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This dissertation undertakes theoretical research into the adsorption, pattern formation, and reactions of atoms, molecules, and layered materials on catalyst surfaces. These investigations are carried out from first-principles calculations of electronic and geometric structures using density functional theory (DFT) for predictions and simulations at the atomic scale. The results should be useful for further study of the catalytic activities of materials and for engineering functional nanostructures. The first part of the dissertation focuses on systematic first-principles simulations of the energetic pathways of CO oxidation on the Cu2O(100) surface. These simulations show CO to oxidize spontaneously on the O-terminated Cu2O(100) surface by consuming surface oxygen atoms. The O-vacancy on Cu2O(100) then is subsequently healed by dissociative adsorption of atmospheric O2 molecules. The second part discusses the pattern formation of hydrogen on two and three layers of Co film grown on the Cu(111) surface. It is found that increasing the pressure of H2 changes the hydrogen structure from 2H-(2 × 2) to H-p(1 × 1) through an intermediate structure of 6H-(3 × 3). The third part compares the results of different ways of introducing van der Waals (vdW) interactions into DFT simulations of the adsorption and pattern formation of various molecules on certain substrates. Examinations of the physisorption of five nucleobases on iii graphene and of n-alkane on Pt(111) demonstrate the importance of taking vdW interactions into account, and of doing so in a way that is best suited to the particular system in question. More importantly, as the adsorption of 1,4 diaminebenzene molecules on Au(111) shows inclusion of vdW interactions is crucial for accurate simulation of the pattern formation. The final part carries out first-principles calculations of the geometric and electronic structure of the Moir´e pattern of a single layer of Molybdenum disulfide (MoS2 ) on Cu(111). The results reveal three possible stacking types. They also demonstrate that the MoS2 layer to be chemisorbed, albeit weakly, and that, while Cu surface atoms are vertically disordered, the layer itself is not strongly buckled.

We study the fluctuation effects in the seminal cyclic predator-prey model in population dynamics due to Robert May and Warren Leonard both in the zero-dimensional and two-dimensional spatial version. We compute the mean time to extinction of a stable set of coexisting populations driven by large fluctuations. We see that the contribution of large fluctuations to extinction can be captured by a quasi-stationary approximation and the Wentzel–Kramers–Brillouin (WKB) eikonal ansatz. We see that near the Hopf bifurcation, extinctions are fast owing to the flat non-Gaussian distribution whereas away from the bifurcation, extinctions are dominated by large fluctuations of the fat tails of the distribution. We compare our results to Gillespie simulations and a single-species theoretical calculation. In addition, we study the spatio-temporal pattern formation of the stochastic May--Leonard model through the Doi-Peliti coherent state path integral formalism to obtain a coarse-grained Langevin description, i.e. the Complex Ginzburg Landau equation with stochastic noise in one complex field. We see that when one restricts the internal reaction noise to small amplitudes, one can obtain a simple form for the stochastic noise correlations that modify the Complex Ginzburg Landau equation. Finally, we study the effect of coupling a spatially extended May--Leonard model in two dimensions with symmetric predation rates to one with asymmetric rates that is prone to reach extinction. We show that the symmetric region induces otherwise unstable coexistence spiral patterns in the asymmetric May--Leonard lattice. We obtain the stability criterion for this pattern induction as we vary the strength of the extinction inducing asymmetry. This research was sponsored by the Army Research Office and was accomplished under Grant Number W911NF-17-1-0156. / Doctor of Philosophy / In the field of ecology, the cyclic predator-prey patterns in a food web are relevant yet independent to the hierarchical archetype. We study the paradigmatic cyclic May--Leonard model of three species, both analytically and numerically. First, we employ well--established techniques in large-deviation theory to study the extinction of populations induced by large but rare fluctuations. In the zero--dimensional version of the model, we compare the mean time to extinction computed from the theory to numerical simulations. Secondly, we study the stochastic spatial version of the May--Leonard model and show that for values close to the Hopf bifurcation, in the limit of small fluctuations, we can map the coarse-grained description of the model to the Complex Ginsburg Landau Equation, with stochastic noise corrections. Finally, we explore the induction of ecodiversity through spatio-temporal spirals in the asymmetric version of the May--Leonard model, which is otherwise inclined to reach an extinction state. This is accomplished by coupling to a symmetric May-Leonard counterpart on a two-dimensional lattice. The coupled system creates conditions for spiral formation in the asymmetric subsystem, thus precluding extinction.

Pattern formation in ecological systems refers to a nonuniform distribution of animal and plant species across a landscape. Pattern formation can be observed in many aquatic and terrestrial systems and can provide important insights into their dynamics and ability to cope with environmental changes. In this dissertation, we focus on pattern formation in tidal marshes and oyster reefs, two important habitats that provide a number of essential ecosystem services. Both of these systems have also experienced dramatic losses, prompting much research to investigate their dynamics as and viable restoration and management strategies. The first part of this dissertation focuses on understanding the spatial patterning of the marsh shoreline, which can range from a uniform to a more wave-like shoreline. We present a mathematical framework for modeling the spatial variation of the shoreline as a result of interactions between marsh vegetation, mussels and their impact on marsh sedimentation and erosion. While both species are known to significantly impact marsh dynamics, no mathematical model describing this phenomenon has been previously proposed. Numerical and analytical investigation of our model indicates that the interactions between these species can drive the spatial variation of the marsh edge, increase the system’s productivity and allow it to withstand harsh erosion conditions. The second part of this dissertation focuses on pattern formation in intertidal oyster reef communities, where both round and elongated reefs of various orientations dominate the landscape. Most of what is currently known about reef geometry has been anecdotal, with no comprehensive, quantitative study of reef pattern formation carried out. In particular, the interaction of oyster reefs of various geometric configuration with tidal flow remains poorly understood. This is important in reef restoration, where understanding the interaction of reef geometry with flow and other environmental factors can inform the construction of artificial oyster reefs. In this dissertation, we present a comprehensive analysis of remotely sensed aerial imagery of an intertidal oyster reef network in conjunction with information on tidal flow dynamics and bathymetry. Using texture and color properties of the aerial imagery, we identify and delineate over six thousand individual reefs. We then classify reefs into natural classes based on geometric attributes such as reef shape, size and orientation. Finally, we use multiple spatial analysis techniques to determine the spatial clustering of different reef types and investigate the role of flow and bathymetry in their spatial distribution.

Pattern formation, or the generation of coordinated, emergent behavior, is ubiquitous in nature. Researchers have long sought to understand the mechanisms behind such systems as zebra stripes, repeating flower petals, and fingers on hands, within fields such as physics and developmental biology. Notably, a diverse array of bacteria species naturally self-organize into durable macroscale patterns on solid surfaces via swarming motility—a highly coordinated, rapid movement of bacteria powered by flagella. Meanwhile, researchers in the synthetic biology field, which aims to rationally engineer living organisms for biotechnological applications, have been engineering synthetic pattern formation in microbes over the last several decades. Engineering swarming is an untapped opportunity to increase the scale and robustness of coordinated synthetic microbial systems. In this thesis, we expand the field of engineered pattern formation by applying the tools of synthetic biology and deep learning to engineer and characterize the swarming of Proteus mirabilis, which natively forms a centimeter-scale ring pattern. We engineer P. mirabilis to “write” external inputs into visible spatial records. Specifically, we engineer tunable expression of swarming-related genes that modify pattern features, and we develop quantitative approaches to decoding. Next, we develop a dual-input system that modulates two swarming-related genes simultaneously, and we apply convolutional neural networks (CNNs) to decode the resulting patterns with over 90% top-3 accuracy. We separately show growing colonies can record dynamic environmental changes which can be decoded with a U-Net model. We show the robustness of the engineered strains’ readout to fluctuations in temperature and environmental water samples. Lastly, we engineer strains which sense and respond to heavy metals. Our pCopA-flgM strain records the presence of 0 to 50 mM aqueous copper with decreased colony ring width. We conclude in this chapter that engineering native swarm patterns can thus be applied for building bacterial recorders with a visible macroscale readout. In parallel, to better characterize the swarm patterns of P. mirabilis, we develop a pipeline using deep learning approaches to segment colony images. We develop easy-to-use, semi-automated ground truth annotation and preprocessing methods. We separately segment the (1) colony background from agar and (2) the internal colony ring boundaries. The first task is achieved with a patch-classification approach; in the process, we find that the combination of the trained CNN and the “majority voting” method of label fusion achieves a test DICE score of 93% and correctly segments even faint outer swarm rings. The second task is accomplished with a U-Net which achieves over 83% test DICE. We show that our trained models easily segment a set of colonies generated at two relevant conditions, enabling automated analysis of features such as area and ring width. We apply our pipeline to analyze the more complex patterns of our engineered strains, such as the pCopA-flgM strain. The work in this chapter altogether advances the ability to analyze swarm patterns of P. mirabilis. We also aim to expand the use of our colony-characterization approaches beyond P. mirabilis to other microbes. Therefore, we present our work using deep learning to classify a set of Bacillus species isolated from soil samples. We generate datasets of the species grown under different conditions and apply transfer learning to train well-known CNN architectures such as ResNet and Inception to classify these datasets. This approach allows the models to easily learn these small datasets, and the models generalize to correctly predict a species which forms branching patterns regardless of exact growth condition. We visualize the attributions of the models with the integrated gradients method and find that model predictions are attributable to colony regions. This work sets the stage for classification, segmentation, and characterization of a wider array of microbial species with distinctive macroscale colony morphologies. Finally, we conclude by discussing ongoing efforts to expand upon the work presented in this thesis towards the sensing of dynamic inputs such as light, engineering of species other than P. mirabilis, and further optimization of the system of an engineered swarm pattern as a macroscale biosensor readout. Such work can contribute not only to the fields of synthetic pattern formation and the study of bacterial swarming, but also to the fields of engineered living materials and bio-inspired design.

Ion channels and pumps play critical roles during sea urchin development including mediating the blocks to polyspermy, regulating left-right and dorsal-ventral axis specification, directing ventral PMC migration, and controlling biomineralization of the larval skeleton. We performed a screen of pharmacological ion channel inhibitors, and we chose two inhibitors to investigate further. First, we found that tricaine, a potent inhibitor of voltage-gated sodium channels (VGSCs), induces aberrant skeletal patterning in Lytechinus variegatus larvae. The larval skeleton is secreted by the primary mesenchyme cells (PMCs), which migrate within the blastocoel into a stereotypical pattern. We show that VGSC activity is required for normal PMC migration and skeletal patterning. Timed inhibitor studies identified VGSC activity as specifically required from early gastrula to the onset of late gastrula for normal skeletal patterning. Tricaine inhibits the voltage-gated sodium channel LvScn5a which is strongly expressed in the developing nervous system in pluteus larvae. We found that exogenous expression of an anesthetic-insensitive version of LvScn5a is sufficient to rescue hallmark tricaine-mediated skeletal patterning defects, demonstrating the specificity of the inhibitor. LvScn5a exhibits a ventrolateral ectodermal expression domain in gastrulating embryos that is spatiotemporally congruent with triradiate formation in the ventrolateral PMC clusters at the onset of skeletogenesis. This ectodermal territory normally expresses the patterning cue Wnt5, and we find that the expression of Wnt5 is dramatically spatially expanded by tricaine treatment. We also observe ectopic PMC clusters in tricaine-treated embryos. We found that knockdown of Wnt5 expression is sufficient to rescue tricaine-mediated skeletal patterning defects. These results are consistent with a model in which LvScn5a activity in the ventrolateral ectoderm functions to spatially restrict the expression of the ectodermal patterning cue Wnt5 that in turn induces PMC cluster formation. Together, these findings show that spatially restricted sodium channel activity regulates ectodermal cue expression that, in turn, regulates PMC differentiation and skeletal morphogenesis. Second, we show that V-type H⁺ ATPase (VHA) activity is required for specification of the dorsal-ventral (DV) axis. DV specification is controlled by the TGF-β signal Nodal that specifies the ventral territory and indirectly activates dorsal specification via induction of BMP 2/4 expression. Nodal expression occurs downstream of p38 MAPK, which is transiently, asymmetrically inactive on the presumptive dorsal side of the blastula embryo. VHA activity is required for that transient inactivation of p38 MAPK, and it is required for the subsequent spatial restriction of Nodal expression. We show that VHA inhibition is sufficient to induce global Nodal expression during the blastula stage, resulting in ventralization of the embryo. We show that this phenotype can be rescued by experimentally imposing asymmetric Nodal expression at the 4-cell stage. We discover a VHA-dependent voltage gradient across the DV axis and find that VHA activity is required for hypoxia inducible factor (HIF) activation. We show that neither hyperpolarization nor HIF activation is sufficient to perturb DV specification, which implicates a third unknown pathway connecting VHA activity and p38 MAPK symmetry breaking. These results are consistent with a model in which dorsal VHA activity is required to inhibit Nodal expression and signaling, potentially via dorsal p38 MAPK inhibition. Together, these studies demonstrate that ion channels are required for both DV specification and for normal skeletal patterning.

Skeletal muscles drive voluntary movements. Striated muscles allow fish to swim, birds to fly and our heart to beat. Skeletal muscles are built of multiple fascicles, which are bundles containing many muscle fibers. Looking at these structures under a microscope, smaller structures of muscle fibers, so-called myofibrils, become visible. These structures are highly organized and show regular patterns of specific units. These specific periodic subunits are the sarcomeres. Sarcomeres self-assemble as the smallest unit of skeletal muscles. Mature sarcomeres are crystal-like structures with a specific size of 2-3 micrometer. Sarcomeres are bounded by the so-called Z-disc, which contains more than thirty different proteins. Polar actin filaments are cross-linked to the Z-disc. Myosin motor filaments are anchored, facing the center of the sarcomere. The giant protein titin links myosin and actin filaments and stabilizes the sarcomere. Sarcomeres shorten in length during muscle contraction, by relative sliding of myosin through actin filaments. The myosin motor filaments walk through the polar actin filament, under energy conversion. While this sliding mechanism is known, it is unclear how sarcomeres form during the multi-stage developmental process of skeletal muscles. How to build a sarcomere? Despite many years of research, it is poorly understood how sarcomeres self-assemble into regular patterns. In this context, the main questions are: which sarcomere components regularly align first, and how are actin filaments orientated with the correct polarity? To answer these questions, we observe early stages of myofibrillogenesis in the fruit fly Drosophila melanogaster and quantify the regular alignment of selected proteins using a new algorithm. Our result: Data of early stages of myofibrillogenesis display a temporal order during sarcomere assembly. Myosin, titin (Sallimus in fruit fly) and the Z-disc proteins alpha-actinin pattern first, while actin filaments only follow later. With these experimental observations, we postulate a new theoretical framework of sarcomere assembly. We establish a minimal mathematical model, including possible molecular interactions between myosin and Z-disc proteins. In particular, we show that a non-local interaction with the protein titin is sufficient to drive the pattern formation process. With this non-local interaction, we take into account that myosin and titin are extended filaments of a specific size, setting the sarcomere length. With agent-based simulations we demonstrate that the model is robust to stochastic small number fluctuations. In addition, it is known that mechanical tension is induced during myofibrillogenesis. Local tension, produced by myosin motor activity can guide the assembly of sarcomeres, too. Thus, we formulate a second minimal mathematical model accounting for local tension. Specifically, we set the focus on the non-covalent binding of alpha-actinin (catch-bond behavior). In the presence of local tension, the lifetime of alpha-actinin increases. We demonstrate for this second model that such an alternative non-local interaction can give rise to periodic patterns of a specific length under presence of mechanical tension, even though it is less robust. We discuss similarities and differences of both models and propose the possibility that myofibrillogenesis in biological systems is a combination of both models.

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京都大学 / 新制・課程博士 / 博士(理学) / 甲第23675号 / 理博第4765号 / 新制||理||1683(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)教授 坂上 貴之, 教授 泉 正己, 教授 國府 寛司 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM