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.Comment: Submitted to PLoS Computational Biology. Supplementary Information available in "Other Formats" bundle. Discussion slightly revised to add historical contex

Measurements of the Solid-body Rotation of Anisotropic Particles in 3D Turbulence

We introduce a new method to measure Lagrangian vorticity and the rotational dynamics of anisotropic particles in a turbulent fluid flow. We use 3D printing technology to fabricate crosses (two perpendicular rods) and jacks (three mutually perpendicular rods). Time-resolved measurements of their orientation and solid-body rotation rate are obtained from stereoscopic video images of their motion in a turbulent flow between oscillating grids with $R_\lambda$=$91$. The advected particles have a largest dimension of 6 times the Kolmogorov length, making them a good approximation to anisotropic tracer particles. Crosses rotate like disks and jacks rotate like spheres, so these measurements, combined with previous measurements of tracer rods, allow experimental study of ellipsoids across the full range of aspect ratios. The measured mean square tumbling rate, $\langle \dot{p}_i \dot{p}_i \rangle$, confirms previous direct numerical simulations that indicate that disks tumble much more rapidly than rods. Measurements of the alignment of crosses with the direction of the solid-body rotation rate vector provide the first direct observation of the alignment of anisotropic particles by the velocity gradients of the flow.Comment: 15 pages, 7 figure

Inversion of stellar statistics equation for the Galactic Bulge

A method based on Lucy (1974, AJ 79, 745) iterative algorithm is developed to invert the equation of stellar statistics for the Galactic bulge and is then applied to the K-band star counts from the Two-Micron Galactic Survey in a number of off-plane regions (10 deg.>|b|>2 deg., |l|<15 deg.). The top end of the K-band luminosity function is derived and the morphology of the stellar density function is fitted to triaxial ellipsoids, assuming a non-variable luminosity function within the bulge. The results, which have already been outlined by Lopez-Corredoira et al.(1997, MNRAS 292, L15), are shown in this paper with a full explanation of the steps of the inversion: the luminosity function shows a sharp decrease brighter than M_K=-8.0 mag when compared with the disc population; the bulge fits triaxial ellipsoids with the major axis in the Galactic plane at an angle with the line of sight to the Galactic centre of 12 deg. in the first quadrant; the axial ratios are 1:0.54:0.33, and the distance of the Sun from the centre of the triaxial ellipsoid is 7860 pc. The major-minor axial ratio of the ellipsoids is found not to be constant. However, the interpretation of this is controversial. An eccentricity of the true density-ellipsoid gradient and a population gradient are two possible explanations. The best fit for the stellar density, for 1300 pc<t<3000 pc, are calculated for both cases, assuming an ellipsoidal distribution with constant axial ratios, and when K_z is allowed to vary. From these, the total number of bulge stars is ~ 3 10^{10} or ~ 4 10^{10}, respectively.Comment: 19 pages, 23 figures, accepted in MNRA

Oriented tensor reconstruction: tracing neural pathways from diffusion tensor MRI

In this paper we develop a new technique for tracing anatomical fibers from 3D tensor fields. The technique extracts salient tensor features using a local regularization technique that allows the algorithm to cross noisy regions and bridge gaps in the data. We applied the method to human brain DT-MRI data and recovered identifiable anatomical structures that correspond to the white matter brain-fiber pathways. The images in this paper are derived from a dataset having 121x88x60 resolution. We were able to recover fibers with less than the voxel size resolution by applying the regularization technique, i.e., using a priori assumptions about fiber smoothness. The regularization procedure is done through a moving least squares filter directly incorporated in the tracing algorithm