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Abstract The effect of thermal stress on beneficial symbiosis, in the face of rapid climate change, remains poorly understood. We investigate this using the model system, Euprymna scolopes (Es), the Hawaiian bobtail squid, and its bioluminescent symbiont, Vibrio fischeri (Vf), which enables the squid to camouflage itself through counter-illumination. Successful colonization of the squid by Vf must occur hours after hatching and is mediated by fluid flow due to respiration within the squid mantle cavity. To study this process, we develop a mathematical model using the method of regularized stokeslets to simulate the flow and resulting bacterial trajectories within the squid. We explore how thermal stress, mediated by physiological changes in respiration, ciliary dynamics and internal geometry, affects early colonization by analysing the time bacteria spend in regions crucial to the establishment of symbioses in these simulations. A variance-based sensitivity analysis of physiologically relevant parameters on these metrics demonstrated that changes in the breath cycle significantly affect and reduce the time bacteria spend in the critical zone within the squid, hindering colonization. 

Abstract Bacteria often develop distinct phenotypes to adapt to environmental stress. In particular, they can produce biofilms, dense communities of bacteria that live in a complex extracellular matrix. While previous studies have investigated how bacterial biofilms are regulated under laboratory conditions, they have not considered (1) the data requirements necessary to estimate model parameters and (2) how bacteria respond to recurring stressors in their natural habitats. To address (1), we adapted a mechanistic population model to explore the dynamics of biofilm formation in the presence of predator stress, using synthetic data. We used a Maximum Likelihood Estimation framework to measure crucial parameters underpinning the biofilm formation dynamics. We used genetic algorithms to propose an optimal data collection schedule that minimised parameter identifiability confidence interval widths. Our sensitivity analysis revealed that, within the explored regimes, we could simplify the binding dynamics and eliminate biofilm detachment. To address (2), we proposed a structured version of our model to capture the long-term behaviour and evolutionary selection. In our extended model, the subpopulations feature different maximal rates of biofilm formation. We compared the selection under different predator types and amounts and identified key parameters that affected the speed of selection via sensitivity analysis. 

Resistance to treatment, which comes from the heterogeneity of cell types within tumors, is a leading cause of poor treatment outcomes in cancer patients. Previous mathematical work modeling cancer over time has neither emphasized the relationship between cell heterogeneity and treatment resistance nor depicted heterogeneity with sufficient nuance. To respond to the need to depict a wide range of resistance levels, we develop a random differential equation model of tumor growth. Random differential equations are differential equations in which the parameters are random variables. In the inverse problem, we aim to recover the sensitivity to treatment as a probability mass function. This allows us to observe what proportions of cells exist at different sensitivity levels. After validating the method with synthetic data, we apply it to monoclonal and mixture cell population data of isogenic Ba/F3 murine cell lines to uncover each tumor’s levels of sensitivity to treatment as a probability mass function. 

Agent-based modeling (ABM) is a powerful tool for understanding self-organizing biological systems, but it is computationally intensive and often not analytically tractable. Equation learning (EQL) methods can derive continuum models from ABM data, but they typically require extensive simulations for each parameter set, raising concerns about generalizability. In this work, we extend EQL to Multi-experiment equation learning (ME-EQL) by introducing two methods: (i) one-at-a-time ME-EQL (OAT ME-EQL), which learns individual models for each parameter set and connects them via interpolation, and (ii) embedded structure ME-EQL (ES ME-EQL), which builds a unified model library across parameters. We demonstrate these methods by learning continuum models from a noisy birth–death mean-field model and from an on-lattice agent-based model of birth, death, and migration with spatial structure, often used to investigate cell biology experiments. We show that both methods significantly reduce the relative error in recovering parameters from agent-based simulations, with OAT ME-EQL offering better generalizability across parameter space. Our findings highlight the potential of equation learning from multiple experiments to enhance the generalizability and interpretability of learned models for complex biological systems. 

Coded aperture imaging has emerged as a solution to enhance light sensitivity and enable imaging in challenging conditions. However, the computational expense of image reconstruction poses limitations in processing efficiency. To address this, we propose a direct classification method using convolutional neural networks. By leveraging raw coded measurements, our approach eliminates the need for explicit image reconstruction, reducing computational overhead. We evaluate the effectiveness of this approach compared to traditional methods on the MNIST and CIFAR10 datasets. Our results demonstrate that direct image classification using raw coded measurements achieves comparable performance to traditional methods while reducing computational overhead and enabling real-time processing. These findings highlight the potential of machine learning in enhancing the decoding process and improving the overall performance of coded aperture imaging systems. 

Abstract In response to the COVID-19 pandemic, many higher educational institutions moved their courses on-line in hopes of slowing disease spread. The advent of multiple highly-effective vaccines offers the promise of a return to “normal” in-person operations, but it is not clear if—or for how long—campuses should employ non-pharmaceutical interventions such as requiring masks or capping the size of in-person courses. In this study, we develop and fine-tune a model of COVID-19 spread to UC Merced’s student and faculty population. We perform a global sensitivity analysis to consider how both pharmaceutical and non-pharmaceutical interventions impact disease spread. Our work reveals that vaccines alone may not be sufficient to eradicate disease dynamics and that significant contact with an infectious surrounding community will maintain infections on-campus. Our work provides a foundation for higher-education planning allowing campuses to balance the benefits of in-person instruction with the ability to quarantine/isolate infectious individuals. 

We investigate methods for learning partial differential equation (PDE) models from spatio-temporal data under biologically realistic levels and forms of noise. Recent progress in learning PDEs from data have used sparse regression to select candidate terms from a denoised set of data, including approximated partial derivatives. We analyse the performance in using previous methods to denoise data for the task of discovering the governing system of PDEs. We also develop a novel methodology that uses artificial neural networks (ANNs) to denoise data and approximate partial derivatives. We test the methodology on three PDE models for biological transport, i.e. the advection–diffusion, classical Fisher–Kolmogorov–Petrovsky–Piskunov (Fisher–KPP) and nonlinear Fisher–KPP equations. We show that the ANN methodology outperforms previous denoising methods, including finite differences and both local and global polynomial regression splines, in the ability to accurately approximate partial derivatives and learn the correct PDE model.