Teaching to Fail: Creating Vulnerable Learning Communities to Facilitate Students\u27 Growth

In today’s academic environment, students perceive no room for failure. Thus, they do not explore or take risks, and this limits their growth. As a result, the instructor must create opportunities for failure while mitigating the stress associated with failure. Opportunities for failure can be created in the curriculum and course structure through scaffolding, formative assessments, and extensive feedback. The instructor must also adopt a growth mindset when it comes to the students’ abilities. Instructors can create an environment where failure is expected by being vulnerable in the classroom themselves and highlighting their failures and subsequent growth. Graduate students are particularly well-placed to do so because of the proximity of their experience to that of their students. Higher education institutions emphasize learning as a transaction that can be measured and count failure against both students and instructors. Thus, instructors (and students) are incentivized to present themselves as having control and mastery rather than being vulnerable in the classroom. We must overcome these forces to create a shared learning community that emphasizes strong interpersonal relationships in the classroom

A Traveling-Wave Solution for Bacterial Chemotaxis with Growth

Bacterial cells navigate around their environment by directing their movement along chemical gradients. This process, known as chemotaxis, can promote the rapid expansion of bacterial populations into previously unoccupied territories. However, despite numerous experimental and theoretical studies on this classical topic, chemotaxis-driven population expansion is not understood in quantitative terms. Building on recent experimental progress, we here present a detailed analytical study that provides a quantitative understanding of how chemotaxis and cell growth lead to rapid and stable expansion of bacterial populations. We provide analytical relations that accurately describe the dependence of the expansion speed and density profile of the expanding population on important molecular, cellular, and environmental parameters. In particular, expansion speeds can be boosted by orders of magnitude when the environmental availability of chemicals relative to the cellular limits of chemical sensing is high. As analytical understanding of such complex spatiotemporal dynamic processes is rare, the results derived here provide a mathematical framework for further investigations of the different roles chemotaxis plays in diverse ecological contexts.Comment: 27 pages main text, 34 pages Supplemental Informatio

Stress-induced Metabolic Exchanges Between Complementary Bacterial Types Underly a Dynamic Mechanism of Inter-species Stress Resistance

Metabolic cross-feeding plays vital roles in promoting ecological diversity. While some microbes depend on exchanges of essential nutrients for growth, the forces driving the extensive cross-feeding needed to support the coexistence of free-living microbes are poorly understood. Here we characterize bacterial physiology under self-acidification and establish that extensive excretion of key metabolites following growth arrest provides a collaborative, inter-species mechanism of stress resistance. This collaboration occurs not only between species isolated from the same community, but also between unrelated species with complementary (glycolytic vs. gluconeogenic) modes of metabolism. Cultures of such communities progress through distinct phases of growth-dilution cycles, comprising of exponential growth, acidification-triggered growth arrest, collaborative deacidification, and growth recovery, with each phase involving different combinations of physiological states of individual species. Our findings challenge the steady-state view of ecosystems commonly portrayed in ecological models, offering an alternative dynamical view based on growth advantages of complementary species in different phases

Exploring How We Teach: Lived Experiences, Lessons, and Research about Graduate Instructors by Graduate Instructors

This book combines the knowledge of 30 graduate student instructors sharing about how they teach and how they’ve learned how to teach

Quorum Sensing in Bacterial Biofilms: Regulating Matrix Production through Communication

Bacteria grow on surfaces in complex communities known as biofilms. Biofilms are composed of cells embedded in extracellular matrix. Within biofilms, bacteria often communicate, cooperate, and compete within their own species and with other species using Quorum Sensing (QS). QS refers to the process by which bacteria produce, secrete, and subsequently detect small molecules called autoinducers (AIs) to assess the local population density of their species, or of other species. QS is known to regulate the production of extracellular matrix. We investigated the benefit of QS in regulating matrix production to gain access to a nutrient that diffuses from a source far from the biofilm. We employed Agent-Based Modeling (ABM), a simulation framework that allows cells to modify their behavior based on local inputs, e.g. nutrient and AI concentrations. We first determined the optimal fixed strategies (that do not use QS) for simulated pairwise competitions between strains, and identified the conditions that favor matrix production. To understand if QS can provide a competitive advantage, we modified our model to include QS with constitutive AI production. We demonstrated that simple QS-based strategies can be superior to any fixed strategy. However, we found that if AI production is not constitutive but rather depends on nutrient intake, then QS-based strategies fail to provide an advantage. We explain this failure of QS using analytic methods. We derive an expression for the biophysically limited dynamic range of AI concentration detection in nutrient limited environments. This expression implies that for QS to provide an advantage in biofilms, production of AI should be privileged and not limited by overall metabolic rates

Phenomenological Modeling of Bacterial Populations

In this dissertation, we present a comprehensive study on two sets of phenomenological models examining bacterial population dynamics, focusing on chemotaxis-driven expansion and microbial interactions in non-steady-state environments. Our first model provides a quantitative understanding of how chemotaxis and cell growth lead to the rapid expansion of bacterial populations. We establish analytical relations that describe the dependence of expansion speed and density profile on molecular, cellular, and environmental parameters. We demonstrate that expansion speeds can significantly increase when the environmental availability of chemicals is high relative to the cellular limits of chemical sensing. Our results offer a mathematical framework for investigating the roles of taxis in diverse ecological contexts across broad parameter regimes.The second set of models explores microbial interactions in non-steady-state environments, as ecological dynamics often feature large self-generated environmental changes driving microbes through distinct physiological states. We introduce a phenomenological model to investigate the dynamic coexistence of microbes in cyclic environments. By considering growth according to a global ecological coordinate, specifically total community biomass, our model bypasses specific interactions leading to different physiological states. Our analysis provides rigorous, quantitative criteria for the dynamic coexistence of many species in terms of differential species' dominance ("growth niche") along the ecological coordinates. Our research shifts the focus of ecosystem dynamics from bottom-up studies based on inter-species interaction to top-down studies based on accessible macroscopic observables such as growth rates and total biomass. This approach allows for a quantitative examination of community-wide characteristics. In summary, this dissertation presents a detailed analytical investigation of bacterial population dynamics, shedding light on the underlying processes of chemotaxis-driven expansion and microbial interactions in changing environments. The mathematical frameworks and insights provided have broad applicability to diverse ecological contexts and open up new avenues for understanding complex spatiotemporal dynamic processes in microbial ecosystems

A biophysical limit for quorum sensing in biofilms

Bacteria grow on surfaces in complex immobile communities known as biofilms, which are composed of cells embedded in an extracellular matrix. Within biofilms, bacteria often interact with members of their own species, and cooperate or compete with members of other species via quorum sensing (QS). QS is a process by which microbes produce, secrete, and subsequently detect small molecules called autoinducers (AIs) to assess their local population density. We explore the competitive advantage of QS through agent-based simulations of a spatial model in which colony expansion via extracellular matrix production provides greater access to a limiting diffusible nutrient. We note a significant difference in results based on whether AI production is constitutive or limited by nutrient availability: If AI production is constitutive, simple QS-based matrix-production strategies can be far superior to any fixed strategy. However, if AI production is limited by nutrient availability, QS-based strategies fail to provide a significant advantage over fixed strategies. To explain this dichotomy, we derive a novel biophysical limit for the dynamic range of nutrient-limited AI concentrations in biofilms. This range is remarkably small (less than 10-fold) for the realistic case in which a growth-limiting diffusible nutrient is taken up within a narrow active growth layer. This biophysical limit implies that for QS to be most effective in biofilms, AI production should be a protected function not directly tied to metabolism

A traveling-wave solution for bacterial chemotaxis with growth.

Bacterial cells navigate their environment by directing their movement along chemical gradients. This process, known as chemotaxis, can promote the rapid expansion of bacterial populations into previously unoccupied territories. However, despite numerous experimental and theoretical studies on this classical topic, chemotaxis-driven population expansion is not understood in quantitative terms. Building on recent experimental progress, we here present a detailed analytical study that provides a quantitative understanding of how chemotaxis and cell growth lead to rapid and stable expansion of bacterial populations. We provide analytical relations that accurately describe the dependence of the expansion speed and density profile of the expanding population on important molecular, cellular, and environmental parameters. In particular, expansion speeds can be boosted by orders of magnitude when the environmental availability of chemicals relative to the cellular limits of chemical sensing is high. Analytical understanding of such complex spatiotemporal dynamic processes is rare. Our analytical results and the methods employed to attain them provide a mathematical framework for investigations of the roles of taxis in diverse ecological contexts across broad parameter regimes

Dynamic coexistence driven by physiological transitions in microbial communities

Microbial ecosystems are commonly modeled by fixed interactions between species in steady exponential growth states. However, microbes often modify their environments so strongly that they are forced out of the exponential state into stressed or non-growing states. Such dynamics are typical of ecological succession in nature and serial-dilution cycles in the laboratory. Here, we introduce a phenomenological model, the Community State model, to gain insight into the dynamic coexistence of microbes due to changes in their physiological states. Our model bypasses specific interactions (e.g., nutrient starvation, stress, aggregation) that lead to different combinations of physiological states, referred to collectively as "community states", and modeled by specifying the growth preference of each species along a global ecological coordinate, taken here to be the total community biomass density. We identify three key features of such dynamical communities that contrast starkly with steady-state communities: increased tolerance of community diversity to fast growth rates of species dominating different community states, enhanced community stability through staggered dominance of different species in different community states, and increased requirement on growth dominance for the inclusion of late-growing species. These features, derived explicitly for simplified models, are proposed here to be principles aiding the understanding of complex dynamical communities. Our model shifts the focus of ecosystem dynamics from bottom-up studies based on idealized inter-species interaction to top-down studies based on accessible macroscopic observables such as growth rates and total biomass density, enabling quantitative examination of community-wide characteristics.Comment: 14 pages main text with 24 pages supplementary information. Submitted for peer revie