Browsing by Subject "Bistability"
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Item Open Access Analyzing the bistability of the minimally bistable ERK network using the discriminant locus(2022-04-18) Hwang, DanielThe extracurricular signal regulated kinase (ERK) system is a biological signaling network with “important roles in regulating cellular activity." For this project, we will analyze the bistability, i.e, its capacity to hold two or more positive steady states that are stable to small perturbations, of the minimally bistable ERK network by analyzing its number of real positive steady states for different parameterizations of the network. Previous research used mixed volume computations to determine that the possible range of positive steady states is 1 to 5, however, it has been conjectured that the maximum number of positive steady states is 3. While this system has been analyzed from a convex geometry perspective, our goal is to analyze the ERK system from an algebraic perspective by generalizing the behavior of the steady states of the ERK system over a two-dimensional parameter space in terms of parameters {kcat, kon}, which primarily impact bistability. We use homotopy continuation to discretely sample the discriminant locus and inflection curves of the parameter space, which separates the parameter space into distinct regions each corresponding to a constant number of positive real solutions. Our results demonstrate that in two different parameterizations of the network that the maximum number of positive steady states was 3 and that the relationship between the rate constants was the primary factor in determining this upper bound.Item Open Access Bistability, Synthetic Biology, and Antibiotic Treatment(2010) Tan, CheemengBistable switches are commonly observed in the regulation of critical processes such as cell cycles and differentiation. The switches possess two fundamental properties: memory and bimodality. Once switched ON, the switches can remember their ON state despite a drastic drop in stimulus levels. Furthermore, at intermediate stimulus levels with cellular noise, the switches can cause a population to exhibit bimodal distribution of cell states. Till date, experimental studies have focused primarily on cellular mechanisms that generate bistable switches and their impact on cellular dynamics.
Here, I study emergent bistability due to bacterial interactions with either synthetic gene circuits or antibiotics. A synthetic gene circuit is often engineered by considering the host cell as an invariable "chassis". Circuit activation, however, may modulate host physiology, which in turn can drastically impact circuit behavior. I illustrate this point by a simple circuit consisting of mutant T7 RNA polymerase (T7 RNAP*) that activates its own expression in bacterium Escherichia coli. Although activation by the T7 RNAP* is noncooperative, the circuit caused bistable gene expression. This counterintuitive observation can be explained by growth retardation caused by circuit activation, which resulted in nonlinear dilution of T7 RNAP* in individual bacteria. Predictions made by models accounting for such effects were verified by further experimental measurements. The results reveal a novel mechanism of generating bistability and underscore the need to account for host physiology modulation when engineering gene circuits.
In the context of antibiotic treatment, I investigate bistability as the underlying mechanism of inoculum effect. The inoculum effect refers to the decreasing efficacy of an antibiotic with increasing bacterial density. Despite its implication for the design of antibiotic treatment strategies, its mechanism remains poorly understood. Here I show that, for antibiotics that target the core replication machinery, the inoculum effect can be explained by bistable bacterial growth. My results suggest that a critical requirement for this bistability is sufficiently fast turnover of the core machinery induced by the antibiotic via the heat shock response. I further show that antibiotics that exhibit the inoculum effect can cause a "band-pass" response of bacterial growth on the frequency of antibiotic treatment, whereby the treatment efficacy drastically diminishes at intermediate frequencies. The results have implications on optimal design of antibiotic treatment.
Item Open Access Metamaterial Waveguide Holography and Optical Bistability(2019) Huang, ZhiqinOver the last twenty years, progress on metamaterials (MMs), defined as three-dimensional artificial composites, has sprouted unprecedented phenomena through the manipulation of electromagnetic, acoustic and other waves, making the connection \textit{from structure to function}. By virtue of their spatial and spectral control of wave-matter interactions, MMs have emerged as a powerful building block for practical applications, including imaging, sensing, energy harvesting, beam shaping and steering, and many more. In recent years, the metasurface, as an alternative to volumetric metamaterials, with its reduced 2D profile, has gained increased attention for applications where weight, power and cost are of importance. In this dissertation, I will mainly explore two optical applications where the flexibility in design of a metasurface provides unique capabilities. In one application, waveguide holography, a multifunctional metasurface is used to couple light from a waveguide to free space, forming multicolor or multipolarization holograms. In the second application, a metasurface is used to enhance optical bistability.
First, in this dissertation I will present an investigation of a multicolor computer-generated hologram (CGH) in an all-dielectric metamaterial waveguide system. Light beams from three different color laser sources (red, green and blue) are coupled into the waveguide via a single period grating without any beam-splitters or prisms. A multicolor holographic image can be decoupled in the far field through a binary CGH without any lenses. This technology enables lens-free, ultra-miniature augmented and virtual reality displays. Then, I will continue to illustrate polarization-selective waveguide holography at optical frequencies based on a similar metamaterial multilayer system. I will show that two orthogonally polarized, spatially separated or overlapped holographic images can be incorporated into a single binary CGH, and use these two images to produce composite, stereo vision, 3D effect images observable using linear or circularly polarized lens glasses. Both polarizations are also used to construct radially and azimuthally polarized beams. The fundamental mode and the second mode of TM and TE modes in the waveguide are used to guide the two polarization states. We envision that incorporating polarization selection into waveguide holograms may be used to realize chip-scale displays and beams for optical trapping.
Furthermore, I will introduce another example of the principle \textit{from structure to function}, optical bistablity, in a film-coupled metasurface system, which is a promising platform for low-energy and all-optical switches. The large field enhancements that can be achieved in the dielectric spacer region between a nanopatch optical antenna and a metallic substrate can substantially enhance optical nonlinear processes. Utilizing a dielectric material that exhibits an optical Kerr effect as the spacer layer, we propose a new simulation method to vividly show the optical bistability processes. We expect this new method to be highly accurate compared with other numerical approaches, such as those based on graphical post-processing techniques, since it self-consistently solves for both the spatial field distribution and the intensity-dependent refractive index distribution of the spacer layer. This method offers an alternative approach to finite-difference time-domain (FDTD) modelling. One of the bistability metasurface designs exhibits exceptionally low switching intensities, corresponding to switching energies on the order of tens of attojoules. We propose our method as an effective tool for designing all-optical switches and modulators.
Item Open Access Stochastic Dynamics and Epigenetic Regulation of Gene Expression: from Stimulus Response to Evolutionary Adaptation(2016) GomezSchiavon, MarianaHow organisms adapt and survive in continuously fluctuating environments is a central question of evolutionary biology. Additionally, organisms have to deal with the inherent stochasticity in all cellular processes. The purpose of this thesis is to gain insights into how organisms can use epigenetics and the stochasticity of gene expression to deal with a fluctuating environment. To accomplish this, two cases at different temporal and structural scales were explored: (1) the early transcriptional response to an environmental stimulus in single cells, and (2) the evolutionary dynamics of a population adapting to a recurring fluctuating environment. Mathematical models of stochastic gene expression, population dynamics, and evolution were developed to explore these systems.
First, the information available in sparse single cell measurements was analyzed to better characterize the intrinsic stochasticity of gene expression regulation. A mathematical and statistical model was developed to characterize the kinetics of a single cell, single gene behavior in response to a single environmental stimulus. Bayesian inference approach was used to deduce the contribution of multiple gene promoter states on the experimentally measured cell-to-cell variability. The developed algorithm robustly estimated the kinetic parameters describing the early gene expression dynamics in response a stimulus in single neurons, even when the experimental samples were small and sparse. Additionally, this algorithm allowed testing and comparing different biological hypotheses, and can potentially be applied to a variety of systems.
Second, the evolutionary adaptation dynamics of epigenetic switches in a recurrent fluctuating environment were studied by observing the evolution of gene regulatory circuit in a population under multiple environmental cycles. The evolutionary advantage of using epigenetics to exploit the natural noise in gene expression was tested by competing this strategy against the classical genetic adaptation through mutations in a variety of evolutionary conditions. A trade-off between minimizing the adaptation time after each environmental transition and increasing the robustness of the phenotype during the constant environment between transitions was observed. Surviving lineages evolved bistable, epigenetic switching to adapt quickly in fast fluctuating environments, whereas genetic adaptation with high robustness was favored in slowly fluctuating environments.