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The Best PhD Thesis in the Faculties of Dentistry, Engineering, Medicine and Science (University of Hong Kong), Li Ka Shing Prize,2010-11 / published_or_final_version / Biochemistry / Doctoral / Doctor of Philosophy

Quantitative biology is an emerging field that attracts intensive research interests. Pattern formation is a widely studied topic both in biology and physics. Scientists have been trying to figure out the basic principles behind the fascinating patterns in the nature. It’s still difficult to lift the complex veil on the underling mechanisms, especially in biology, although lots of the achievements have been achieved. The new developments in synthetic biology provide a different approach to study the natural systems, test the theories, and develop new ones. Biological systems have many unique features different from physics and chemistry, such as growth and active movement. In this project, a link between cell density and cell motility is established through cell-cell signaling. The genetic engineered Escherichia coli cell regulates its motility by sensing the local cell density. The regulation of cell motility by cell density leads to sequential and periodical stripe patterns when the cells grow and expand on a semi-solid agar plate. This synthetic stripe pattern formation system is quantitative studied by quantitative measurements, mathematical modeling and theoretical analysis. To characterize the stripe pattern, two novel methods have been developed to quantify the key parameters, including cell growth, spatiotemporal cell density profile and cell density-dependent motility, besides the standard molecular biological measurements. To better understand the underlying principle of the stripe pattern formation, a quantitative model is developed based on the experiments. The detailed dynamic process is studied by computer simulation. Besides, the model predicts that the number of stripes can be tuned by varying the parameters in the system. This has been tested by quantitatively modulation of the basal expression level of a single gene in the genetic circuit. Moreover, theoretical analysis of a simplified model provides us a clear picture of the stripe formation process. The steady state traveling wave solution is obtained, which leads to an analytic ansatz that can determine the phase boundary between the stripe and the no-stripe phases. This study does not only provide a quantitative understanding about the novel mechanism of stripe pattern formation, but also sets an good example of quantitative studies in biology. The techniques, methods and knowledge gleaned here may be applied in various interdisciplinary fields. / published_or_final_version / Physics / Doctoral / Doctor of Philosophy

Cyanobacteria are prokaryotes that can grow photoautotrophically using oxygenic photosynthesis. Some filamentous cyanobacteria in media with insufficient fixed nitrogen develop a regular pattern of heterocyst cells that fix nitrogen for the remaining vegetative cells. We have built an integrated computational model of fixed nitrogen transport and cell growth for filamentous cyanobacteria. With our model, two qualitatively different experimentally observed nitrogen distributions between a pair of heterocysts are reconciled. By adding dynamic heterocyst placement into our model, we can optimize heterocyst frequency with respect to growth. Further introduction of modest leakage leads to distinct growth rates between different heterocyst placement strategies. A local placement strategy yields maximal growth and steady state heterocyst spacings similar to those observed experimentally. Adding more realistic fixed nitrogen storage based heterocyst commitment together with lateral inhibition to the model allows us to address initial heterocyst commitment and qualitatively reproduces many aspects of heterocyst differentiation. We also investigate patterns of starving cells and correlations of fixed nitrogen in filaments without heterocysts. We find percolation transitions in both spatial one dimensional patterns and space-time two dimensional patterns.

Thesis (M.S.)--Villanova University, 2009. / Biology Dept. Includes bibliographical references.

sand hops and bounces -see the dunes grow, run, collide -form the field's pattern.Aeolian sand dune morphologies and sizes are strongly connected to the environmental context and physical processes active since dune formation. As such, the patterns and measurable features found within dunes and dune fields can be interpreted as records of environmental conditions. Using mathematical models of dune and dune field evolution, it should be possible to quantitatively predict dune field dynamics from current conditions or to determine past field conditions based on present-day observations.In this dissertation, we focus on the construction and quantitative analysis of a continuum dune evolution model. We then apply this model towards interpretation of the formative history of terrestrial and martian dunes and dune fields. Our first aim is to identify the controls for the characteristic lengthscales seen in patterned dune fields. Variations in sand flux, binary dune interactions, and topography are evaluated with respect to evolution of individual dunes. Through the use of both quantitative and qualitative multiscale models, these results are then extended to determine the role such processes may play in (de)stabilization of the dune field. We find that sand flux variations and topography generally destabilize dune fields, while dune collisions can yield more similarly-sized dunes. We construct and apply a phenomenological macroscale dune evolution model to then quantitatively demonstrate how dune collisions cause a dune field to evolve into a set of uniformly-sized dunes. Our second goal is to investigate the influence of reversing winds and polar processes in relation to dune slope and morphology. Using numerical experiments, we investigate possible causes of distinctive morphologies seen in Antarctic and martian polar dunes. Finally, we discuss possible model extensions and needed observations that will enable the inclusion of more realistic physical environments in the dune and dune field evolution models.By elucidating the qualitative and quantitative connections between environmental conditions, physical processes, and resultant dune and dune field morphologies, this research furthers our ability to interpret spacecraft images of dune fields, and to use present-day observations to improve our understanding of past terrestrial and martian environments.

This paper considers a free energy functional and corresponding free boundary problem for multilayered structures which arise from a mixture of a block copolymer and a weak solvent. The free boundary problem is formally derived from the limit of large solvent/polymer segregation and intermediate segregation between monomer species. A change of variables based on Legendre transforms of the effective bulk energy is used to explicitly construct a family of equilibrium solutions. The second variation of the effective free energy of these solutions is shown to be positive. This result is used to show more generally that equilibria are local minimizers of the free energy.

We study the Faraday waves with liquid crystal MBBA and oleic acid. When we drive a disc of fluid on a shaker periodically, we find a series of symmetrically regular patterns of standing waves. The pattern variations with the viscosity of fluid, the depth of fluid and the size of the container are studied in this paper. It is noted that novel patterns of pentagon and heptagon are formed in some special parameters. In higher frequency region, patterns form in grid and ring with shorter wavelength of standing waves usually.