Macroscopic Models and Phase Resetting of Coupled Biological Oscillators

This thesis concerns the derivation and analysis of macroscopic mathematical models for coupled biological oscillators. Circadian rhythms, heart beats, and brain waves are all examples of biological rhythms formed through the aggregation of the rhythmic contributions of thousands of cellular oscillations. These systems evolve in an extremely high-dimensional phase space having at least as many degrees of freedom as the number of oscillators. This high-dimensionality often contrasts with the low-dimensional behavior observed on the collective or macroscopic scale. Moreover, the macroscopic dynamics are often of greater interest in biological applications. Therefore, it is imperative that mathematical techniques are developed to extract low-dimensional models for the macroscopic behavior of these systems. One such mathematical technique is the Ott-Antonsen ansatz. The Ott-Antonsen ansatz may be applied to high-dimensional systems of heterogeneous coupled oscillators to derive an exact low-dimensional description of the system in terms of macroscopic variables. We apply the Ott-Antonsen technique to determine the sensitivity of collective oscillations to perturbations with applications to neuroscience. The power of the Ott-Antonsen technique comes at the expense of several limitations which could limit its applicability to biological systems. To address this we compare the Ott-Antonsen ansatz with experimental measurements of circadian rhythms and numerical simulations of several other biological systems. This analysis reveals that a key assumption of the Ott-Antonsen approach is violated in these systems. However, we discover a low-dimensional structure in these data sets and characterize its emergence through a simple argument depending only on general phase-locking behavior in coupled oscillator systems. We further demonstrate the structure's emergence in networks of noisy heterogeneous oscillators with complex network connectivity. We show how this structure may be applied as an ansatz to derive low-dimensional macroscopic models for oscillator population activity. This approach allows for the incorporation of cellular-level experimental data into the macroscopic model whose parameters and variables can then be directly associated with tissue- or organism-level properties, thereby elucidating the core properties driving the collective behavior of the system. We first apply our ansatz to study the impact of light on the mammalian circadian system. To begin we derive a low-dimensional macroscopic model for the core circadian clock in mammals. Significantly, the variables and parameters in our model have physiological interpretations and may be compared with experimental results. We focus on the effect of four key factors which help shape the mammalian phase response to light: heterogeneity in the population of oscillators, the structure of the typical light phase response curve, the fraction of oscillators which receive direct light input and changes in the coupling strengths associated with seasonal day-lengths. We find these factors can explain several experimental results and provide insight into the processing of light information in the mammalian circadian system. In a second application of our ansatz we derive a pair of low-dimensional models for human circadian rhythms. We fit the model parameters to measurements of light sensitivity in human subjects, and validate these parameter fits with three additional data sets. We compare our model predictions with those made by previous phenomenological models for human circadian rhythms. We find our models make new predictions concerning the amplitude dynamics of the human circadian clock and the light entrainment properties of the clock. These results could have applications to the development of light-based therapies for circadian disorders.PHDApplied and Interdisciplinary MathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/138766/1/khannay_1.pd

Buffering by gene duplicates: an analysis of molecular correlates and evolutionary conservation

<p>Abstract</p> <p>Background</p> <p>One mechanism to account for robustness against gene knockouts or knockdowns is through buffering by gene duplicates, but the extent and general correlates of this process in organisms is still a matter of debate. To reveal general trends of this process, we provide a comprehensive comparison of gene essentiality, duplication and buffering by duplicates across seven bacteria (<it>Mycoplasma genitalium, Bacillus subtilis, Helicobacter pylori, Haemophilus influenzae, Mycobacterium tuberculosis, Pseudomonas aeruginosa, Escherichia coli</it>), and four eukaryotes (<it>Saccharomyces cerevisiae </it>(yeast), <it>Caenorhabditis elegans </it>(worm), <it>Drosophila melanogaster </it>(fly), <it>Mus musculus </it>(mouse)).</p> <p>Results</p> <p>In nine of the eleven organisms, duplicates significantly increase chances of survival upon gene deletion (P-value ≤ 0.05), but only by up to 13%. Given that duplicates make up to 80% of eukaryotic genomes, the small contribution is surprising and points to dominant roles of other buffering processes, such as alternative metabolic pathways. The buffering capacity of duplicates appears to be independent of the degree of gene essentiality and tends to be higher for genes with high expression levels. For example, buffering capacity increases to 23% amongst highly expressed genes in <it>E. coli</it>. Sequence similarity and the number of duplicates per gene are weak predictors of the duplicate's buffering capacity. In a case study we show that buffering gene duplicates in yeast and worm are somewhat more similar in their functions than non-buffering duplicates and have increased transcriptional and translational activity.</p> <p>Conclusion</p> <p>In sum, the extent of gene essentiality and buffering by duplicates is not conserved across organisms and does not correlate with the organisms' apparent complexity. This heterogeneity goes beyond what would be expected from differences in experimental approaches alone. Buffering by duplicates contributes to robustness in several organisms, but to a small extent – and the relatively large amount of buffering by duplicates observed in yeast and worm may be largely specific to these organisms. Thus, the only common factor of buffering by duplicates between different organisms may be the by-product of duplicate retention due to demands of high dosage.</p

Mitigating man-in-the-middle attacks on mobile devices by blocking insecure http traffic without using vpn

Mobile devices are constantly connected to the Internet, making countless connections with remote services. Unfortunately, many of these connections are in cleartext, visible to third-parties while in transit. This is insecure and opens up the possibility for man-in-the-middle attacks. While there is little control over what kind of connection running apps can make, this paper presents a solution in blocking insecure HTTP packets from leaving the device. Specifically, the proposed solution works on the device, without the need to tunnel packets to a remote VPN server, and without special privileges such as root access. Speed tests were performed to quantify how much network speed is being impacted while filtering. To investigate how blocking HTTP traffic can affect day-to-day usage, common tasks were put to the tests, tasks such as browsing, searching, emailing, instant messaging, social networking, consuming streaming content, and gaming. The results from the tests are interesting, websites that do not support HTTPS were exposed, apps that do not fully support HTTPS were also being uncovered. One surprisingly, and arguably pleasant, side effect was discovered – the filtering solution blocks out advertisements in all of the games being tested, hence contributing to an improved gaming experience

Effects of spatial network structure on competitive coexistence in a metacommunity

Species dispersal patterns are often assumed to take place on a uniform environment and do not allow species to move through a habitat without effecting the dynamics locally. We examine the effects of migration network topology on a the outcome of competitive interactions between two competing species which may disperse non-uniformly and are allowed to jump between habitats without effecting the populations between. We develop a perturbation model for a fully- connected migration network and apply this approximate model to networks with highly clustered subsets. We show that highly clustered networks allow for the coexistence of competitors and that these coexistence states disappear quickly when the highly clustered networks are randomly rewired. Moreover, we examine the effect of migration network topology on the colonization of habitat by an invasive species and show the relation between this problem and our previous results.Biological Sciences, School o

Toward an AI-based external scenario event controller for crisis response simulations

There is a need for tool support for structured planning, execution and analysis of simulation-based training for crisis response and management. As a central component of an architecture for such tool support, we outline the design of an AI-based scenario event controller. The event controller is a component that uses machine reasoning to compute the next state in a scenario, given the actions performed in the corresponding simulation (execution of the scenario). Scenarios are specified in Answer Set Programming (ASP), which is a logic programming language we use for automated planning of training scenarios. A plan encoding in ASP adds expressivity in scenario specification and enables machine reasoning. For exercise managers this gives AI-based tool support for before-action and during-action reviews to optimize learning. In line with Modelling and Simulation as as Service, our approach externalizes event control from any particular simulation platform. The scenario, and its unfolding in terms of events, is externalized as a service. This increases interoperability and enables scenarios to be designed and modified readily and rapidly to adapt to new training requirements

Validation of the Entrainment Signal Regularity Index and associations with children\u27s changes in BMI

OBJECTIVE: This study examined the validity of a novel metric of circadian health, the Entrainment Signal Regularity Index (ESRI), and its relationship to changes in BMI during the school year and summer. METHODS: In a longitudinal observational data set, this study examined the relationship between ESRI score and children\u27s (n = 119, 5- to 8-year-olds) sleep and physical activity levels during the school year and summer, differences in ESRI score during the school year and summer, and the association of ESRI score during the school year and summer with changes in BMI across those time periods. RESULTS: The ESRI score was higher during the school year (0.70 ± 0.10) compared with summer (0.63 ± 0.11); t(111) = 5.484, p \u3c 0.001. Whereas the ESRI score at the beginning of the school year did not significantly predict BMI change during the school year (β = 0.05 ± 0.09 SE, p = 0.57), having a higher ESRI score during summer predicted smaller increases in BMI during summer (β = -0.22 ± 0.10 SE, p = 0.03). CONCLUSIONS: Overall, children demonstrated higher entrainment regularity during the school year compared with the summer. During summer, having a higher entrainment signal was associated with smaller changes in summertime BMI. This effect was independent of the effects of children\u27s sleep midpoint, sleep regularity, and physical activity on children\u27s BMI