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.Comment: New content adde

The Influence of Different Stresses on Glomalin Levels in an Arbuscular Mycorrhizal Fungus—Salinity Increases Glomalin Content

Glomalin is a glycoprotein produced by arbuscular mycorrhizal (AM) fungi, and the soil fraction containing glomalin is correlated with soil aggregation. Thus, factors potentially influencing glomalin production could be of relevance for this ecosystem process and for understanding AM fungal physiology. Previous work indicated that glomalin production in AM fungi may be a stress response, or related to suboptimal mycelium growth. We show here that environmental stress can enhance glomalin production in the mycelium of the AM fungus Glomus intraradices. We applied NaCl and glycerol in different intensities to the medium in which the fungus was grown in vitro, causing salinity stress and osmotic stress, respectively. As a third stress type, we simulated grazing on the extraradical hyphae of the fungus by mechanically injuring the mycelium by clipping. NaCl caused a strong increase, while the clipping treatment led to a marginally significant increase in glomalin production. Even though salinity stress includes osmotic stress, we found substantially different responses in glomalin production due to the NaCl and the glycerol treatment, as glycerol addition did not cause any response. Thus, our results indicate that glomalin is involved in inducible stress responses in AM fungi for salinity, and possibly grazing stress

Optimization in computational systems biology

Optimization aims to make a system or design as effective or functional as possible. Mathematical optimization methods are widely used in engineering, economics and science. This commentary is focused on applications of mathematical optimization in computational systems biology. Examples are given where optimization methods are used for topics ranging from model building and optimal experimental design to metabolic engineering and synthetic biology. Finally, several perspectives for future research are outlined

A Test of Highly Optimized Tolerance Reveals Fragile Cell-Cycle Mechanisms Are Molecular Targets in Clinical Cancer Trials

Robustness, a long-recognized property of living systems, allows function in the face of uncertainty while fragility, i.e., extreme sensitivity, can potentially lead to catastrophic failure following seemingly innocuous perturbations. Carlson and Doyle hypothesized that highly-evolved networks, e.g., those involved in cell-cycle regulation, can be resistant to some perturbations while highly sensitive to others. The “robust yet fragile” duality of networks has been termed Highly Optimized Tolerance (HOT) and has been the basis of new lines of inquiry in computational and experimental biology. In this study, we tested the working hypothesis that cell-cycle control architectures obey the HOT paradigm. Three cell-cycle models were analyzed using monte-carlo sensitivity analysis. Overall state sensitivity coefficients, which quantify the robustness or fragility of a given mechanism, were calculated using a monte-carlo strategy with three different numerical techniques along with multiple parameter perturbation strategies to control for possible numerical and sampling artifacts. Approximately 65% of the mechanisms in the G1/S restriction point were responsible for 95% of the sensitivity, conversely, the G2-DNA damage checkpoint showed a much stronger dependence on a few mechanisms; ∼32% or 13 of 40 mechanisms accounted for 95% of the sensitivity. Our analysis predicted that CDC25 and cyclin E mechanisms were strongly implicated in G1/S malfunctions, while fragility in the G2/M checkpoint was predicted to be associated with the regulation of the cyclin B-CDK1 complex. Analysis of a third model containing both G1/S and G2/M checkpoint logic, predicted in addition to mechanisms already mentioned, that translation and programmed proteolysis were also key fragile subsystems. Comparison of the predicted fragile mechanisms with literature and current preclinical and clinical trials suggested a strong correlation between efficacy and fragility. Thus, when taken together, these results support the working hypothesis that cell-cycle control architectures are HOT networks and establish the mathematical estimation and subsequent therapeutic exploitation of fragile mechanisms as a novel strategy for anti-cancer lead generation

Modeling and Analysis of the Molecular Basis of Pain in Sensory Neurons

Intracellular calcium dynamics are critical to cellular functions like pain transmission. Extracellular ATP plays an important role in modulating intracellular calcium levels by interacting with the P2 family of surface receptors. In this study, we developed a mechanistic mathematical model of ATP-induced P2 mediated calcium signaling in archetype sensory neurons. The model architecture, which described 90 species connected by 162 interactions, was formulated by aggregating disparate molecular modules from literature. Unlike previous models, only mass action kinetics were used to describe the rate of molecular interactions. Thus, the majority of the 252 unknown model parameters were either association, dissociation or catalytic rate constants. Model parameters were estimated from nine independent data sets taken from multiple laboratories. The training data consisted of both dynamic and steady-state measurements. However, because of the complexity of the calcium network, we were unable to estimate unique model parameters. Instead, we estimated a family or ensemble of probable parameter sets using a multi-objective thermal ensemble method. Each member of the ensemble met an error criterion and was located along or near the optimal trade-off surface between the individual training data sets. The model quantitatively reproduced experimental measurements from dorsal root ganglion neurons as a function of extracellular ATP forcing. Hypothesized architecture linking phosphoinositide regulation with P2X receptor activity explained the inhibition of P2X-mediated current flow by activated metabotropic P2Y receptors. Sensitivity analysis using individual and the whole system outputs suggested which molecular subsystems were most important following P2 activation. Taken together, modeling and analysis of ATP-induced P2 mediated calcium signaling generated qualitative insight into the critical interactions controlling ATP induced calcium dynamics. Understanding these critical interactions may prove useful for the design of the next generation of molecular pain management strategies

A quantitative systems pharmacology consortium approach to managing immunogenicity of therapeutic proteins

Immunogenicity is a major challenge in drug development and patient care. Currently, most efforts are dedicated to the elimination of the unwanted immune responses through T‐cell epitope prediction and protein engineering. However, because it is unlikely that this approach will lead to complete eradication of immunogenicity, we propose that quantitative systems pharmacology models should be developed to predict and manage immunogenicity. The potential impact of such a mechanistic model‐based approach is precedented by applications of physiologically‐based pharmacokinetics

An evaluation of yield and Maxwell fluid behaviors of fly ash suspensions in alkali-silicate solutions

The rheological behavior of fly ash suspensions in alkali-silicate solutions used to prepare geopolymers is investigated. The transient stress response of fly ash suspensions at a constant applied strain rate is influenced by both the solids loading and the rheological behavior of the activating solution. The alkali-silicate solution itself behaves like a Newtonian fluid. The fundamental response of alkali-silicate fly ash suspension under constant applied shear strain rate exhibits a transition from a yield type to Maxwell flow. The variability in the Maxwell flow to yield type behavior depends upon the solids loading given by the solution to binder ratio and the composition of the activating solution. In both Maxwell flow and yield type responses, the maximum stress before initiation of flow is directly influenced by the viscosity of the activating solution. At specific solid loading, the transition between the Maxwell flow to yield type behavior is controlled by the composition of the activating solution. The viscous nature of the alkali-silicate solution produces a rate dependent transient response under constant applied strain rate