Dimension reduction for systems with slow relaxation

We develop reduced, stochastic models for high dimensional, dissipative dynamical systems that relax very slowly to equilibrium and can encode long term memory. We present a variety of empirical and first principles approaches for model reduction, and build a mathematical framework for analyzing the reduced models. We introduce the notions of universal and asymptotic filters to characterize `optimal' model reductions for sloppy linear models. We illustrate our methods by applying them to the practically important problem of modeling evaporation in oil spills.Comment: 48 Pages, 13 figures. Paper dedicated to the memory of Leo Kadanof

Ensemble Models of Neutrophil Trafficking in Severe Sepsis

A hallmark of severe sepsis is systemic inflammation which activates leukocytes and can result in their misdirection. This leads to both impaired migration to the locus of infection and increased infiltration into healthy tissues. In order to better understand the pathophysiologic mechanisms involved, we developed a coarse-grained phenomenological model of the acute inflammatory response in CLP (cecal ligation and puncture)-induced sepsis in rats. This model incorporates distinct neutrophil kinetic responses to the inflammatory stimulus and the dynamic interactions between components of a compartmentalized inflammatory response. Ensembles of model parameter sets consistent with experimental observations were statistically generated using a Markov-Chain Monte Carlo sampling. Prediction uncertainty in the model states was quantified over the resulting ensemble parameter sets. Forward simulation of the parameter ensembles successfully captured experimental features and predicted that systemically activated circulating neutrophils display impaired migration to the tissue and neutrophil sequestration in the lung, consequently contributing to tissue damage and mortality. Principal component and multiple regression analyses of the parameter ensembles estimated from survivor and non-survivor cohorts provide insight into pathologic mechanisms dictating outcome in sepsis. Furthermore, the model was extended to incorporate hypothetical mechanisms by which immune modulation using extracorporeal blood purification results in improved outcome in septic rats. Simulations identified a sub-population (about of the treated population) that benefited from blood purification. Survivors displayed enhanced neutrophil migration to tissue and reduced sequestration of lung neutrophils, contributing to improved outcome. The model ensemble presented herein provides a platform for generating and testing hypotheses in silico, as well as motivating further experimental studies to advance understanding of the complex biological response to severe infection, a problem of growing magnitude in humans

Multiplexing information flow through dynamic signalling systems

We consider how a signalling system can act as an information hub by multiplexing information arising from multiple signals. We formally define multiplexing, mathematically characterise which systems can multiplex and how well they can do it. While the results of this paper are theoretical, to motivate the idea of multiplexing, we provide experimental evidence that tentatively suggests that the NF-κB transcription factor can multiplex information about changes in multiple signals. We believe that our theoretical results may resolve the apparent paradox of how a system like NF-κB that regulates cell fate and inflammatory signalling in response to diverse stimuli can appear to have the low information carrying capacity suggested by recent studies on scalar signals. In carrying out our study, we introduce new methods for the analysis of large, nonlinear stochastic dynamic models, and develop computational algorithms that facilitate the calculation of fundamental constructs of information theory such as Kullback–Leibler divergences and sensitivity matrices, and link these methods to a new theory about multiplexing information. We show that many current models such as those of the NF-κB system cannot multiplex effectively and provide models that overcome this limitation using post-transcriptional modifications

Identification of neutral biochemical network models from time series data

<p>Abstract</p> <p>Background</p> <p>The major difficulty in modeling biological systems from multivariate time series is the identification of parameter sets that endow a model with dynamical behaviors sufficiently similar to the experimental data. Directly related to this parameter estimation issue is the task of identifying the structure and regulation of ill-characterized systems. Both tasks are simplified if the mathematical model is canonical, <it>i.e</it>., if it is constructed according to strict guidelines.</p> <p>Results</p> <p>In this report, we propose a method for the identification of admissible parameter sets of canonical S-systems from biological time series. The method is based on a Monte Carlo process that is combined with an improved version of our previous parameter optimization algorithm. The method maps the parameter space into the network space, which characterizes the connectivity among components, by creating an ensemble of decoupled S-system models that imitate the dynamical behavior of the time series with sufficient accuracy. The concept of sloppiness is revisited in the context of these S-system models with an exploration not only of different parameter sets that produce similar dynamical behaviors but also different network topologies that yield dynamical similarity.</p> <p>Conclusion</p> <p>The proposed parameter estimation methodology was applied to actual time series data from the glycolytic pathway of the bacterium <it>Lactococcus lactis </it>and led to ensembles of models with different network topologies. In parallel, the parameter optimization algorithm was applied to the same dynamical data upon imposing a pre-specified network topology derived from prior biological knowledge, and the results from both strategies were compared. The results suggest that the proposed method may serve as a powerful exploration tool for testing hypotheses and the design of new experiments.</p

Information use and plasticity in the reproductive decisions of malaria parasites

BACKGROUND: Investment in the production of transmissible stages (gametocytes) and their sex ratio are malaria parasite traits that underpin mosquito infectivity and are therefore central to epidemiology. Malaria parasites adjust their levels of investment into gametocytes and sex ratio in response to changes in the in-host environment (including red blood cell resource availability, host immune responses, competition from con-specific genotypes in mixed infections, and drug treatment). This plasticity appears to be adaptive (strategic) because parasites prioritize investment (in sexual versus asexual stages and male versus female stages) in manners predicted to maximize fitness. However, the information, or ‘cues’ that parasites use to detect environmental changes and make appropriate decisions about investment into gametocytes and their sex ratio are unknown. METHODS: Single genotype Plasmodium chabaudi infections were exposed to ‘cue’ treatments consisting of intact or lysed uninfected red blood cells, lysed parasitized RBCs of the same clone or an unrelated clone, and an unmanipulated control. Infection dynamics (proportion of reticulocytes, red blood cell and asexual stage parasite densities) were monitored, and changes in gametocyte investment and sex ratio in response to cue treatments, applied either pre- or post-peak of infection were examined. RESULTS AND CONCLUSIONS: A significant reduction in gametocyte density was observed in response to the presence of lysed parasite material and a borderline significant increase in sex ratio (proportion of male gametocytes) upon exposure to lysed red blood cells (both uninfected and infected) was observed. Furthermore, the changes in gametocyte density and sex ratio in response to these cues depend on the age of infection. Demonstrating that variation in gametocyte investment and sex ratio observed during infections are a result of parasite strategies (rather than the footprint of host physiology), provides a foundation to investigate the fitness consequences of plasticity and explore whether drugs could be developed to trick parasites into making suboptimal decisions

Global distributions of acetone in the upper troposphere from MIPAS spectra

This study reports the first global measurements of acetone (C&lt;sub&gt;3&lt;/sub&gt;H&lt;sub&gt;6&lt;/sub&gt;O) in the upper troposphere (UT). Profiles were obtained between 9 km and 15 km from measurements made by the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) onboard Envisat in August 2003. Errors per profile are lower than 40 % between 180 hPa and 350 hPa. We report strong hemispheric differences in the acetone volume mixing ratios (VMRs), with average concentrations highest in the Northern Hemisphere (NH) mid-latitude UT, between 1000 pptv and 1600 pptv with maxima up to 2300 pptv. Our results show a strong enhancement of acetone relative to CO, particularly over Europe (7 pptv ppbv&lt;sup&gt;−1&lt;/sup&gt;), confirming aircraft studies. Ten-day backward trajectories from these high European values show strong contributions from air flows over North America (56 %) and 25 % from Southernmost Asia. Enhanced acetone is also observed over Greenland, Siberia and biomass burning regions of Africa. Zonal distributions show that acetone VMRs decrease rapidly with increasing altitude (decreasing pressure), particularly in the NH. Poleward of 45° S, acetone VMRs remain fairly consistent with average VMRs between 400 pptv and 500 pptv. In 5-day averages at 9 km, NH VMRs poleward of 45° N are consistently higher than Southern Hemisphere observations poleward of 45° S, by between 750 pptv and 1100 pptv. The results show a clear influence of mid-latitude and transport processes on the acetone summertime distribution

Fast cloud parameter retrievals of MIPAS/Envisat

The infrared limb spectra of the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) on board the Envisat satellite include detailed information on tropospheric clouds and polar stratospheric clouds (PSC). However, no consolidated cloud product is available for the scientific community. Here we describe a fast prototype processor for cloud parameter retrieval from MIPAS (MIPclouds). Retrieval of parameters such as cloud top height, temperature, and extinction are implemented, as well as retrieval of microphysical parameters, e.g. effective radius and the integrated quantities over the limb path (surface area density and volume density). MIPclouds classifies clouds as either liquid or ice cloud in the upper troposphere and polar stratospheric clouds types in the stratosphere based on statistical combinations of colour ratios and brightness temperature differences. Comparison of limb measurements of clouds with model results or cloud parameters from nadir looking instruments is often difficult due to different observation geometries. We therefore introduce a new concept, the limb-integrated surface area density path (ADP). By means of validation and radiative transfer calculations of realistic 2-D cloud fields as input for a blind test retrieval (BTR), we demonstrate that ADP is an extremely valuable parameter for future comparison with model data of ice water content, when applying limb integration (ray tracing) through the model fields. In addition, ADP is used for a more objective definition of detection thresholds of the applied detection methods. Based on BTR, a detection threshold of ADP Combining double low line 107 μm2 cm -2 and an ice water content of 10 -5 g m -3 is estimated, depending on the horizontal and vertical extent of the cloud. Intensive validation of the cloud detection methods shows that the limb-sounding MIPAS instrument has a sensitivity in detecting stratospheric and tropospheric clouds similar to that of space-and ground-based lidars, with a tendency for higher cloud top heights and consequently higher sensitivity for some of the MIPAS detection methods. For the high cloud amount (HCA, pressure levels below 440 hPa) on global scales the sensitivity of MIPAS is significantly greater than that of passive nadir viewers. This means that the high cloud fraction will be underestimated in the ISCCP dataset compared to the amount of high clouds deduced by MIPAS. Good correspondence in seasonal variability and geographical distribution of cloud occurrence and zonal means of cloud top height is found in a detailed comparison with a climatology for subvisible cirrus clouds from the Stratospheric Aerosol and Gas Experiment II (SAGE II) limb sounder. Overall, validation with various sensors shows the need to consider differences in sensitivity, and especially the viewing geometries and field-of-view size, to make the datasets comparable (e.g. applying integration along the limb path through nadir cloud fields). The simulation of the limb path integration will be an important issue for comparisons with cloud-resolving global circulation or chemical transport models. © 2012 Author(s)

Data-Informed Modeling in the Health Sciences

The adoption of automation and technology by health professionals is triggering an explosion of databases and data streams in that sector. The emergence of this data torrent creates the pressing need to mine it for value, which in turn requires investment for the development of modeling and analysis tools. In view of this, dynamicists are presented with the terrific opportunity to enrich their discipline by supplying it with new tools, expanding its scope, and elevating its social impact. This chapter is written in that spirit, examining three concrete case studies encountered in the field: quantifying the salmonellosis risk posed by distinct food sources, assimilating genetic data into a dynamical model for avian influenza transmission, and statistically decontaminating gas chromatography/mass spectroscopy time series. We review available prototypical models and build on them guided by data and mathematical abstraction, demonstrating in the process how to root a model into data. This takes us quite naturally into the realm of probabilistic and statistical modeling and reopens a decades-old discussion on the role of discrete models in applied mathematics. We also touch briefly on the timely subject of mathematicians being employed as such outside math departments and attempt a short outlook on their prospects and opportunities