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Texas A&M University
Mathematics

Mathematical Biology Seminar

Spring 2025

 

Date:March 6, 2025
Time:4:00pm
Location:BLOC 302
Speaker:Chuliang Song, UCLA
Title:Observer invariance: a meta-law for ecological models
Abstract:The dynamics of an ecological model should remain unchanged if we choose to group identical individuals within a species into subspecies. This fundamental constraint, which we call observer invariance, necessarily holds because individuals interact via their traits and not some abstract notion of ``species identity''. While the principle looks self-evident, we show that many models in common use violate observer invariance. This exposes an implicit assumption of hidden trait differences between species that often leads to strong niche differentiation. We meticulously examine the root causes of these violations across various levels of ecological interaction (intraspecific, pairwise interspecific, and higher-order), and offer corresponding recipes for restoring observer invariance.

Date:April 10, 2025
Time:3:00pm
Location:BLOC 628
Speaker:Gregory Reeves, Texas A&M University (Chemical Engineering)
Title:Analysis of fluctuation spectroscopy methods for systems biology
Abstract:Human health depends crucially on the ability of our cells to integrate extracellular information (e.g., cell-cell signaling) to make proper decisions, such as in stem cell differentiation and tissue development. My current focus is to deduce the rules of cell-cell signaling to advance signaling-based therapies. To approach this goal, my lab synergizes quantitative measurements in live tissues together with mechanistic computational modeling. In this talk, I will first discuss a huge conundrum in systems biology: On the one hand, models are needed to make sense of the high volume of experimental data. On the other, the sheer number of unknown model parameters significantly reduces the utility of models. To overcome this challenge, I will next discuss the mathematical analysis of data from raster image correlation spectroscopy (RICS), which is a derivative of the better-known fluorescence correlation spectroscopy (FCS). Finally, I will frame these results in the context of the Drosophila melanogaster (fruit fly) NF-κB/Dorsal signaling pathway. Studying the fruit fly has many advantages, such as a simple geometry, a short life cycle, and advanced tools for imaging, genetics, and transgenesis. These advantages make Drosophila the premiere model organism for quantitative and computational studies of tissue development. Furthermore, given that most signaling pathways, including NF-κB/Dorsal, are highly conserved from flies to humans, studying fruit flies as a model organism is relevant to all animals. Our work on signaling and differentiation in fruit flies aligns with my long-term goal: to deduce the rules of life in multicellular biology, aiding the design of therapies for human health.

Date:April 17, 2025
Time:3:00pm
Location:BLOC 628
Speaker:Jiaxin Jin, University of Louisiana at Lafayette
Title:Infinitesimal Homeostasis in Mass-Action Systems
Abstract:Homeostasis occurs in a biological system when a chosen output variable remains approximately constant despite changes in an input variable. In this work we specifically focus on biological systems which may be represented as chemical reaction networks and consider their infinitesimal homeostasis, where the derivative of the input-output function is zero. The specific challenge of chemical reaction networks is that they often obey various conservation laws complicating the standard input-output analysis. We derive several results that allow to verify the existence of infinitesimal homeostasis points both in the absence of conservation and under conservation laws where conserved quantities serve as input parameters. In particular, we introduce the notion of infinitesimal concentration robustness, where the output variable remains nearly constant despite fluctuations in the conserved quantities. We provide several examples of chemical networks which illustrate our results both in deterministic and stochastic settings.

Date:April 24, 2025
Time:4:00pm
Location:BLOC 306
Speaker:Razeen Shaikh, Texas A&M University (Chemical Engineering)
Title:Optimal performance objectives in the highly conserved bone morphogenetic protein signaling pathway
Abstract:Throughout development, complex networks of cell signaling pathways drive cellular decision-making across different tissues and contexts. The transforming growth factor β (TGF-β) pathways, including the BMP/Smad pathway, play crucial roles in determining cellular responses. However, as the Smad pathway is used reiteratively throughout the life cycle of all animals, its systems-level behavior varies from one species or context to another, despite protein sequences and pathway connectivity remaining almost perfectly conserved. For instance, the Smad pathway has the flexibility to enact a rapid response in some cell types, but a high-noise-filtering response in others. Our work examines how the BMP-Smad pathway balances trade-offs among three such systems-level behaviors, or “Performance Objectives (POs)”: response speed, noise amplification, and the sensitivity of pathway output to receptor input. Using a mathematical model of the Smad pathway fit to human cell data, we show that varying non-conserved parameters (NCPs), such as protein concentrations, the Smad pathway can be tuned to emphasize any of the three POs and that the concentration of nuclear phosphatase has the greatest effect on tuning the POs. However, due to competition among the POs, the pathway cannot simultaneously optimize all three, but at best must balance trade-offs among the POs. We applied the multi-objective optimization concept of the Pareto Front, a widely used concept in economics, to identify optimal trade-offs among the various requirements. We show that the BMP pathway efficiently balances competing POs across species and is largely Pareto optimal. Finally, we validate the relationship between relative phosphatase levels and approximate BMP signaling response time for three biological systems: Human Aorta, Zebrafish embryo and Drosophila embryo. Our findings reveal that varying the concentration of NCPs allows the Smad signaling pathway to generate a diverse range of POs. This insight identifies how signaling pathways can be optim