Nathaniel Linden

Selected Publications

1. 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}
   }

2. J.R.Soc.Interface

   Go with the FLOW: visualizing spatiotemporal dynamics in optical widefield calcium imaging

   Linden, Nathaniel J, Tabuena, Dennis R, Steinmetz, Nicholas A, Moody, William J, Brunton, Steven L, and Brunton, Bingni W

   J. R. Soc. Interface 2021

   Abs Bib Website

   Widefield calcium imaging has recently emerged as a powerful experimental technique to record coordinated large-scale brain activity. These measurements present a unique opportunity to characterize spatiotemporally coherent structures that underlie neural activity across many regions of the brain. In this work, we leverage analytic techniques from fluid dynamics to develop a visualization framework that highlights features of flow across the cortex, mapping wavefronts that may be correlated with behavioural events. First, we transform the time series of widefield calcium images into time-varying vector fields using optic flow. Next, we extract concise diagrams summarizing the dynamics, which we refer to as FLOW (flow lines in optical widefield imaging) portraits. These FLOW portraits provide an intuitive map of dynamic calcium activity, including regions of initiation and termination, as well as the direction and extent of activity spread. To extract these structures, we use the finite-time Lyapunov exponent technique developed to analyse time-varying manifolds in unsteady fluids. Importantly, our approach captures coherent structures that are poorly represented by traditional modal decomposition techniques. We demonstrate the application of FLOW portraits on three simple synthetic datasets and two widefield calcium imaging datasets, including cortical waves in the developing mouse and spontaneous cortical activity in an adult mouse.

   @article{Linden2021-FLOW,
     bibtex_show = {true},
     title = {Go with the {FLOW}: visualizing spatiotemporal dynamics in
                   optical widefield calcium imaging},
     author = {Linden, Nathaniel J and Tabuena, Dennis R and Steinmetz, Nicholas A and Moody, William J and Brunton, Steven L and Brunton, Bingni W},
     journal = {J. R. Soc. Interface},
     volume = {18},
     number = {181},
     pages = {20210523},
     month = aug,
     year = {2021},
     keywords = {coherent structures; computational neuroscience; dynamical
                   systems; finite-time Lyapunov exponents; widefield calcium
                   imaging},
     language = {en},
     abbr = {J.R.Soc.Interface},
     website = {http://dx.doi.org/10.1098/rsif.2021.0523},
     selected = {true}
   }