Nathaniel Linden

I am currently a Ph.D. student in the Department of Mechanical and Aerospace Engineering and the Interfaces Graduate Training Programming at University of California San Diego, where I work in the labs of Boris Kramer and Padmini Rangamani. My research focuses on developing data-driven modeling and uncertainty quantification methods for systems biology. Specifically, I am interested in improving how we use experimental data to calibrate and inform mathematical models of intracellular signaling systems. To learn more about my current research, please visit the Projects page.

In 2020, I received my BS of Bioengineering with a minor in Applied Mathematics from the University of Washington in Seattle. At UW, I worked with Bing Brunton to develop a novel method to visualize spatiotemporal structures in widefield optical recordings of neural calcium activity.

News

Mar 28 2023	I will be giving a talk on my new research on multimodel modeling for clinical applications at the SOCAMS 2023 at UC Irvine in April.
Jan 15 2023	I presented a poster on my work on Bayesian inference for systems biology at the Biophysical Society 2023 Annual Meeting.
Oct 25 2022	My paper titled “Bayesian Parameter Estimation for Dynamical Models in Systems Biology” was published is PLoS Computational Biology and is available here.
Sep 30 2022	I co-organized a minisymposium on Parameter Inference and Uncertainty Quantification for Systems Biology and Medicine at the SIAM Conference on Mathematics of Data Science in San Diego, CA. Additionally, I presented my work on Bayesian parameter estimation and uncertainty quantification for systems biology.
May 21 2022	I presented my work on Bayesian parameter estimation in systems biology at the Southern California Applied Mathematics Symposium 2022 at Harvey Mudd College in Claremont, CA in May, 2022.
Apr 15 2022	I presented my work on Bayesian parameter estimation in systems biology at the 2022 SIAM Conference on Uncertainty Quantification in Atlanta, GA on April 12 - 15, 2022. My presentation was included in the minisymposium on Efficient Uncertainty Quantification with Physics-Informed and Data-Driven Models.
Apr 11 2022	My paper titled “Bayesian Parameter Estimation for Dynamical Models in Systems Biology” is available as a preprint here.
Sep 10 2021	I was accepted to join the UCSD Interfaces Training Program in Multi-scale Biology and was awarded funding through an NIH training grant.
Aug 25 2021	My paper, Go with the FLOW: visualizing spatiotemporal dynamics in optical widefield calcium imaging, with Bing Brunton, Steve Brunton, Nick Steinmetz, Bill Moody and Dennis Tabuena was published in the Journal of the Royal Society Interface.
Jul 30 2021	I was featured on the UCSD Jacobs School of Engineering blog!

Selected Publications

SIAM News

Identifiability and Sensitivity Analysis for Bayesian Parameter Estimation in Systems Biology

Linden, Nathaniel J., Rangamani, Padmini, and Kramer, Boris

SIAM News 2023

Abs Website

An ongoing challenge in systems biology—the field of computational biology that employs mathematical modeling to study signal transduction in cells—is the estimation of model parameters to constrain a model against experimental data [9]. Despite recent advances in experimental technologies, direct measurement of these parameters remains difficult. Researchers throughout the computational sciences have developed many parameter...
PLoS Comput. Biol
Bayesian parameter estimation for dynamical models in systems biology

Linden, Nathaniel J., Kramer, Boris, and Rangamani, Padmini

PLOS Computational Biology 2022

Abs Bib Website

Dynamical systems modeling, particularly via systems of ordinary differential equations, has been used to effectively capture the temporal behavior of different biochemical components in signal transduction networks. Despite the recent advances in experimental measurements, including sensor development and ‘-omics’ studies that have helped populate protein-protein interaction networks in great detail, modeling in systems biology lacks systematic methods to estimate kinetic parameters and quantify associated uncertainties. This is because of multiple reasons, including sparse and noisy experimental measurements, lack of detailed molecular mechanisms underlying the reactions, and missing biochemical interactions. Additionally, the inherent nonlinearities with respect to the states and parameters associated with the system of differential equations further compound the challenges of parameter estimation. In this study, we propose a comprehensive framework for Bayesian parameter estimation and complete quantification of the effects of uncertainties in the data and models. We apply these methods to a series of signaling models of increasing mathematical complexity. Systematic analysis of these dynamical systems showed that parameter estimation depends on data sparsity, noise level, and model structure, including the existence of multiple steady states. These results highlight how focused uncertainty quantification can enrich systems biology modeling and enable additional quantitative analyses for parameter estimation.
@article{10.1371/journal.pcbi.1010651, bibtex_show = {true}, doi = {10.1371/journal.pcbi.1010651}, author = {Linden, Nathaniel J. and Kramer, Boris and Rangamani, Padmini}, journal = {PLOS Computational Biology}, publisher = {Public Library of Science}, title = {Bayesian parameter estimation for dynamical models in systems biology}, year = {2022}, month = oct, volume = {18}, url = {https://doi.org/10.1371/journal.pcbi.1010651}, pages = {1-48}, number = {10}, selected = {true}, abbr = {PLoS Comput. Biol}, website = {https://doi.org/10.1371/journal.pcbi.1010651} }