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

Jun 22 2023	I am excited to learn more about optimal transport and normalizing flows at the Uncertainty Quantification Summer School in August, 2023!
Jun 22 2023	Looking forward to presenting my work on model averaging to account for model uncetainty when making predictions from blood glucose and insulin measurements in Diabetes at the Society for Mathematical Biology Annual Meeting in July 2023.
Jun 19 2023	Our paper on uncertainty quantification for progression damage simulation of composite materials was accepted in Composite Structures (link). This work part of an international collaboration, including Jonnahes Reiner at Deakin University, Navid Zobeiry at the University of Washington, Reza Vaziri at the University of British Columbia, and my advisor Boris Kramer at UCSD.
Jun 16 2023	I presented my current work on applications of Bayesian parameter estimation to study intracellular AMP-activated protein kinase signaling at the National Institutes of Health, National Institute of Bioimaging and Bioengineering (NIH NIBIB) Training Grantees Meeting in Bethesda, MD.
Jun 10 2023	I completed my first year of volunteer tutoring at the Preuss School UCSD. Throughout the school year, I had to the opportunity to support students in a 7th grade science classroom! I am looking forward to continuing this work next school year.
Mar 28 2023	I gave a talk on my 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.

Selected Publications

Compos Struct

Bayesian parameter estimation for the inclusion of uncertainty in progressive damage simulation of composites

Reiner, Johannes, Linden, Nathaniel, Vaziri, Reza, Zobeiry, Navid, and Kramer, Boris

Composite Structures 2023

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Despite gradual progress over the past decades, the simulation of progressive damage in composite laminates remains a challenging task, in part due to inherent uncertainties of material properties. This paper combines three computational methods—finite element analysis (FEA), machine learning and Markov Chain Monte Carlo—to estimate the probability density of FEA input parameters while accounting for the variation of mechanical properties. First, 15,000 FEA simulations of open-hole tension tests are carried out with randomly varying input parameters by applying continuum damage mechanics material models. This synthetically-generated data is then used to train and validate a neural network consisting of five hidden layers and 32 nodes per layer to develop a highly efficient surrogate model. With this surrogate model and the incorporation of statistical test data from experiments, the application of Markov Chain Monte Carlo algorithms enables Bayesian parameter estimation to learn the probability density of input parameters for the simulation of progressive damage evolution in fibre reinforced composites. This methodology is validated against various open-hole tension test geometries enabling the determination of virtual design allowables.
SIAM News

Identifiability and Sensitivity Analysis for Bayesian Parameter Estimation in Systems Biology

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

SIAM News 2023

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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, Kramer, Boris, and Rangamani, Padmini

PLOS Computational Biology 2022

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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 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} }