Archives: Fall 2019 / Winter 2020 / Spring 2020 / Fall 2020 / Winter 2021 / Spring 2021 / Fall 2021 / Winter 2022 / Spring 2022 / Fall 2022 / Winter 2023 / Spring 2023 / Fall 2023 / Winter 2024

Links : Interdisciplinary Center for Quantitative Modeling in Biology (ICQMB) seminar

             UCR Math Department seminar 

In Spring 2024, the PDE & Applied Math seminar will be held through Zoom or in person (Skye 268). Specific information about the format of each talk will be provided in the email announcement and posted below. If you're interested in attending the seminar, please contact Dr. Qixuan Wang (qixuan.wang@ucr.edu) and Dr. Jia Gou (jia.gou@ucr.edu).

Spring 2024 Schedule 

Apr 03 10:00 AM (Wed) Organizational meeting

Apr 09 02:00 PM (Tue) Dr. Xiaochuan Tian (University of California, San Diego)

Apr 10 10:00 AM (Wed) Dr. Xiaoyu Shi (University of California, Irvine) , in joint with ICQMB seminar

Apr 17 10:00 AM (Wed) Dr. Elena Koslover (University of California, San Diego)

Apr 24 10:00 AM (Wed) Dr. Mykhailo Potomkin (University of California, Riverside)

May 01 10:00 AM (Wed) Dr. Paola Vera-Licona (University of Connecticut)

May 08 10:00 AM (Wed) Dr. Sean Lawley (University of Utah)

May 15  10:00 AM (Wed) Dr. Michael Blinov (University of Connecticut)

May 22 10:00 AM (Wed) Dr. Sui Tang (University of California, Santa Barbara)

May 29 10:00 AM (Wed) Dr. Paul Macklin (Indiana University)

Jun 05 10:00 AM (Wed) Mingye Gao & Minh Vu (University of California, Riverside)

Upcoming Talks:

June 5th, 2024, 10:00 AM - 10:50 AM PT 

Mingye Gao, Minh Vu (Mathematics, UCR)

Title: Modeling of hair follicle growth and cell fate decisions

Abstract: Hair follicles (HFs) are mammalian skin mini organs that are rich in stem cells and undergo cyclic growth. During the HF growth phase - anagen, a group of fast-dividing HF epithelial cells locating at the HF bottom and encompassing the mesenchymal dermal papillae, known as the matrix cells, differentiate into multiple components that form the concentric structure in the follicle stem. From inside to outside, three major layers are formed: medulla, cortex, and inner root sheath. A robust cell fate mechanism is needed to guarantee this multi branched lineage dynamics. In this talk, we present our recent modeling research on HF cell fate decisions and growth control. In the first part of this talk, we develop a multi-scale model on the HF bulb – the bottom part of an anagen HF, integrating an agent-based submodel of cell movement and divisions, and a PDE submodel for signaling dynamics. Using the model, we explore the mechanisms that regulate anagen HF bulb replenishment and the formation of the HF concentric layer. In the second part, we develop a data-driven model to study the anagen HF cell fate decisions. We extract the graph geometry of the HF epithelial cell lineage, then apply a reaction-diffusion-advection based PDE model on the graph to study the HF epithelial cell lineage dynamics, with a focus on how the intermediate cell states affect each cell fate decision. 

Past Talks:

May 29, 2024, 10:00 AM - 10:50 AM PT 

Dr. Paul Macklin (Indiana University)

Title: A new cell behavior language to rapidly capture and translate biological insights to dynamical models

Abstract: Healthy and diseased tissues—including cancer—are adaptive ecosystems that are driven by individual cell behaviors, interactions, and biophysical constraints. Traditional reductionist approaches—which study components of these systems in isolation—have yielded key insights on controlling or altering individual cell behaviors, but often fail to account for systems reactions that can ultimately render treatments ineffective. Agent-based modeling—which simulate individual cells and their interactions in dynamical environments—can serve as virtual laboratories to understand how individual cell behaviors and interactions drive emergent systems behavior. We discuss PhysiCell, our open source agent-based modeling framework, with examples drawn from COVID-19 and cancer. We also show how the complexity of agent-based models requires new thinking if they are to scale to the level needed to understand immunologic problems of interest, and show a new modeling language that facilitates more rapid and reproducible modeling, real-time modeling with user-friendly tools, and better integration of human expertise with machine learning.

Bio: Paul Macklin is a mathematician, Associate Professor of Intelligent Systems Engineering, and Associate Dean for Undergraduate Education at the Luddy School of Informatics, Computing and Engineering at Indiana University. He leads the open source PhysiCell multicellular simulation platform, and he works on developing patient-tailored models for cancer patient digital twins.

May 22, 2024, 10:00 AM - 10:50 AM PT 

Dr. Sui Tang (UC Santa Barbara)

Title: Data-driven discovery of particle-based systems with Gaussian process. 

Abstract: System of interacting particles that display a wide variety of collective behaviors are ubiquitous in science and engineering, such as self-propelled particles, flocking of birds, and milling of fish. Modeling interacting particle systems by a system of differential equations plays an essential role in exploring how individual behavior engenders collective behaviors, which is one of the most fundamental and important problems in various disciplines. Although the recent theoretical and numerical study bring a flood of models that can reproduce many macroscopical qualitative collective patterns of the observed dynamics, the quantitative study towards matching the well-developed models to observational data is scarce.

We consider the data-driven discovery of microscopic particle models with latent interactions. We propose a learning approach that models the latent interactions as Gaussian processes, which provides an uncertainty-aware modeling of interacting particle systems. We introduce an operator-theoretic framework to provide a detailed analysis of recoverability conditions, and establish statistical optimality of the proposed approach. Numerical results on prototype systems and real  fish swarming data demonstrate the effectiveness of the proposed approach.

Related papers

1. Learning particle swarm models from data with Gaussian process (with Jinchao Feng, Charles Kulick, and Yunxiang Ren), To appear at Mathematics of Computation

2. Data-Driven Model Selections of Second-Order Particle Dynamics via Integrating Gaussian Processes with Low-Dimensional Interacting Structures (with Charles Kulick,Jinchao Feng),  To appear at Special Issue ``Machine learning and dynamical systems", Physica D: Nonlinear Phenomena.

Bio: Sui Tang is an Assistant Professor in the Department of Mathematics at the University of California, Santa Barbara. She received her PhD in Mathematics from Vanderbilt University, followed by a role as Assistant Research Professor in Johns Hopkins University. In the fall of 2021, she was a visiting scientist at the Simons Institute for the Theory of Computing at UC Berkeley. Her research encompasses Statistical Learning, Harmonic Analysis, Approximation Theory, and Probability. She focuses particularly on solving data science problems at the intersection of machine learning, inverse problems, signal processing, and dynamical systems. Currently, her work is centered on utilizing data-driven approaches to effectively model complex systems and to connect theoretical insights with real-world applications.

May 15, 2024, 10:00 AM - 10:50 AM PT 

Dr. Michael Blinov (Center for Cell Analysis and Modeling, University of Connecticut School of Medicine)

Title: From simple motifs to complex phenotypes at multiple scales

Abstract: Biological regulatory networks typically contain motifs of activatory and inhibitory signals, such as positive and negative feedback.  Simple motifs often lead to complex phenotypes such as bistable responses to a signal for biological systems described by ODEs or Turing patterns for biological systems described by PDE. In this talk, we describe two models utilizing simple biological motifs and complex data. A model of aging in elderly humans suggested the existence of a robust phenotype in aging, where some individuals live longer in a healthy state. A model of pigmentation in flower petals explains the observed pigmentation patterns. We will discuss the use of machine learning to explore the parameter space of models to predict mutations corresponding to the different patterns.

Bio: Michael Blinov is an Associate Professor of Genetics at the University of Connecticut School of Medicine. He obtained his PhD in Pure Mathematics from the Weizmann Institute of Science in Israel.  He is interested in the mathematical modeling of complex biological systems ranging from cellular to organismal scale, algorithms and software for mathematical modeling, and methods for processing, storage and visualization of biological data (https://health.uconn.edu/blinov-lab/). He is one of the inventors of the rule-based modeling approach and BioNetGen software.

May 08, 2024, 10:00 AM - 10:50 AM PT 

Dr. Sean Lawley (Mathematics Department, University of Utah)

Title: Stochastics in medicine: Delaying menopause and missing drug doses

Abstract: Stochastic modeling and analysis can help answer pressing medical questions. In this talk, I will attempt to justify this claim by describing recent work on two problems in medicine. The first problem concerns ovarian tissue cryopreservation, which is a proven tool to preserve ovarian follicles prior to gonadotoxic treatments. Can this procedure be applied to healthy women to delay or eliminate menopause? How can it be optimized? The second problem concerns medication nonadherence. What should you do if you miss a dose of medication? How can physicians design dosing regimens that are robust to missed/late doses? I will describe (a) how stochastics theory offers insights into these questions and (b) the mathematical questions that emerge from this investigation. The first problem is based on joint work with Joshua Johnson (University of Colorado School of Medicine), John Emerson (Yale University), and Kutluk Oktay (Yale School of Medicine).

May 1, 2024, 10:00 AM - 10:50 AM PT 

Dr. Paola Vera-Licona (UConn Health)

Title: Unveiling Patterns of Cancer Cell Reversion: Steps Toward an Encyclopedic Understanding

Abstract: Phenotypic cancer reversion describes the remarkable process by which malignant tumor cells can revert to a benign or non-cancerous state, demonstrating decreased malignancy or resembling normal cellular behavior. This phenomenon highlights the inherent plasticity of cancer cells and offers promising therapeutic avenues by exploiting tumors' capacity to revert to a less harmful state. In this talk, we will introduce a pioneering initiative: the development of a comprehensive encyclopedia aimed at elucidating the mechanisms of cancer reversion across various cancer subtypes. Focusing on claudin-low triple-negative breast cancer, we will detail our investigative approach, emphasizing the integration of multi-omics data and advanced computational modeling. We will also outline the strategic roadmap for our ongoing research efforts, discussing the potential implications for targeted cancer therapies and improved patient outcomes.

Bio: Dr. Paola Vera-Licona is an Assistant Professor at the Center for Quantitative Medicine and the Center for Cell Analysis and Modeling at UConn Health. With a Ph.D. in Mathematics, she specializes in the design, implementation, and application of mathematical and computational tools for modeling biological networks. Her research integrates multi-omics data to develop data-driven models for cell fate determination and reprogramming in cancer and biogerontology.

April 24th, 2024, 10:00 AM - 10:50 AM PT 

Dr. Mykhailo Potomkin (Department of Mathematics, University of California, Riverside)

Title: Well-posedness of orientational dynamics of a microswimmer in nematic liquid crystal

Abstract: I will present the analysis of a nonlinear partial differential equation system describing the motion of a microswimmer in a nematic liquid crystal environment. The model was developed to elucidate how a bacterium navigates itself in biofluids with properties different from isotropic Newtonian fluid but rather those of liquid crystal. First, I will discuss the existence of the steady state corresponding to the traveling wave solution. Next, the finite-time existence of the time-dependent problem in a periodic domain will be presented. Finally, I will show how the homogenization theory can be used to capture the dynamics of a squirmer colony. This work was done jointly with L. Berlyand (Penn State U.), H. Chi (Penn State U.), and A. Yip (Purdue U.).

Bio: Dr. Potomkin is an assistant professor at UC Riverside. He previously held a postdoctoral position at the Pennsylvania State University, and he received his Ph.D. from V.N. Karazin Kharkiv National University (Ukraine). Dr. Potomkin’s area of research includes modeling, analysis, and numerical simulation of problems involving various types of differential equations, with a specific focus on problems arising in Mathematical Biology and Soft Matter Physics.    

April 09, 2024, 02:00 PM - 02:50 PM PT

Dr. Xiaochuan Tian (Department of Mathematics, University of California, San Diego)

Title: Enhancing Meshfree Methods for Solving PDEs through Nonlocal Analysis

Abstract: Meshfree and particle methods are widely used in computational studies of partial differential equations, offering many advantages compared to traditional mesh- or grid-based numerical methods.  Nevertheless, many practical questions revolve around meshfree methods, encompassing concerns about stability and accuracy.  We propose a new paradigm of designing meshfree methods for solving partial differential equations (PDEs) through nonlocal analysis, inspired by the recent development of nonlocal calculus and its applications.  We propose that the development of stable, accurate, and efficient meshfree methods relies on two key factors: (1) the formulation of well-posed continuum nonlocal models to approximate the PDE models and (2) the development of asymptotically compatible schemes for robust discretization of nonlocal models that allow a flexible coupling of the modeling and discretization parameters.  We will review several aspects of nonlocal calculus and asymptotically compatible schemes and demonstrate the idea with a monotone meshfree method for solving linear elliptic equations in non-divergence form.

April 10, 2024, 10:00 AM - 10:50 AM PT 

in joint with ICQMB seminar 

Dr. Xiaoyu Shi (Department of Developmental & Cell Biology, University of California, Irvine)

Title: Super-resolution Visualization of Organelle-organelle Interactions with Expansion Microscopy

Abstract: Expansion microscopy has revolutionized cell biology and neuroscience by unveiling intricate spatial relationships in organelles since 2015. In this talk, we'll delve into two new methods from the Xiaoyu Shi lab that enhance detection resolution in imaging organelle-organelle and protein-protein interactions. One technique is the Label-Retention Expansion Microscopy (LR-ExM), which captures molecular-resolution images of structures like the nuclear envelope, microtubules, clathrin-coated pits, mitochondria, nucleolus, and ER. The other method is the Proximity-Labeling Expansion Microscopy (PL-ExM), revealing the 3D structure of protein interactome within cells and tissues at resolutions up to 12 nm. Remarkably, these chemical techniques enable super-resolution using conventional microscopes, such as confocal and Airyscan. The Shi lab pledges to provide the science community with LR-ExM probes and protocols at no cost from now to 2025.

Apr 17, 2024, 10:00 AM - 10:50 AM PT 

Dr. Elena Koslover (Department of Physics, University of California, San Diego)

Title: Tunneling Through the Cell: Structure and Transport in Organelle Networks

Abstract: Eukaryotic cells contain a variety of complex architectures that modulate the transport, distribution, and encounter kinetics of molecular components. In this talk we will explore the emergent structure and transport properties of the peripheral endoplasmic reticulum (ER), which forms an interconnected network of tubules spanning throughout the cell.  Analytic calculations of mean first passage times, numerical reaction-diffusion simulations, and analysis of live-cell imaging data are used to demonstrate how the reticulated architecture of this organelle supports its ability to rapidly disperse and deliver proteins and calcium ions. Furthermore, we will show how a novel liquid network model, incorporating edge tension and new tubule growth, describes the emergent steady-state structure and dynamic rearrangements of the peripheral ER. The specific intracellular system discussed here highlights the role of mathematical modeling in elucidating interplay of structure and function in living cells.

Bio: Elena Koslover is a professor of physics at the University of California, San Diego. She obtained her undergraduate degrees in biology and mathematics at the California Institute of Technology, an MPhil in Chemistry from the University of Cambridge, and a PhD in Biophysics at Stanford University, where she worked on modeling genome mechanics and intracellular fluid dynamics. Her research group uses theoretical and computational techniques, together with analysis of quantitative data provided by collaborating groups, to understand how the morphology and organization of cellular structures determine the spatiotemporal distribution and interaction kinetics of intracellular components.