arXiv subjects

Kevin S. Brown

Publications and source records attributed to Kevin S. Brown.

6 recordsLinked to original sources

arXiv2022

Analysis of sloppiness in model simulations: unveiling parameter uncertainty when mathematical models are fitted to data

This work introduces a comprehensive approach to assess the sensitivity of model outputs to changes in parameter values, constrained by the combination of prior beliefs and data. This novel approach identifies stiff parameter combinations strongly affecting the quality of the model-data fit while simultaneously revealing which of these key parameter combinations are informed primarily by the data or are also substantively influenced by the priors. We focus on the very common context in complex systems where the amount and quality of data are low compared to the number of model parameters to be collectively estimated, and showcase the benefits of this technique for applications in biochemistry, ecology, and cardiac electrophysiology. We also show how stiff parameter combinations, once identified, uncover controlling mechanisms underlying the system being modeled and inform which of the model parameters need to be prioritized in future experiments for improved parameter inference from collective model-data fitting.

stat.ME↗

arXiv2018

Universal Features in Phonological Neighbor Networks

Human speech perception involves transforming a countinous acoustic signal into discrete linguistically meaningful units, such as phonemes, while simultaneously causing a listener to activate words that are similar to the spoken utterance and to each other. The Neighborhood Activation Model (NAM~\cite{Luce:1986,Luce:1998}) posits that phonological neighbors (two forms [words] that differ by one phoneme) compete significantly for recognition as a spoken word is heard. This definition of phonological similarity can be extended to an entire corpus of forms to produce a phonological neighbor network~\cite{Vitevitch:2008} (PNN). We study PNNs for five languages: English, Spanish, French, Dutch, and German. Consistent with previous work, we find that the PNNs share a consistent set of topological features. Using an approach that generates random lexicons with increasing levels of phonological realism, we show that even random forms with minimal relationship to any real language, combined with only the empirical distribution of language-specific phonological form lengths, are sufficient to produce the topological properties observed in the real language PNNs. The resulting pseudo-PNNs are insensitive to the level of lingusitic realism in the random lexicons but quite sensitive to the shape of the form length distribution. We therefore conclude that "universal" features seen across multiple languages are really string universals, not language universals, and arise primarily due to limitations in the kinds of networks generated by the one-step neighbor definition. Taken together, our results indicate that caution is warranted when linking the dynamics of human spoken word recognition to the topological properties of PNNs, and that the investigation of alternative similarity metrics for phonological forms should be a priority.

q-bio.NC↗

arXiv2007

Universally Sloppy Parameter Sensitivities in Systems Biology

Quantitative computational models play an increasingly important role in modern biology. Such models typically involve many free parameters, and assigning their values is often a substantial obstacle to model development. Directly measuring \emph{in vivo} biochemical parameters is difficult, and collectively fitting them to other data often yields large parameter uncertainties. Nevertheless, in earlier work we showed in a growth-factor-signaling model that collective fitting could yield well-constrained predictions, even when it left individual parameters very poorly constrained. We also showed that the model had a `sloppy' spectrum of parameter sensitivities, with eigenvalues roughly evenly distributed over many decades. Here we use a collection of models from the literature to test whether such sloppy spectra are common in systems biology. Strikingly, we find that every model we examine has a sloppy spectrum of sensitivities. We also test several consequences of this sloppiness for building predictive models. In particular, sloppiness suggests that collective fits to even large amounts of ideal time-series data will often leave many parameters poorly constrained. Tests over our model collection are consistent with this suggestion. This difficulty with collective fits may seem to argue for direct parameter measurements, but sloppiness also implies that such measurements must be formidably precise and complete to usefully constrain many model predictions. We confirm this implication in our signaling model. Our results suggest that sloppy sensitivity spectra are universal in systems biology models. The prevalence of sloppiness highlights the power of collective fits and suggests that modelers should focus on predictions rather than on parameters.

q-bio.QM↗

arXiv2006

Optimal experimental design in an EGFR signaling and down-regulation model

We apply the methods of optimal experimental design to a differential equation model for epidermal growth factor receptor (EGFR) signaling, trafficking, and down-regulation. The model incorporates the role of a recently discovered protein complex made up of the E3 ubiquitin ligase, Cbl, the guanine exchange factor (GEF), Cool-1 (Beta-Pix), and the Rho family G protein Cdc42. The complex has been suggested to be important in disrupting receptor down-regulation. We demonstrate that the model interactions can accurately reproduce the experimental observations, that they can be used to make predictions with accompanying uncertainties, and that we can apply ideas of optimal experimental design to suggest new experiments that reduce the uncertainty on unmeasurable components of the system.

q-bio.MN↗

arXiv2006

The sloppy model universality class and the Vandermonde matrix

In a variety of contexts, physicists study complex, nonlinear models with many unknown or tunable parameters to explain experimental data. We explain why such systems so often are sloppy; the system behavior depends only on a few `stiff' combinations of the parameters and is unchanged as other `sloppy' parameter combinations vary by orders of magnitude. We contrast examples of sloppy models (from systems biology, variational quantum Monte Carlo, and common data fitting) with systems which are not sloppy (multidimensional linear regression, random matrix ensembles). We observe that the eigenvalue spectra for the sensitivity of sloppy models have a striking, characteristic form, with a density of logarithms of eigenvalues which is roughly constant over a large range. We suggest that the common features of sloppy models indicate that they may belong to a common universality class. In particular, we motivate focusing on a Vandermonde ensemble of multiparameter nonlinear models and show in one limit that they exhibit the universal features of sloppy models.

cond-mat.stat-mech↗

arXiv2004

The statistical mechanics of complex signaling networks : nerve growth factor signaling

It is becoming increasingly appreciated that the signal transduction systems used by eukaryotic cells to achieve a variety of essential responses represent highly complex networks rather than simple linear pathways. While significant effort is being made to experimentally measure the rate constants for individual steps in these signaling networks, many of the parameters required to describe the behavior of these systems remain unknown, or at best, estimates. With these goals and caveats in mind, we use methods of statistical mechanics to extract useful predictions for complex cellular signaling networks. To establish the usefulness of our approach, we have applied our methods towards modeling the nerve growth factor (NGF)-induced differentiation of neuronal cells. Using our approach, we are able to extract predictions that are highly specific and accurate, thereby enabling us to predict the influence of specific signaling modules in determining the integrated cellular response to the two growth factors. We show that extracting biologically relevant predictions from complex signaling models appears to be possible even in the absence of measurements of all the individual rate constants. Our methods also raise some interesting insights into the design and possible evolution of cellular systems, highlighting an inherent property of these systems wherein particular ''soft'' combinations of parameters can be varied over wide ranges without impacting the final output and demonstrating that a few ''stiff'' parameter combinations center around the paramount regulatory steps of the network. We refer to this property -- which is distinct from robustness -- as ''sloppiness.''

q-bio.MN↗