Parameter estimation in the Core network.

<p>A) Solved Pareto front for the Core network, showing the 3-D front (left) and projections (right 3 plots). Plotted in log space to accentuate small errors, showing: Pareto front (blue line), local solutions (red ), Pareto optimal solutions (), Anchor points (), and Utopian point (). Projection views are bounded by the relevant Anchor points, so many solved points may not be visible and scales vary (e.g. Wild Type and Behavioral values are very similar and produce a negligible front with no Pareto points other than the Anchors, 3rd from left). B) Sample of model outputs and optimally scaled surrogate data for the Pareto point closest to the Utopian, indicated by black arrows in A. Plot titles indicate measurement: experiment; relative error (). Notation as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003498#pcbi-1003498-g002" target="_blank">Figure 2A</a>.</p

Informed network comparison.

<p>A) Informed hypothetical networks, each adding elements to the Core network. * indicates an indirect interaction, potentially involving many intermediaries. Coloring as previously, with white boxes where effects are not conceptually clear. B) Solved Pareto fronts for informed hypothetical networks, including Alt1 which performs similarly to the Core. Arrows indicate the only distinguishable feature among them, where Ago1 improves over other networks, though only at one point.</p

Table of data employed to fit models.

<p>^<i>B</i>Assigned to Behavioral data category.</p

Experiment design.

<p>A) Heatmaps showing relative information gain expected from qualitative data, with experiments on the ordinate and species to measure on the abscissa. Darker boxes indicate greater information (i.e. a more preferable experiment), via expected prediction variance among models (upper), dissimilarity of Representative prediction distributions (center), or variance among Representatives (lower). B) Heatmaps showing experiment design for quantitative data. Based on local sensitivity to a parameter affecting the indicated system feature (ordinate), and ranked by variance among models of mean sensitivity (upper) or variance among Representatives (lower).</p

Estimation of representative parameters.

<p>A) Diagram of fitness quantification by Optimal Scaling. Images are mapped to qualitative data (left, image reproduced/adapted from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003498#pcbi.1003498-Li1" target="_blank">[58]</a>). Surrogate data (blue ) are chosen to best fit model outputs (green line) within intervals that match data (shaded boxes). Intervals are additionally constrained by minimum gaps and sizes. B) Diagram of the global optimization procedure. (Left) Parameter space is screened by sparse grid () and pseudo-random sampling ()A. Color indicates cost (blue: low, red: high). (Right) Multiple gradient-based searches are started from the best samples (blue ), and find local minima (blue ). Finding all minima is not guaranteed (no solution in upper right quadrant). C) Diagram of the multiobjective optimization procedure. (Left and center) Example Pareto fronts (solid line) for objectives and , showing Anchor points ( and ), and Utopian points (). (Right) Example solution via the modified NNC method, showing: Anchor points (), Utopian (), gradient search starts (), normal constraints (dashed line), gradient solutions ().</p

Naive network comparison.

<p>A) Solved Pareto fronts for naively generated networks, superimposed for comparison. Insets enlarge view near Utopian point. B) Examples of model fitness, comparing the Core network with the two closest alternatives (based on Pareto front placement) and a poor alternative. Only Alt1 remains similar to the Core on examination. Simulated from Pareto points closest to the Utopian, black arrows in A. Notation as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003498#pcbi-1003498-g003" target="_blank">Figures 3</a> and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003498#pcbi-1003498-g002" target="_blank">2A</a>.</p

Naive regulatory networks.

<p>Yellow and blue boxes refer to differentiation- and self-renewal-promoting elements, respectively.</p

Simulated experiments designed for qualitative data.

<p>Example simulated results for recommended experiments, showing for each model: qualitative interpretations (upper) and quantitative model outputs for all Representatives, normalized by the mean value to visualize all curves (lower). A) Simulations for experiments recommended directly for model discrimination. B) Simulations for an experiment recommended to first refine acceptable parameter estimates in each model.</p

Effects of Carbon Nanotube-Tethered Nanosphere Density on Amperometric Biosensing: Simulation and Experiment

Nascent nanofabrication approaches are being applied to reduce electrode feature dimensions from the microscale to the nanoscale, creating biosensors that are capable of working more efficiently at the biomolecular level. The development of nanoscale biosensors has been driven largely by experimental empiricism to date. Consequently, the precise positioning of nanoscale electrode elements is typically neglected, and its impact on biosensor performance is subsequently overlooked. Herein, we present a bottom-up nanoelectrode array fabrication approach that utilizes low-density and horizontally oriented single-walled carbon nanotubes (SWCNTs) as a template for the growth and precise positioning of Pt nanospheres. We further develop a computational model to optimize the nanosphere spatial arrangement and elucidate the trade-offs among kinetics, mass transport, and charge transport in an enzymatic biosensing scenario. Optimized model variables and experimental results confirm that tightly packed Pt nanosphere/SWCNT nanobands outperform low-density Pt nanosphere/SWCNT arrays in enzymatic glucose sensing. These computational and experimental results demonstrate the profound impact of nanoparticle placement on biosensor performance. This integration of bottom-up nanoelectrode array templating with analysis-informed design produces a foundation for controlling and optimizing nanotechnology-based electrochemical biosensor performance