RESPONSIBLE FOR THE DEGRADATION OF PGPG IN CYCLIC DI-GMP SIGNALING

Bis-(3´-5´)-cyclic dimeric guanosine monophosphate, or cyclic di-GMP (c-di-GMP) is a ubiquitous bacterial second messenger that regulates processes such biofilm formation, motility, and virulence. C-di-GMP is synthesized by diguanylate cyclases (DGCs), while phosphodiesterases (PDE-As) end signaling by linearizing c-di-GMP to 5ʹ-phosphoguanylyl-(3ʹ,5ʹ)-guanosine (pGpG), which is then hydrolyzed to two GMPs by previously unidentified enzymes termed PDE-Bs. To identify the PDE-B responsible for pGpG turnover, a screen for pGpG binding proteins in a Vibrio cholerae open reading frame library was conducted to identify potential pGpG binding proteins. This screen led to identification of oligoribonuclease (Orn). Purified Orn binds to pGpG and can cleave pGpG to GMP in vitro. A deletion mutant of orn in Pseudomonas aeruginosa was highly defective in pGpG turnover and accumulated pGpG. Deletion of orn also resulted in accumulation c-di-GMP, likely through pGpG-mediated inhibition of the PDE-As, causing an increase in c-di-GMP-governed auto-aggregation and biofilm. Thus, we found that Orn serves as the primary PDE-B enzyme in P. aeruginosa that removes pGpG, which is necessary to complete the final step in the c-di-GMP degradation pathway. However, not all bacteria that utilize c-di-GMP signaling also have an ortholog of orn, suggesting that other PDE-Bs must be present. Therefore, we asked whether RNases that cleave small oligoribonucleotides in other species could also act as PDE-Bs. NrnA, NrnB, and NrnC can rapidly degrade pGpG to GMP. Furthermore, they can reduce the elevated aggregation and biofilm formation in P. aeruginosa ∆orn. Together, these results indicate that rather than having a single dedicated PDE-B, different bacteria utilize distinct RNases to cleave pGpG and complete c-di-GMP signaling. The ∆orn strain also has a growth defect, indicating changes in other regulatory processes that could be due to pGpG accumulation, c-di-GMP accumulation, or another effect due to loss of Orn. We sought to investigate the genetic pathways responsible for these growth defect phenotypes by use of a transposon suppressor screen, and also investigated transcriptional changes using RNA-Seq. This work identifies that c-di-GMP degradation intersects with RNA degradation at the point of the Orn and the functionally related RNases.

Leader Based Cyclic Pursuit

In this work a system of autonomous agents engaged in cyclic pursuit (under constant bearing (CB) strategy) is considered, for which one informed agent (the leader) also senses and responds to a stationary beacon. Building on the framework proposed in a previous work on beacon-referenced cyclic pursuit, necessary and suffi- cient conditions for the existence of circling equilibria in a system with one informed agent are derived, with discussion of stability and performance. In a physical testbed, the leader (robot) is equipped with a sound sensing apparatus composed of a real time embedded system, estimating direction of arrival of sound by an Interaural Level and Phase Difference Algorithm, using empirically determined phase and level signatures, and breaking front-back ambiguity with appropriate sensor placement. Furthermore a simple framework for implementing and evaluating the performance of control laws with the Robot Operating System (ROS) is proposed, demonstrated, and discussed.

STRUCTURAL AND FUNCTIONAL STUDIES OF CYCLIC K48-LINKED DIUBIQUITIN

K48-linked di-ubiquitin exists in a dynamic equilibrium between open and closed states. The structure of K48-Ub2 in the closed conformation features a hydrophobic interface formed between the two Ub domains. The same hydrophobic residues at the interface are involved in binding to ubiquitin-associated (UBA) domains. Cyclization of K48-Ub2 should limit the range of conformations available for such interactions. Interestingly, cyclic K48-linked Ub2 (cycUb2) has been found in vivo and can be isolated in vitro to study its structure and dynamics. In this study, a crystal structure of cycUb2 was obtained, and the dynamics of cycUb2 were characterized by solution NMR. The crystal structure of cycUb2, which is in agreement with solution NMR data, is closed with the hydrophobic patches of each Ub domain buried at the interface. Despite its structural constraints, cycUb2 was still able to interact with UBA domains, albeit with lower affinity.