BackgroundMost of the modeling performed in the area of systems biology aims at achieving a quantitative description of the intracellular pathways within a "typical cell". However, in many biologically important situations even clonal cell populations can show a heterogeneous response. These situations require study of cell-to-cell variability and the development of models for heterogeneous cell populations.ResultsIn this paper we consider cell populations in which the dynamics of every single cell is captured by a parameter dependent differential equation. Differences among cells are modeled by differences in parameters which are subject to a probability density. A novel Bayesian approach is presented to infer this probability density from population snapshot data, such as flow cytometric analysis, which do not provide single cell time series data. The presented approach can deal with sparse and noisy measurement data. Furthermore, it is appealing from an application point of view as in contrast to other methods the uncertainty of the resulting parameter distribution can directly be assessed.ConclusionsThe proposed method is evaluated using artificial experimental data from a model of the tumor necrosis factor signaling network. We demonstrate that the methods are computationally efficient and yield good estimation result even for sparse data sets.

The regulation of metabolic activity by tuning enzyme expression levels is crucial to sustain cellular growth in changing environments. Metabolic networks are often studied at steady state using constraint-based models and optimization techniques. However, metabolic adaptations driven by changes in gene expression cannot be analyzed by steady state models, as these do not account for temporal changes in biomass composition.Here we present a dynamic optimization framework that integrates the metabolic network with the dynamics of biomass production and composition. An approximation by a timescale separation leads to a coupled model of quasi steady state constraints on the metabolic reactions, and differential equations for the substrate concentrations and biomass composition. We propose a dynamic optimization approach to determine reaction fluxes for this model, explicitly taking into account enzyme production costs and enzymatic capacity. In contrast to the established dynamic flux balance analysis, our approach allows predicting dynamic changes in both the metabolic fluxes and the biomass composition during metabolic adaptations. Discretization of the optimization problems leads to a linear program that can be efficiently solved.We applied our algorithm in two case studies: a minimal nutrient uptake network, and an abstraction of core metabolic processes in bacteria. In the minimal model, we show that the optimized uptake rates reproduce the empirical Monod growth for bacterial cultures. For the network of core metabolic processes, the dynamic optimization algorithm predicted commonly observed metabolic adaptations, such as a diauxic switch with a preference ranking for different nutrients, re-utilization of waste products after depletion of the original substrate, and metabolic adaptation to an impending nutrient depletion. These examples illustrate how dynamic adaptations of enzyme expression can be predicted solely from an optimization principle.

Knowledge about the molecular structure of protein kinase A (PKA) isoforms is substantial. In contrast, the dynamics of PKA isoform activity in living primary cells has not been investigated in detail. Using a high content screening microscopy approach, we identified the RIIb subunit of PKA-II to be predominantly expressed in a subgroup of sensory neurons. The RIIb-positive subgroup included most neurons expressing nociceptive markers (TRPV1, NaV1.8, CGRP, IB4) and responded to pain-eliciting capsaicin with calcium influx. Isoform-specific PKA reporters showed in sensory-neuronderived F11 cells that the inflammatory mediator PGE 2 specifically activated PKA-II but not PKA-I. Accordingly, pain-sensitizing inflammatory mediators and activators of PKA increased the phosphorylation of RII subunits (pRII) in subgroups of primary sensory neurons. Detailed analyses revealed basal pRII to be regulated by the phosphatase PP2A. Increase of pRII was followed by phosphorylation of CREB in a PKA-dependent manner. Thus, we propose RII phosphorylation to represent an isoform-specific readout for endogenous PKA-II activity in vivo, suggest RIIb as a novel nociceptive subgroup marker, and extend the current model of PKA-II activation by introducing a PP2A-dependent basal state.

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Cellular signaling networks have evolved an astonishing ability to function reliably and with high fidelity in uncertain environments. A crucial prerequisite for the high precision exhibited by many signaling circuits is their ability to keep the concentrations of active signaling compounds within tightly defined bounds, despite strong stochastic fluctuations in copy numbers and other detrimental influences. Based on a simple mathematical formalism, we identify topological organizing principles that facilitate such robust control of intracellular concentrations in the face of multifarious perturbations. Our framework allows us to judge whether a multiple-input-multiple-output reaction network is robust against large perturbations of network parameters and enables the predictive design of perfectly robust synthetic network architectures. Utilizing the Escherichia coli chemotaxis pathway as a hallmark example, we provide experimental evidence that our framework indeed allows us to unravel the topological organization of robust signaling. We demonstrate that the specific organization of the pathway allows the system to maintain global concentration robustness of the diffusible response regulator CheY with respect to several dominant perturbations. Our framework provides a counterpoint to the hypothesis that cellular function relies on an extensive machinery to fine-tune or control intracellular parameters. Rather, we suggest that for a large class of perturbations, there exists an appropriate topology that renders the network output invariant to the respective perturbations.

Ultrasound-assisted nucleation is a promising method of controlling the crystal length within a narrow range in antisolvent crystallization. This article proposes novel model equations representing crystal nucleation and growth under ultrasound application in the antisolvent system of ethanol (solvent), water (antisolvent), and aspirin (pharmaceutical ingredient). The model considers the enhancement of nucleation by ultrasound, and also accounts for the heat generated from both the application of ultrasound and the mixing of solvent and antisolvent. We further employ a global sensitivity analysis to determine the parameters that have the most significant impact on model outputs before validating multiple experimental case studies that represent crystal growth for different antisolvent contents and initial supersaturation ratios. The model successfully captures the effect of the ultrasound, which is a function of temperature and supersaturation ratio, and has a strong impact on the refinement and the

We introduce the concept of an affine flat input to a nonlinear system with a given output function. This approach can be seen as dual to the search for a flat output of a control system with given input. Our results provide a necessary and sufficient condition for the existence of a flat input in the SISO case, which also allows to construct the vector field associated to the flat input. In addition, a relation between the flat input vector field and nonlinear observer design is discussed. A population model is used to illustrate the construction of a flat input.

We address the observability problem for ensembles that are described by probability distributions. The problem is to reconstruct a probability distribution of the initial state from the time-evolution of the probability distribution of the output under a classical finite-dimensional linear system. We present two solutions to this problem, one based on formulating the problem as an inverse problem and the other one based on reconstructing all the moments of the distribution. The first approach leads us to a connection between the reconstruction problem and mathematical tomography problems. In the second approach we use the framework of tensor systems to describe the dynamics of the moments which leads to a more systems theoretic treatment of the reconstruction problem. Furthermore we show that both frameworks are inherently related. The appeal of having two dual viewpoints, the first being more geometric and the second one being more systems theoretic, is illuminated in several examples of theoretical or practical importance.