Links :  UCR Interdisciplinary Center for Quantitative Modeling in Biology

     UCR Math Department seminar

               PDE and Applied Math Seminar

The format of the seminar is hybrid. One might join the seminars in Skye Hall 361 (unless another location is announced for a specific talk) or online through Zoom (unless the talk is joint with the departmental colloquium). Please contact Dr. Yiwei Wang(yiweiw@ucr.edu) if you are interested in attending this seminar in the spring quarter.

Spring 2024 

April 2, 2:00 PM,  (Zoom) Dr. Tracy Stepien (University of Florida)

April 3, 4:00 PM (Skye 284, Colloquium),  Dr. Bjorn Birnir (University of California, Santa Barbara)

April 10, 10:00 AM (unusual time, Skye 268),  Dr. Xiaoyu Shi (University of California, Irvine)

April 16, 2:00 PM, (Zoom) Dr. Leili Shahriyari (University of Massachusetts, Amherst)

April 30, 2:00 PM,  (Zoom) Dr. Mengyang Gu (University of California, Santa Barbara)

May 14, 2:00 PM, (Zoom)  Dr. Rolf J. Ryham (Fordham University)

May 21, 2:00 PM, (Zoom) Dr. Pei Liu (Florida Institute of Technology)

May 28, 2:00 PM, (Zoom)  Dr. Nina Miolane (University of California, Santa Barbara)

Jun 4, 2:00 PM, (Sky 361) Dr. Min-Jhe Lu (University of California, Irvine)

Upcoming talks:

May 21, 2024, 02:00 PM - 03:00 PM Pacific Time

Dr.Pei Liu, Florida Institute of Technology

Title: Liquid Crystal Structure of DNA in Bacteriophage Capsids

Abstract: Bacteriophages densely pack their long dsDNA genome inside a protein capsid. The conformation of the viral genome inside the capsid is consistent with a hexagonal liquid crystalline structure. Experiments have confirmed that the details of the hexagonal packing depend on the electrochemistry of the capsid and its environment.

In this talk, I will introduce how we develop a mathematical model and analyze the model to study the equilibrium configurations of ds-DNA in a viral capsid. In our approach, the DNA is described by a unit helical vector field, tangent to an associated center curve, passing through properly selected locations. We postulate an expression for the energy of the encapsulated DNA based on that of columnar chromonic liquid crystals. A thorough analysis of the Euler-Lagrange equations yields multiple solutions to the corresponding boundary value problems. We demonstrate that there is a trivial, non-helical solution, together with two other solutions with nonzero helicity of the opposite sign. Using bifurcation analysis, we derive the conditions for local stability of such solutions and determine when the preferred coiling state is helical. The relevant bifurcation parameters are the ratio of the twist versus the bend moduli of DNA and the ratio between the sizes of the ordered and the disordered regions. The DNA curve is then reconstructed through integrating the tangent vector field, with some stochastic noise. 

Previous talks:

April 2, 2024, 02:00 PM - 03:00 PM Pacific Time

Dr. Tracy Stepien, University of Florida

Title: An approximate Bayesian computation approach for embryonic astrocyte migration model selection

Zoom

Abstract: During embryonic development of the retina of the eye, astrocytes, a type of glial cell, migrate over the retinal surface and form a dynamic mesh. This mesh then serves as scaffolding for blood vessels to form the retinal vasculature network that supplies oxygen and nutrients to the inner portion of the retina. Astrocyte spreading proceeds in a radially symmetric manner over the retinal surface. Additionally, astrocytes mature from astrocyte precursor cells (APCs) to immature perinatal astrocytes (IPAs) during this embryonic stage. We extend a previously developed continuum model that describes tension-driven migration and oxygen and growth factor influenced proliferation and differentiation. Comparing numerical simulations to experimental data, we identify model equation components that can be removed via model comparison using approximate Bayesian computation (ABC). Our results verify experimental studies indicating that choroid oxygen supply plays a negligible role in promoting differentiation of APCs into IPAs and in promoting IPA proliferation, and the hyaloid artery oxygen supply and APC apoptosis play negligible roles in astrocyte spreading and differentiation.

April 3, 2024, 04:00 PM - 05:00 PM Pacific Time

Dr. Bjorn Birnir, University of California, Santa Barbara.

Title: The Statistical Theory of Angiogenesis.

Location is  Skye 284

Abstract: Angiogenesis is a multiscale process by which a primary blood vessel issues secondary vessel sprouts that reach regions lacking oxygen. Angiogenesis can be a natural process of organ growth and development or a pathological one induced by a cancerous tumor. A mean-field approximation for a stochastic model of angiogenesis consists of a partial differential equation (PDE) for the density of active 

vessel tips. Addition of Gaussian and jump noise terms to this equation produces a stochastic PDE that defines an infinite-dimensional Lévy process and is the basis of a statistical theory of angiogenesis. The associated functional equation has been solved and the invariant measure obtained. The results of this theory are compared to direct numerical simulations of the underlying angiogenesis model. The invariant measure and the moments are functions of a Korteweg–de Vries-like soliton, which approximates the deterministic density of active vessel tips.

April 10, 2024, 10:00 AM - 11:00 AM Pacific Time

Dr. Xiaoyu Shi, UC Irvine

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

Skye 268

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 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.

April 16, 2024, 02:00 PM - 03:00 PM Pacific Time

Dr. Leili Shahriyari, University of Massachusetts Amherst

Title: Exploring Personalized Cancer Treatment: Integrating Digital Twins and Quantitative Systems Pharmacology

zoom

Abstract: The exploration of digital twins in the context of cancer treatment presents an emerging approach aimed at enhancing our understanding of cancer's individualized progression and treatment response. Our work is an initial step towards integrating advanced computational techniques, including mechanistic modeling, artificial intelligence, and stochastic processes, to develop a foundational digital twin framework. This framework endeavors to utilize a broad range of data, from molecular biology and clinical diagnostics to patient electronic health records, with the goal of providing more personalized treatment insights.

Central to our approach is the adaptation of a mechanistic model informed by quantitative systems pharmacology (QSP), a computational method with potential in drug response analysis. One of the notable challenges in QSP modeling is the accurate calibration of model parameters, which traditionally rely on broad data sources that may not account for individual patient variability.

Our approach seeks to contribute to this field by focusing on individual patient data to refine model parameters, aiming for a more personalized digital twin representation. Through sensitivity analysis and uncertainty quantification, we attempt to understand the complex interactions within the model, striving to improve the reliability of our predictions. This effort to personalize the QSP model, while still in its early stages, is driven by a desire to better understand the intricate network of cellular and molecular interactions in cancer and to provide insights that may eventually support more tailored treatment strategies. Our work represents a cautious step forward in the pursuit of personalized medicine in oncology, acknowledging the vast complexities and challenges that lie ahead.

April 30, 2024, 02:00 PM - 03:00 PM Pacific Time

Dr. Mengyang Gu, University of California, Santa Barbara

Title: Fast ab initio uncertainty quantification for soft and active matter

Zoom

Abstract: Estimating parameters from data is a fundamental problem, which is customarily done by minimizing a loss function between a model and observed statistics. In this talk, we discuss another paradigm termed the ab initio uncertainty quantification (AIUQ) method, for improving loss-minimization estimation in two steps. In step one, we define a probabilistic generative model from the beginning of data processing, and show the equivalence between loss-minimization estimation and a statistical estimator. In step two, we develop better models or estimators, such as the maximum marginal likelihood or Bayesian estimators by marginalizing out random components to improve estimation. Furthermore, we develop scalable methods for computing large matrix multiplication and inversion, to overcome the primary computational bottleneck of efficient estimation in science. To illustrate, we introduce two approaches to estimate dynamical systems, one in Fourier analysis of microscopy videos, and the other in inversely estimating the particle interaction kernel from trajectory. In the first approach, we utilized the Fast Fourier transform and generalized Schur method, and in the second approach, we developed a new method called the inverse Kalman filter and integrated it into the conjugate gradient algorithm for accelerating the computation. We achieved pseudolinear computational complexity with respect to the number of observations, with nearly no approximation in both approaches. These new approaches outline a wide range of applications, such as probing optically dense systems, automated determination of gelation time, and estimating cellular interaction and alignment dynamics for fibroblasts on liquid-crystalline substrates.

[1] Gu, M., He, Y., Liu, X., & Luo, Y. (2023). Ab initio uncertainty quantification in scattering analysis of microscopy. arXiv preprint arXiv:2309.02468.

[2] Gu, M., Liu, X., Fang, X., & Tang, S. (2022). Scalable marginalization of correlated latent variables with applications to learning particle interaction kernels. The New England Journal of Statistics in Data Science, 1(2), 172-186,

[3] Gu, M., Fang, X., & Luo, Y. (2023). Data-driven model construction for anisotropic dynamics of active matter. PRX Life, 1(1), 013009

May 14, 2024, 02:00 PM - 03:00 PM Pacific Time

Dr. Rolf J. Ryham, Fordham University

Title: Continuous and Particle-based Approaches to Lipid Bilayer Membranes

Abstract: Lipid bilayer membranes are composed of elongated, amphiphilic molecules that align to shield a hydrophobic core from water.  The first part of the talk will shed light on some unsettled questions concerning Helfrich-type energies used in continuum mechanical studies of bilayers.  In the second part of the talk, motivated by the need to permit for topological changes, self-assembly of amphiphiles as Janus particles under a hydrophobic attraction potential is considered (SIAM J. Multiscale Modeling, 2020, J. Fluid Mech., 2022, Phys. Rev. Fluids, 2023).  The particle-based, hydrodynamic simulations are consistent with continuum vesicle hydrodynamics, and yield further questions in mathematical analysis.