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

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

Thesis (Ph. D.)--University of Hong Kong, 2010. / Includes bibliographical references (leaves 101-109). Also available in print.

In this thesis we examine mathematical models which have been suggested as possibile mechanisms for forming certain biological patterns. We analyse them in detail attempting to produce the requisite patterns both analytically and numerically. A reaction diffusion system in two spatial dimensions with anisotropic diffusion is examined in detail and the results compared with certain snakeskin patterns. We examine two other variants to the standard reaction diffusion system: a system where the reaction kinetics and the diffusion coefficients depend upon the cell density suggested as a possible model for the segmentation sequence in Drosophila and a system where the model parameters have one dimensional spatial gradients. We also analyse a model derived from known cellular processes used to model the branching behaviour in bryozoans and show that, in one dimension, such a model can, in theory, give all the required solution behaviour. A genetic switch model for pattern elements on butterfly wings is also briefly examined to obtain expressions for the solution behaviour under coldshock.

Thesis (Ph. D.)--University of Chicago, Dept. of Biology. / Includes bibliographical references. Also available on the Internet.

Structure, in its many forms, is a central theme in theoretical population ecology. At a mathematical level, it arises as nonuniformities in the topology of nonlinear dynamical systems. I investigate a mechanism wherein a chaotic time series can have episodes of nearly periodic dynamics interspersed with more 'typical' irregular dynamics. This phenomenon frequently appears in biological models, and may explain patterns of alternating biennial and irregular dynamics in measles epidemics. I investigate the interaction between spatial structure and density-dependent population regulation with a simple model of two logistic maps coupled by diffusive migration. I examine two different consequences of spatial structure: scale-dependent interactions ("nonlocal interactions") and spatial variation in resource quality ("environmental heterogeneity"). Nonlocal interactions allow three general dynamical regimes: in-phase, out-of-phase, and uncorrelated. With environmental heterogeneity, the dynamics of the total population size can be approximated by a logistic map with the mean growth parameter of the two patches; the dynamics within a single patch are often less regular. Adding environmental heterogeneity to non-local interactions has little qualitative effect on the dynamics when the differences between patches are small; when the differences are large, uncorrelated dynamics are most likely to be seen, and there are interesting consequences for the stability of source-sink systems. A third type of structure arises when individuals differ from one another. Accurate prediction of extinction risk in small populations requires that a distinction be made between demographic stochasticity (variation among individuals) and environmental stochasticity (variation among years or sites). I describe and evaluate two tests to determine whether all the variation in population survivorship can be explained by demographic stochasticity alone. Both tests have appropriate probabilities of type I error, unless the survival probability is very low or very high. Small amounts of environmental stochasticity are often not detected by the tests, but the hypothesis of demographic stochasticity alone is consistently rejected when environmental stochasticity is large. I also show how to factor out deterministic sources of variability, such as density-dependence. I illustrate these tests with data on a population of Acorn Woodpeckers.

No description available.

The development of spatial structure and form on vertebrate skin is a complex and poorly understood phenomenon. We consider here a new mechanochemical tissue interaction model for generating vertebrate skin patterns. Tissue interaction, which plays a crucial role in vertebrate skin morphogenesis, is modelled by reacting and diffusing signal morphogens. The model consists of seven coupled partial differential equations, one each for dermal and epidermal cell densities, four for the signal morphogen concentrations and one for describing epithelial mechanics. Because of its complexity, we reduce the full model to a small strain quasi-steady-state model, by making several simplifying assumptions. A steady state analysis demonstrates that our reduced system possesses stable time-independent steady state solutions on one-dimensional spatial domains. A linear analysis combined with a multiple time-scale perturbation procedure and numerical simulations are used to examine the range of patterns that the model can exhibit on both one- and two-dimensions domains. Spatial patterns, such as rolls, squares, rhombi and hexagons, which are remarkably similar to those observed on vertebrate skin, are obtained. Although much of the work on pattern formation is concerned with synchronous spatial patterning, many structures on vertebrate skin are laid down in a sequential fashion. Our tissue interaction model can account for such sequential pattern formation. A linear analysis and a regular perturbation analysis is used to examine propagating epithelial contraction waves coupled to dermal cell invasion waves. The results compare favourably with those obtained from numerical simulations of the model. Furthermore, sequential pattern formation on one-dimensional domains is analysed; first by an asymptotic technique, and then by a new method involving the envelopes of the spatio-temporal propagating solutions. Both methods provide analytical estimates for the speeds of the wave of propagating pattern which are in close agreement with those obtained numerically. Finally, by numerical simulations, we show that our tissue interaction model can account for two-dimensional sequential pattern formation. In particular, we show that complex two-dimensional patterns can be determined by simple quasi-one-dimensional patterns.

published_or_final_version / Chemistry / Doctoral / Doctor of Philosophy