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

Methodologies for quantitative systems pharmacology (QSP) models:Design and Estimation

With the increased interest in the application of quantitative systems pharmacology (QSP) models within medicine research and development, there is an increasing need to formalize model development and verification aspects. In February 2016, a workshop was held at Roche Pharma Research and Early Development to focus discussions on two critical methodological aspects of QSP model development: optimal structural granularity and parameter estimation. We here report in a perspective article a summary of presentations and discussions.</p

Methodologies for quantitative systems pharmacology (QSP) models : Design and estimation

With the increased interest in the application of quantitative systems pharmacology (QSP) models within medicine research and development, there is an increasing need to formalize model development and verification aspects. In February 2016, a workshop was held at Roche Pharma Research and Early Development to focus discussions on two critical methodological aspects of QSP model development: optimal structural granularity and parameter estimation. We here report in a perspective article a summary of presentations and discussions

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

An iterative identification procedure for dynamic modeling of biochemical networks

<p>Abstract</p> <p>Background</p> <p>Mathematical models provide abstract representations of the information gained from experimental observations on the structure and function of a particular biological system. Conferring a predictive character on a given mathematical formulation often relies on determining a number of non-measurable parameters that largely condition the model's response. These parameters can be identified by fitting the model to experimental data. However, this fit can only be accomplished when identifiability can be guaranteed.</p> <p>Results</p> <p>We propose a novel iterative identification procedure for detecting and dealing with the lack of identifiability. The procedure involves the following steps: 1) performing a structural identifiability analysis to detect identifiable parameters; 2) globally ranking the parameters to assist in the selection of the most relevant parameters; 3) calibrating the model using global optimization methods; 4) conducting a practical identifiability analysis consisting of two (<it>a priori </it>and <it>a posteriori</it>) phases aimed at evaluating the quality of given experimental designs and of the parameter estimates, respectively and 5) optimal experimental design so as to compute the scheme of experiments that maximizes the quality and quantity of information for fitting the model.</p> <p>Conclusions</p> <p>The presented procedure was used to iteratively identify a mathematical model that describes the NF-<it>κ</it>B regulatory module involving several unknown parameters. We demonstrated the lack of identifiability of the model under typical experimental conditions and computed optimal dynamic experiments that largely improved identifiability properties.</p

Reduced levels of intracellular calcium releasing in spermatozoa from asthenozoospermic patients

<p>Abstract</p> <p>Background</p> <p>Asthenozoospermia is one of the most common findings present in infertile males characterized by reduced or absent sperm motility, but its aetiology remains unknown in most cases. In addition, calcium is one of the most important ions regulating sperm motility. In this study we have investigated the progesterone-evoked intracellular calcium signal in ejaculated spermatozoa from men with normospermia or asthenozoospermia.</p> <p>Methods</p> <p>Human ejaculates were obtained from healthy volunteers and asthenospermic men by masturbation after 4–5 days of abstinence. For determination of cytosolic free calcium concentration, spermatozoa were loaded with the fluorescent ratiometric calcium indicator Fura-2.</p> <p>Results</p> <p>Treatment of spermatozoa from normospermic men with 20 micromolar progesterone plus 1 micromolar thapsigargin in a calcium free medium induced a typical transient increase in cytosolic free calcium concentration due to calcium release from internal stores. Similar results were obtained when spermatozoa were stimulated with progesterone alone. Subsequent addition of calcium to the external medium evoked a sustained elevation in cytosolic free calcium concentration indicative of capacitative calcium entry. However, when progesterone plus thapsigargin were administered to spermatozoa from patients with asthenozoospermia, calcium signal and subsequent calcium entry was much smaller compared to normospermic patients. As expected, pretreatment of normospermic spermatozoa with both the anti-progesterone receptor c262 antibody and with progesterone receptor antagonist RU-38486 decreased the calcium release induced by progesterone. Treatment of spermatozoa with cytochalasin D or jasplakinolide decreased the calcium entry evoked by depletion of internal calcium stores in normospermic patients, whereas these treatments proved to be ineffective at modifying the calcium entry in patients with asthenozoospermia.</p> <p>Conclusion</p> <p>Our results suggest that spermatozoa from asthenozoospermic patients present a reduced responsiveness to progesterone.</p

Computational Modeling and Analysis of Insulin Induced Eukaryotic Translation Initiation

Insulin, the primary hormone regulating the level of glucose in the bloodstream, modulates a variety of cellular and enzymatic processes in normal and diseased cells. Insulin signals are processed by a complex network of biochemical interactions which ultimately induce gene expression programs or other processes such as translation initiation. Surprisingly, despite the wealth of literature on insulin signaling, the relative importance of the components linking insulin with translation initiation remains unclear. We addressed this question by developing and interrogating a family of mathematical models of insulin induced translation initiation. The insulin network was modeled using mass-action kinetics within an ordinary differential equation (ODE) framework. A family of model parameters was estimated, starting from an initial best fit parameter set, using 24 experimental data sets taken from literature. The residual between model simulations and each of the experimental constraints were simultaneously minimized using multiobjective optimization. Interrogation of the model population, using sensitivity and robustness analysis, identified an insulin-dependent switch that controlled translation initiation. Our analysis suggested that without insulin, a balance between the pro-initiation activity of the GTP-binding protein Rheb and anti-initiation activity of PTEN controlled basal initiation. On the other hand, in the presence of insulin a combination of PI3K and Rheb activity controlled inducible initiation, where PI3K was only critical in the presence of insulin. Other well known regulatory mechanisms governing insulin action, for example IRS-1 negative feedback, modulated the relative importance of PI3K and Rheb but did not fundamentally change the signal flow

A TREM2-activating antibody with a blood-brain barrier transport vehicle enhances microglial metabolism in Alzheimer's disease models

van Lengerich et al. developed a human TREM2 antibody with a transport vehicle (ATV) that improves brain exposure and biodistribution in mouse models. ATV:TREM2 promotes microglial energetic capacity and metabolism via mitochondrial pathways. Loss-of-function variants of TREM2 are associated with increased risk of Alzheimer's disease (AD), suggesting that activation of this innate immune receptor may be a useful therapeutic strategy. Here we describe a high-affinity human TREM2-activating antibody engineered with a monovalent transferrin receptor (TfR) binding site, termed antibody transport vehicle (ATV), to facilitate blood-brain barrier transcytosis. Upon peripheral delivery in mice, ATV:TREM2 showed improved brain biodistribution and enhanced signaling compared to a standard anti-TREM2 antibody. In human induced pluripotent stem cell (iPSC)-derived microglia, ATV:TREM2 induced proliferation and improved mitochondrial metabolism. Single-cell RNA sequencing and morphometry revealed that ATV:TREM2 shifted microglia to metabolically responsive states, which were distinct from those induced by amyloid pathology. In an AD mouse model, ATV:TREM2 boosted brain microglial activity and glucose metabolism. Thus, ATV:TREM2 represents a promising approach to improve microglial function and treat brain hypometabolism found in patients with AD

Rule-Based Cell Systems Model of Aging using Feedback Loop Motifs Mediated by Stress Responses

Investigating the complex systems dynamics of the aging process requires integration of a broad range of cellular processes describing damage and functional decline co-existing with adaptive and protective regulatory mechanisms. We evolve an integrated generic cell network to represent the connectivity of key cellular mechanisms structured into positive and negative feedback loop motifs centrally important for aging. The conceptual network is casted into a fuzzy-logic, hybrid-intelligent framework based on interaction rules assembled from a priori knowledge. Based upon a classical homeostatic representation of cellular energy metabolism, we first demonstrate how positive-feedback loops accelerate damage and decline consistent with a vicious cycle. This model is iteratively extended towards an adaptive response model by incorporating protective negative-feedback loop circuits. Time-lapse simulations of the adaptive response model uncover how transcriptional and translational changes, mediated by stress sensors NF-κB and mTOR, counteract accumulating damage and dysfunction by modulating mitochondrial respiration, metabolic fluxes, biosynthesis, and autophagy, crucial for cellular survival. The model allows consideration of lifespan optimization scenarios with respect to fitness criteria using a sensitivity analysis. Our work establishes a novel extendable and scalable computational approach capable to connect tractable molecular mechanisms with cellular network dynamics underlying the emerging aging phenotype

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