Understanding morphogenesis in myxobacteria from a theoretical and experimental perspective

Several species of bacteria exhibit multicellular behaviour, with individuals cells cooperatively working together within a colony. Often this has communal benefit since multiple cells acting in unison can accomplish far more than an individual cell can and the rewards can be shared by many cells. Myxobacteria are one of the most complex of the multicellular bacteria, exhibiting a number of different spatial phenotypes. Colonies engage in multiple emergent behaviours in response to starvation culminating in the formation of massive, multicellular fruiting bodies. In this thesis, experimental work and theoretical modelling are used to investigate emergent behaviour in myxobacteria. Computational models were created using FABCell, an open source software modelling tool developed as part of the research to facilitate modelling large biological systems. The research described here provides novel insights into emergent behaviour and suggests potential mechanisms for allowing myxobacterial cells to go from a vegetative state into a fruiting body. A differential equation model of the Frz signalling pathway, a key component in the regulation of cell motility, is developed. This is combined with a three-dimensional model describing the physical characteristics of cells using Monte Carlo methods, which allows thousands of cells to be simulated. The unified model explains how cells can ripple, stream, aggregate and form fruiting bodies. Importantly, the model copes with the transition between stages showing it is possible for the important myxobacteria control systems to adapt and display multiple behaviours

Network Synchronization and Control Based on Inverse Optimality : A Study of Inverter-Based Power Generation

This thesis dwells upon the synthesis of system-theoretical tools to understand and control the behavior of nonlinear networked systems. This work is at the crossroads of three topics: synchronization in coupled high-order oscillators, inverse optimal control and the application of inverter-based power systems. The control and stability of power systems leverages the theoretical results obtained for synchronization in coupled high-order oscillators and inverse optimal control.First, we study the dynamics of coupled high-order nonlinear oscillators. These are characterized by their rotational invariance, meaning that their dynamics remain unchanged following a static shift of their angles. We provide sufficient conditions for local frequency synchronization based on both direct, indirect Lyapunov methods and center manifold theory. Second, we study inverse optimal control problems, embedded in networked settings. In this framework, we depart from a given stabilizing control law, with an associated control Lyapunov function and reverse engineer the cost functional to guarantee the optimality of the controller. In this way, inverse optimal control generates a whole family of optimal controllers corresponding to different cost functions. This provides analytically explicit and numerically feasible solutions in closed-form. This approach circumvents the complexity of solving partial differential equations descending from dynamic programming and Bellman's principle of optimality. We show this to be the case also in the presence of disturbances in the dynamics and the cost. In networks, the controller obtained from inverse optimal control has a topological structure (e.g., it is distributed) and thus feasible for implementation. The tuning is analogous to that of linear quadratic regulators.Third, motivated by the pressing changes witnessed by the electrical grid toward renewable energy generation, we consider power system stability and control as the main application of this thesis. In particular, we apply our theoretical findings to study a network of power electronic inverters. We first propose a controller we term the matching controller, a control strategy that, based on DC voltage measurements, endows the inverters with an oscillatory behavior at a common desired frequency. In closed-loop with the matching control, inverters can be considered as nonlinear oscillators. Our study of the dynamics of nonlinear oscillator network provides feasible physical conditions that ask for damping on DC- and AC-side of each converter, that are sufficient for system-wide frequency synchronization.Furthermore, we showcase the usefulness of inverse optimal control for inverter-based generation at two different settings to synthesize robust angle controllers with respect to common disturbances in the grid and provable stability guarantees. All the controllers proposed in this thesis, provide the electrical grid with important services, namely power support whenever needed, as well as power sharing among all inverters

Ribosomal RNA dynamics studied by NMR-spectroscopy

The ribosome is a large macromolecular machine that consists of both ribosomal proteins and ribosomal RNA (rRNA). It is a complex consisting of two subunits held together by non- covalent interactions, intersubunit bridges and some of these bridging interactions are mediated by the rRNA. In this PhD-project the dynamics of such regions of rRNA, participating in intersubunit bridges and tertiary interaction within the rRNA have been investigated with solution state NMR- spectroscopy. These studies have been performed in the context of several miniaturized RNA systems, containing sequences of E. coli 16S rRNA. In particular, regions along helix 44 (h44), the penultimate stem of E. coli 16S rRNA have been studied. The stem-loop part of h44 has been studied in detail, this part of the rRNA contains a naturally occurring UUCG-loop and adenines participating in a tertiary interaction with helix (h8) in the 16S rRNA. In order to characterize the dynamics of these RNA constructs with NMR-spectroscopy, purified RNA material in large amounts is a necessity. Because of this we have developed an RNA-sample production method (Paper I) as well an NMR-experiment method (Paper II) that we call SELOPE, a method that can reduce the need of using isotopically enriched RNA material for NMR-studies. The first chapter of this thesis introduces the underlying theory for RNA-sample preparation as well as alternative techniques compared to the ones used in Paper I. In a similar manner the underlying theory for the NMR-technique is introduced and with some emphasis on concepts crucial for understanding the SELOPE experiment, to contextualize Paper II. The usage of NMR-spectroscopy for the measurements of dynamics in RNA molecules is also introduced. The first chapter of the thesis also includes a description of the ribosome to help further understanding of Paper III. In addition, during chapter 2-5 of this thesis some work related to 1H-R1r characterization of chemical exchange and cross-relaxation among RNA imino protons is described and discussed. In Paper I, the development of an RNA-sample preparation method is described. The method is based on in vitro transcription of the wanted RNA sequence followed by a HPLC-purification procedure that uses two different HPLC techniques for the purification, both Reverse Phase Ion Pairing (RP-IP) and Ion Exchange (IE) HPLC. The complete method offers a robust and versatile alternative to other RNA sample preparation methods such as preparative gel electrophoresis techniques. In Paper II, we describe the development of an NMR pulse sequence that utilize a homonuclear magnetization transfer block in unlabeled RNA molecules. The pulse sequence can then for instance be used to transfer NMR signal of unwanted signals to other spectral regions and can for instance be used to remove the signal of pyrimidine H6s from the region of H6/H8/H2 in RNAs. In Paper III, the work of characterizing the stem-loop part of E. coli 16S rRNA h44 is described. This work both shows a UUCG-loop with dynamics on a millisecond time-scale as well as the dynamical behavior of a group of unpaired adenine bases, the study of dynamics of these adenines could aid the understanding of tertiary interactions within rRNA

CFD Analysis, Sensing and Control of a Rotary Pulse Width Modulating Valve to enable a Virtually Variable Displacement Pump

University of Minnesota Ph.D. dissertation. August 2017. Major: Mechanical Engineering. Advisors: Perry Li, Thomas Chase. 1 computer file (PDF); xi, 174 pages.Hydraulic systems have been widely utilized for heavy duty industries for their competitive advantages of high power density, low cost, and flexible circuit design. However, the efficiency of hydraulic systems typically is not very competitive due to high throttling losses, which limits their applications. On/off valve based control of a hydraulic system is an approach that can potentially increase the hydraulic system's efficiency significantly. This approach combines the strengths of throttling valve control and variable displacement unit control. The former has the advantage of high control bandwidth and precision, but the disadvantage of low efficiency due to throttling loss; the latter has the advantage of high efficiency, but the disadvantage of being bulky, heavy, costly, and the control bandwidth is low when compared to valve control. To create a potentially high efficiency with relatively low cost solution, a fixed displacement pump, an accumulator, and a high speed on/off valve are combined to create a virtually variable displacement pump (VVDP). By pulse width modulating (PWM) the flow from the supply to the load via the on/off valve, the average output flow can be varied by adjusting the PWM duty ratio. The key technology to this hydraulic configuration is the pulse width modulated on/off valve. A novel rotary high speed on/off valve concept has been proposed. This concept can enable different digital hydraulic configurations, such as VVDP, VVDPM (pump/motor), and virtually variable displacement transformer. Research conducted in this dissertation supports the design, modeling, and control of the rotary on/off valve. A 3-way, high-speed, rotary, self-spinning on/off valve was developed for the VVDP configuration. The valve has two degrees of freedom. The spool's rotary motion realizes the high-speed switching required for the PWM function. This motion can be self-driven by capturing the fluid's angular momentum via a unique valve spool turbine design. The spool's axial motion determines the valve PWM duty ratio, and this motion is driven externally. Firstly, to understand the flow inside the valve, and to quantify the valve pressure drop with the key valve parameters, a computational fluid dynamics (CFD) analysis is conducted in chapter 2. Analytical and semi-empirical formulas to model the pressure drop across the valve spool as a function of flow rate and key valve geometrical parameters are developed. The torque generated by the valve turbines are also analyzed using CFD to validate the analytical models which calculate the torque as a function of flow rate and key valve geometrical parameters. These equations are utilized in an optimization analysis to optimize the valve geometry, targeted at reducing the valve's power loss. CFD is also utilized to optimize the valve's interior flow path to reduce the fluid volume inside the valve while maintaining a low pressure drop, so that both the compressible loss and the throttling loss of the valve are reduced. The CFD analysis enabled reducing the throttling loss pf a prototype valve design by 62.5% and reducing the compressible loss by 66%. Secondly, the sensing and estimation of the valve spool's rotary position and velocity are addressed in chapter 5. Given the limitation on sensing distance and the requirement of a simple sealing structure, a coarse, non-contacting, optical sensor is proposed to measure the spool's angular position. Measurement events in the form of encoder count changes are obtained at irregular times and infrequently. An event-based Kalman filter is developed to improve the resolution and to provide continuous estimates of the spool's angular position and velocity. Thirdly, the spool's axial motion actuation, sensing, and control development are addressed. The on/off valve's duty ratio is regulated by controlling the valve spool's axial position. In chapter 4, a driving mechanism to work with the self-spinning valve's feature and the corresponding sensing and control methods are developed to manipulate the spool's axial position. In the first generation's driving system, a geroter pump is hydro-statically connected to both ends of the spool chamber to move the spool axially. This design simplifies the sealing structure in order to achieve self-spinning. An optical sensor is utilized as a non-contact approach to measuring the spool's axial displacement. The measurement is corrupted by a structured noise caused by the spool's rotary motion. A periodic time varying model is proposed to model the structured noise, which can capture the main dynamics with a low order system. An analysis of the observability of the augmented system (plant plus structured noise) is conducted. A state observer can be built to distinguish between the axial spool position and the structured noise, and the estimated position can then be used in the control law. The sleeve chamber pressure dynamics are ignored, and a linear feed-forward with a Proportional-Integral controller is developed for spool axial positioning. The self-spinning function ties the spool rotary speed with the valve flow. The controller was experimentally implemented, and achieved good spool regulation results. In order to investigate the PWM frequency and the flow rate properties independently, an external driving mechanism is developed in chapter 5. A new passivity based nonlinear controller has been proposed which considers the pressure dynamics inside the sleeve chamber. This controller can provide more robust axial position control. From theoretical analysis' point of view, a passivity framework for hydraulic actuators is developed by considering the compressibility energy function for a fluid with a pressure dependent bulk modulus. It is shown that the typical actuator's mechanical and pressure dynamics model can be obtained from the Euler-Lagrange equations for this energy function and that the actuator is passive with respect to a hydraulic supply rate. The hydraulic supply rate contains the flow work $(PQ)$ and the compressibility energy, whereas the latter one has typically been ignored. A storage function for the pressure error is then proposed and the pressure error dynamics are shown to be a passive two port subsystem. Trajectory tracking control laws are then derived using the storage function. Since some of the states utilized in the passive controllers are from an estimator instead of being directly measured, the chapter also provides the analysis on the convergence of both tracking errors and the estimation errors to zero. This passivity-based nonlinear controller implemented with a high gain observer is applied experimentally on the valve. Experimental results validate the effectiveness of this new control system. Lastly, the VVDP is implemented as the variable displacement pump in a direct displacement control open circuit, as presented in chapter 6. A variable flow source (VVDP), a directional valve, and a proportional valve are coordinated to manipulate the motion of the hydraulic actuator in an energy efficient way. The passivity-based nonlinear controller as discussed in chapter 5 is proposed to realize accurate actuator trajectory tracking. A nominal method to optimally distribute the control efforts between the control valve and the variable flow pump is proposed. This method can accommodate different control bandwidths from the valve and the pump, so that the valve has a large nominal opening to reduce the throttling loss. Experimental results validate the effectiveness of the control strategy