Archives: Spring 2021

Links : UCR Interdisciplinary Center for Quantitative Modeling in Biology

UCR Math Department seminar

PDE and Applied Math Seminar

Please contact the organizer (weitaoc [at] ucr.edu) if you are interested in attending this seminar.

Spring 2021 Schedule

March 30th Organization meeting

April 6th Dr. Lisa Davis, Montana State University

Continuum and Stochastic Models for Describing Transcription of the rrn Operon

April 13th Dr. Li-Tien Cheng, University of California, San Diego

The Binary Level-Set Method and the Shape of a Biomolecule

April 20th Dr. Celeste M. Nelson, Princeton University

The mechanics of folding tubes into lungs

April 27th Dr. Maria Rita D'Orsogna, California State University at Northridge

A mathematical model of reward-mediated learning in drug addiction

May 4th Dr. Ivana Bozic, University of Washington

Mathematical model of colorectal cancer initiation

May 11th Dr. Alan Lindsay, University of Notre Dame

Mathematics of Diffusive transport with applications to chemoreception and nuclear scaling

May 18th Dr. Min Wu, Worcester Polytechnic Institute

Mapping biophysical processes and their effects during growth and morphogenesis of cell walls and soft tissues

May 25th Dr. Daniel Lobo, University of Maryland, Baltimore County

Systems Biology of Growth and Form

June 1st Dr. Niall Mangan, Northwestern University

Data-driven methods for identifying mechanisms in complex biological systems

Talk Titles & Abstracts:

Speaker: Dr. Lisa Davis

Date: April 6th

Title: Continuum and Stochastic Models for Describing Transcription of the rrn Operon

Abstract: Bacteria are known for their ability to efficiently regulate their growth rate in response to changes in environment. The regulation of growth rate is coupled with ribosome production, and ribosome production rates depend on both transcription of rrn genes and translation of ribosomal mRNA by ribosomes themselves. In the current presentation, we focus on efforts to describe one portion of this coupled system. In fast-transcribing prokaryotic genes, such as an rrn operon, many RNA polymerases (RNAPs) transcribe the DNA simultaneously. Active elongation of RNAPs involves periods of fast forward motion that are often interrupted by pauses. In some literature, this has been observed to cause RNAP traffic jams. However, other studies indicate that elongation is faster in the presence of multiple RNAPs than elongation by a single polymerase. Several types of mathematical models have been proposed to capture the essential behaviors of this phenomena. I will give a brief overview of the essential biological quantities of interest, and the remainder of the talk will focus on two mathematical models we have proposed for characterizing this process. The first is a continuum model taking the form of a nonlinear conservation law PDE where transcriptional pausing is incorporated into the flux term with a piecewise continuous density-velocity relationship. The velocity relation is parametrized according to the user-specified (or randomly generated) spatial locations and time duration of the pauses. The second model is a stochastic one that is based on the classical TASEP model but with added complexity to account for the interactions among neighboring RNAPs that can influence local elongation velocities. I'll mention the algorithms that were used for model simulation for a series of parameter studies. If time permits, I'll discuss future directions where sensitivity with respect to model parameters is crucial for developing a better understanding of the validity of these models. In addition, we would like to combine the lessons learned from previous models into the development of a specific second order PDE formulation which allows for a richer, more adaptive density-velocity relationship.

Short Bio: Dr. Davis’s research interests are in the areas of computational mathematics, sensitivity analysis and mathematical modeling of biological systems. She studies efficient and robust computational algorithms for solving problems in various areas of applied mathematics. She has a background in finite element methods as well as finite volume methods for numerical simulation of systems governed by partial differential equations. Her research has received national funding from the NSF, DEPSCoR and AFOSR. Her most recent work is in the area of model construction and numerical simulation for bio-polymerization models. She is currently the PI on a grant focused on broadening the career pathways for doctoral students in Mathematics and Statistics through interdisciplinary research projects, internship opportunities and targeted course work and professional development called MT PEAKS. She is also the PI on a recent NSF grant focused on developing mathematical models of the ribosome assembly process.

Speaker: Dr. Li-Tien Cheng

Date: April 13th

Title: The Binary Level-Set Method and the Shape of a Biomolecule

Abstract: The problem of the shape of a biomolecule involves studying a biomolecule, comprised of solute atoms, in its natural environment of a solvent that is roughly salt water. Of interest is where the water molecules are located surrounding the biomolecule. This especially affects operations such as protein docking, which is of importance in, for example, tumor suppression. In the implicit solvation framework, the water is represented continuously, thus transforming the problem into one of finding the interface separating the biomolecule from the water, known as the solute-solvent interface. The desired location of this interface minimizes free energy, and a level-set method can be applied to this variational procedure to capture it. Such methods have been successful in other interface problems in, for example, fluid flow, materials science, image processing, and tumor growth. In implicit solvation, it can produce results comparable to those from molecular dynamics simulations, but with much faster simulation speeds, from several days down to a day. Here, we improve on this by introducing, instead, the binary level-set method, which can further speed up the simulations, from a day down to seconds, by removing the slow partial differential equation solves at the expense of accuracy. This allows us to study the protein docking process in more detail using Monte Carlo simulations, where tens of thousands of solute-solvent interfaces are generated at each step.

Short Bio: Dr. Li-Tien Cheng is a Professor of Mathematics at UCSD. He works in the area of scientific computation with an emphasis on computational partial differential equations and interface dynamics via the level-set method. He received his Ph.D. from the Department of Mathematics at UCLA in 2000.

Speaker: Dr. Celeste M. Nelson

Date: April 20th

Title: The mechanics of folding tubes into lungs

Abstract: “Our real teacher has been and still is the embryo, who is, incidentally, the only teacher who is always right.” – Viktor Hamburger

Evolution has generated an enormous diversity of biological form. Given this diversity, it is highly likely that every tissue structure that one can imagine has been built by the embryo of one species or another. We are interested in uncovering the physical (mechanical) mechanisms by which epithelial sheets fold themselves into branching tubes in the embryo, and using those mechanisms to engineer tissues in culture. Over the past half century, developmental biologists have identified several biochemical signaling pathways and genetic control mechanisms necessary for tissue morphogenesis. In parallel, biological systems must obey Newton’s laws of motion, and physical forces need to be generated in order to sculpt simple populations of cells into complex tissue forms. Inspired by the evolutionary diversity of embryonic forms, we have created microfabrication- and lithographic tissue engineering-based approaches to investigate the mechanical forces and downstream signaling pathways that are responsible for generating the airways of the lung. I will discuss how we combine these experimental techniques with computational models to uncover the physical forces that drive morphogenesis. I will also describe efforts to uncover and actuate the different physical mechanisms used to build the airways in lungs from birds, mammals, and reptiles.

Short Bio: Celeste M. Nelson is the Wilke Family Professor in Bioengineering and a Professor in the Departments of Chemical & Biological Engineering and Molecular Biology at Princeton University. She earned S.B. degrees in Chemical Engineering and Biology at MIT in 1998, a Ph.D. in Biomedical Engineering from the Johns Hopkins University School of Medicine in 2003, followed by postdoctoral training in Life Sciences at Lawrence Berkeley National Laboratory until 2007. Her laboratory specializes in using engineered tissues and computational models to understand how mechanical forces direct developmental patterning events during tissue morphogenesis and during disease progression. She has authored more than 140 peer-reviewed publications. Dr. Nelson’s contributions to the fields of tissue mechanics and morphogenesis have been recognized by a number of awards, including a Burroughs Wellcome Fund Career Award at the Scientific Interface (2007), a Packard Fellowship (2008), a Sloan Fellowship (2010), the MIT TR35 (2010), the Allan P. Colburn Award (2011), a Dreyfus Teacher-Scholar Award (2012), and a Faculty Scholar Award from the Howard Hughes Medical Institute (2016).

Speaker: Dr. Maria Rita D'Orsogna

Date: April 27th

Title: A mathematical model of reward-mediated learning in drug addiction

Abstract: We propose a mathematical model that unifies the psychiatric concepts of drug-induced incentive salience (IST), reward prediction error (RPE) and opponent process theory (OPT) to describe the emergence of addiction within substance abuse. The biphasic reward response (initially positive, then negative) of the OPT is activated by a drug-induced dopamine release, and evolves according to neuro-adaptative brain processes. Successive drug intakes enhance the negative component of the reward response, which the user compensates for by increasing the drug dose. Further neuroadaptive processes ensue, creating a positive feedback between physiological changes and user-controlled drug intake. Our drug response model can give rise to qualitatively different pathways for an initially naive user to become fully addicted. The path to addiction is represented by trajectories in parameter space that depend on the RPE, drug intake, and neuroadaptive changes. We will discuss how our model can be used to guide detoxification protocols using auxiliary substances such as methadone, to mitigate withdrawal symptoms.

Short Bio: Dr. Maria Rita D’Orsogna is a professor in Mathematics Department of California State University at Northridge and adjunct professor in Computational Medicine at UCLA. She is also Associate Director of Institute of Pure and Applied Math at UCLA. Dr. D’Orsogna got her PhD in Physics from UCLA. After that, she was a postdoctoral scholar in Chemical Engineering Department at Caltech and Mathematics Department at UCLA. Her research focuses on quantitative modeling, data analysis, numerical simulation of biological, psychological and social systems.

Speaker: Dr. Ivana Bozic

Date: May 4th

Title: Mathematical model of colorectal cancer initiation

Abstract: Cancer evolution cannot be observed directly in patients, and new methodologies are needed for obtaining a quantitative understanding of this obscure process. We developed and analyzed a stochastic model of malignant transformation in the colon that precisely quantifies the process of colorectal carcinogenesis in patients through loss of tumor suppressors APC and TP53 and gain of the KRAS oncogene. Our study employs experimentally measured mutation rates in the colon and growth advantages provided by driver mutations. We calculate the probability of a colorectal malignancy, the sizes of premalignant lesions, and the order of acquisition of driver mutations during colorectal tumor evolution. We demonstrate that the order of driver events in colorectal cancer is determined primarily by the fitness effects that they provide, rather than their mutation rates.

Short Bio: Dr. Bozic is an assistant professor in the Department of Applied Mathematics at the University of Washington. She received BSc and MA degrees in Mathematics from the University of Belgrade, Serbia, and a PhD in Mathematics from Harvard University. Dr. Bozic research interests include mathematical and computational modeling of biological systems, in particular cancer evolution, and analysis of genomic and clinical data. She is the recipient of a 2021 NSF CAREER award.

Speaker: Dr. Alan Lindsay

Date: May 11th

Title: Mathematics of Diffusive transport with applications to chemoreception and nuclear scaling

Abstract: Cells grow, divide, and move based on chemical signals received at localized surface receptors. Receptors occupy only a small fraction of the cell surface area, yet cells exhibit exquisite sensory capacity. In this talk I will describe mathematical tools that can be used to analyze the role that receptor organization or clustering plays in biophysical phenomena. This involves a wide array of techniques from asymptotic analysis, homogenization theory, computational PDEs and Bayesian statistical methodologies. I will also describe some recent work on scaling problems with particular focus on the nucleus. In this work, we aim to combine the above mentioned mathematical methods with experimental data to isolate the mechanisms controlling organelle dynamics and equilibrium size.

Short Bio: Dr. Alan Lindsay got his PhD in Applied Mathematics from University of British Columbia in 2010, followed by a postdoc training in University of Arizona and Heriot-Watt University. He became an assistant professor of Applied Mathematics in University of Notre Dame in 2013 and associated professor in 2019. His research uses computational and analytical techniques to study PDEs arising in modeling of physical and biological systems, including micro electro mechanical systems, mathematical ecology, imaging and inverse problems.

Speaker: Dr. Min Wu

Date: May 18th

Title: Mapping biophysical processes and their effects during growth and morphogenesis of cell walls and soft tissues

Abstract: Cutting-edge development in biotechnology and medicine involves reconstructing cells, tissues, and organs. Mapping biophysical processes and their effects during the growth and morphogenesis of cells and tissues can aid in understanding and accelerating this work. In this talk, I will first discuss our theoretical and computational efforts to understand the cellular control of wall expansion and shape regulation by mapping the distribution of biophysical properties such as cell wall elastic moduli, cell wall extension rate, and new material addition rate from exocytosis. Then, I will introduce our new mathematical model to describe the growth and morphogenesis of large-scale soft living tissues and discuss its application in understanding tumor spheroid growth undergoing external compression. This model captures soft tissues’ elastic and fluidic properties and growth dynamics in response to chemomechanical stimuli. I will conclude the talk with our ongoing study in planar tissue growth and morphogenesis.

Short Bio: Dr. Min Wu is an Assistant Professor at the Department of Mathematical Sciences, Worcester Polytechnic Institute and Bioinformatics and Computational Biology Program. Her research centers on the development of mathematical models and numerical methods to understand growth and morphogenesis in living systems. She obtained her Ph.D from the Department of Mathematics at UC Irvine in 2012. After graduation, she has been a Postdoctoral Researcher at the LPS, École Normale Supérieure, Paris from 2013-2014, and has been a Visiting Assistant Professor at the ESAM, Northwestern U from 2015-2017.

Speaker: Dr. Daniel Lobo

Date: May 25th

Title: Systems Biology of Growth and Form

Abstract: Extracting mechanistic knowledge from spatial and temporal phenotypes is a current challenge due to the complexity of biological regulation and their feedback loops. Furthermore, these regulatory interactions can include biophysical forces shaping a developing organism, creating complex interactions responsible for emergent patterns and forms. In this talk I’ll present how an approach combining computational and molecular systems biology can aid in the understanding of biological growth and form from a mechanistic perspective. This methodology integrates the mathematical modeling of gene regulation, metabolic networks, and tissue growth and patterning with dynamical systems, the automatic reverse engineering of parameters or complete equations from phenotypic data with machine learning, and the generation of precise computational predictions that can be tested at the bench. We have successfully applied this approach to obtain mechanistic insights in developmental, cancer, and synthetic biology.

Short Bio: Dr. Daniel Lobo is an Assistant Professor at the University of Maryland, Baltimore County. He obtained his PhD in Computer Science from the University of Malaga in Spain, and completed a postdoc in Developmental, Regenerative, and Cancer Biology at Tufts University. His research in systems biology aims to understand, control, and design the dynamic regulatory mechanisms governing complex biological processes. To this end, his lab develops new computational methods, mathematical models, and formalized databases together with molecular assays at the bench to reverse-engineer biological mechanisms from experimental data and design new regulatory networks for specific functions. They seek to discover the mechanisms of development and regeneration, find therapies for cancer and other diseases, and streamline the application of systems and synthetic biology. Dr. Lobo received an Outstanding Investigator Award (R35) in 2020 from the National Institutes of Health and his work has been featured in popular media such as PBS, Popular Mechanics, and Wired.

Speaker: Dr. Niall M Mangan

Date: June 1st

Title: Data-driven methods for identifying mechanisms in complex biological systems

Abstract: Inferring the structure and dynamical interactions of complex biological systems is critical to understanding and controlling their behavior. I am interested in discovering mechanistic informative models, assuming I have time-series data of important state variables and knowledge of the possible types of interactions between state variables. The problem is then selecting which interactions, or model terms, are most likely responsible for the observed dynamics. Several challenges make model selection difficult including nonlinearities and unmeasured state variables. I will discuss methods for reframing these problems so that sparse model selection is possible. I will discuss preliminary results on parameter estimation, model selection, and experimental design to characterize a spatially organized metabolism pathway in bacteria and generic chaotic systems. Parameter estimation and model selection are challenging in these cases because only some of the metabolite pools or state variables can be measured and the other variables are hidden or latent. We use a combination of data assimilations techniques and sparse optimization to perform model selection. Experimental design is enabled through sensitivity analysis of the model manifold.

Short Bio: Dr. Niall M. Mangan received the Dual BS degrees in mathematics and physics, with a minor in chemistry, from Clarkson University, Potsdam, NY, USA, in 2008, and the PhD degree in systems biology from Harvard University, Cambridge, MA, USA, in 2013. Dr. Mangan worked as a postdoctoral associate in the Photovoltaics Lab at MIT from 2013-2015 and as an Acting Assistant Professor at the University of Washington, Seattle from 2016-2017. She is currently an Assistant Professor of engineering sciences and applied mathematics with Northwestern University, where she works at the interface of mechanistic modeling and data-driven statistical inference. Her group applies these methods to biological, chemical, and material problems.