mathematical modeling
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Investigating the nonlinear complex dynamics of the tuft cell-microbiome cross-talk: the impact of feedback loops on immune regulation, microbial modulation and response to tissue insults
Project Abstract Tuft cells (TCs) are specialized chemosensory epithelial cells that are emerging as critical regulators of intestinal homeostasis. Named over 70 years ago based on their distinct morphology, a defined function for TCs was only elucidated in the last decade. TCs in the small intestine sense succinate from helminths to initiate type 2 immune responses that mediate parasite expulsion. Recently, we discovered a novel physiologic function for TCs in the colon, where their role had been considered minimal. Succinate, a key microbial metabolite, is produced by colonic microbiota as both a precursor to other metabolites and a cross-feeding fuel source for pathogens. TCs respond to succinate by secreting interleukin-25 (IL-25), which activates type 2 cytokine- producing lymphocytes (T2Ls), amplifying TC expansion and reinforcing barrier function. We recently demonstrated that this SPB–TC–IL-25–T2L feedback loop is essential for protection against pathogen-induced colitis. Our preliminary data further suggest that TCs actively promote colonization by succinate-producing bacteria (SPBs), establishing positive feedback on TC-supporting microbes, while other epithelial cells such as goblet cells (GCs) and Paneth cells (PCs) may exert complementary or counterbalancing influences. Supported by new modeling insights, we hypothesize that these epithelial–immune–microbiome interactions form coordinated feedback loops that collectively optimize intestinal resilience. These loops may create a dynamic, multi-stable system that flexibly transitions between homeostatic and hyperplastic states, buffering against microbial fluctuations and pathogenic insults while preventing uncontrolled type 2 inflammation. Using a combination of mathematical modeling and experimental validation, we will develop a multi- layered systems framework to explore how epithelial–immune–microbial feedbacks shape resilience or breakdown in clinically relevant models of colonic infection and inflammation. Our three Aims will (1) develop, calibrate, and validate a mathematical model that integrates TCs, GCs, PCs, SPBs, and SCBs; (2) define the immunological circuits governing epithelial–microbiome equilibrium; and (3) determine how epithelial feedbacks regulate microbial community structure and resilience. In line with NIH’s new initiative to prioritize human-based research, our proposal combines computational modeling, human colonic organoids, and complementary mouse models. Organoid experiments will provide human-relevant data for model calibration, while in vivo studies validate systemic predictions, ensuring both rigor and translational relevance while minimizing reliance on animal models. This work will generate interoperable models that integrate epithelial, microbial, and immune networks, providing predictive insight into intestinal outcomes under homeostatic, infectious, and inflammatory conditions and informing therapeutic strategies for microbiome-targeted interventions.
Human memory: mathematical models and experiments
I will present my recent work on mathematical modeling of human memory. I will argue that memory recall of random lists of items is governed by the universal algorithm resulting in the analytical relation between the number of items in memory and the number of items that can be successfully recalled. The retention of items in memory on the other hand is not universal and differs for different types of items being remembered, in particular retention curves for words and sketches is different even when sketches are made to only carry information about an object being drawn. I will discuss the putative reasons for these observations and introduce the phenomenological model predicting retention curves.
Mathematical models of neurodegenerative diseases
Neurodegenerative diseases such as Alzheimer’s or Parkinson’s are devastating conditions with poorly understood mechanisms and no cure. Yet, a striking feature of these conditions is the characteristic pattern of invasion throughout the brain, leading to well-codified disease stages associated with various cognitive deficits and pathologies. How can we use mathematical modelling to gain insight into this process and, doing so, gain understanding about how the brain works? In this talk, I will show that by linking new mathematical theories to recent progress in imaging, we can unravel some of the universal features associated with dementia and, more generally, brain functions.
Dr Lindsay reads from "Models of the Mind : How Physics, Engineering and Mathematics Shaped Our Understanding of the Brain" 📖
Though the term has many definitions, computational neuroscience is mainly about applying mathematics to the study of the brain. The brain—a jumble of all different kinds of neurons interconnected in countless ways that somehow produce consciousness—has been described as “the most complex object in the known universe”. Physicists for centuries have turned to mathematics to properly explain some of the most seemingly simple processes in the universe—how objects fall, how water flows, how the planets move. Equations have proved crucial in these endeavors because they capture relationships and make precise predictions possible. How could we expect to understand the most complex object in the universe without turning to mathematics? — The answer is we can’t, and that is why I wrote this book. While I’ve been studying and working in the field for over a decade, most people I encounter have no idea what “computational neuroscience” is or that it even exists. Yet a desire to understand how the brain works is a common and very human interest. I wrote this book to let people in on the ways in which the brain will ultimately be understood: through mathematical and computational theories. — At the same time, I know that both mathematics and brain science are on their own intimidating topics to the average reader and may seem downright prohibitory when put together. That is why I’ve avoided (many) equations in the book and focused instead on the driving reasons why scientists have turned to mathematical modeling, what these models have taught us about the brain, and how some surprising interactions between biologists, physicists, mathematicians, and engineers over centuries have laid the groundwork for the future of neuroscience. — Each chapter of Models of the Mind covers a separate topic in neuroscience, starting from individual neurons themselves and building up to the different populations of neurons and brain regions that support memory, vision, movement and more. These chapters document the history of how mathematics has woven its way into biology and the exciting advances this collaboration has in store.
Deciphering the Dynamics of the Unconscious Brain Under General Anesthesia
General anesthesia is a drug-induced, reversible condition comprised of five behavioral states: unconsciousness, amnesia (loss of memory), antinociception (loss of pain sensation), akinesia (immobility), and hemodynamic stability with control of the stress response. Our work shows that a primary mechanism through which anesthetics create these altered states of arousal is by initiating and maintaining highly structured oscillations. These oscillations impair communication among brain regions. We illustrate this effect by presenting findings from our human studies of general anesthesia using high-density EEG recordings and intracranial recordings. These studies have allowed us to give a detailed characterization of the neurophysiology of loss and recovery of consciousness due to propofol. We show how these dynamics change systematically with different anesthetic classes and with age. As a consequence, we have developed a principled, neuroscience-based paradigm for using the EEG to monitor the brain states of patients receiving general anesthesia. We demonstrate that the state of general anesthesia can be rapidly reversed by activating specific brain circuits. Finally, we demonstrate that the state of general anesthesia can be controlled using closed loop feedback control systems. The success of our research has depended critically on tight coupling of experiments, signal processing research and mathematical modeling.
How to simulate and analyze drift-diffusion models of timing and decision making
My talk will discuss the use of some of these four, simple Matlab functions to simulate models of timing, and to fit models to empirical data. Feel free to examine the code and the relatively brief book chapter that explains the code before the talk if you would like to learn more about computational/mathematical modeling.
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