Philipp Kügler

No facilitator required for membrane transport of hydrogen sulfide

Hydrogen sulfide (H2S) has emerged as a new and important member in the group of gaseous signaling molecules. However, the molecular transport mechanism has not yet been identified. Because of structural similarities with H2O, it was hypothesized that aquaporins may facilitate H2S transport across cell membranes. We tested this hypothesis by reconstituting the archeal aquaporin AfAQP from sulfide reducing bacteria Archaeoglobus fulgidus into planar membranes and by monitoring the resulting facilitation of osmotic water flow and H2S flux. To measure H2O and H2S fluxes, respectively, sodium ion dilution and buffer acidification by proton release (H2S ⇆ H+ + HS−) were recorded in the immediate membrane vicinity. Both sodium ion concentration and pH were measured by scanning ion-selective microelectrodes. A lower limit of lipid bilayer permeability to H2S, PM,H2S ≥ 0.5 ± 0.4 cm/s was calculated by numerically solving the complete system of differential reaction diffusion equations and fitting the theoretical pH distribution to experimental pH profiles. Even though reconstitution of AfAQP significantly increased water permeability through planar lipid bilayers, PM,H2S remained unchanged. These results indicate that lipid membranes may well act as a barrier to water transport although they do not oppose a significant resistance to H2S diffusion. The fact that cholesterol and sphingomyelin reconstitution did not turn these membranes into an H2S barrier indicates that H2S transport through epithelial barriers, endothelial barriers, and membrane rafts also occurs by simple diffusion and does not require facilitation by membrane channels.

Carbon Dioxide Transport through Membranes

Several membrane channels, like aquaporin-1 (AQP1) and the RhAG protein of the rhesus complex, were hypothesized to be of physiological relevance for CO2 transport. However, the underlying assumption that the lipid matrix imposes a significant barrier to CO2 diffusion was never confirmed experimentally. Here we have monitored transmembrane CO2 flux (JCO2) by imposing a CO2 concentration gradient across planar lipid bilayers and detecting the resulting small pH shift in the immediate membrane vicinity. An analytical model, which accounts for the presence of both carbonic anhydrase and buffer molecules, was fitted to the experimental pH profiles using inverse problems techniques. At pH 7.4, the model revealed that JCO2 was entirely rate-limited by near-membrane unstirred layers (USL), which act as diffusional barriers in series with the membrane. Membrane tightening by sphingomyelin and cholesterol did not alter JCO2 confirming that membrane resistance was comparatively small. In contrast, a pH-induced shift of the CO2 hydration-dehydration equilibrium resulted in a relative membrane contribution of about 15% to the total resistance (pH 9.6). Under these conditions, a membrane CO2 permeability (3.2 ± 1.6 cm/s) was estimated. It indicates that cellular CO2 uptake (pH 7.4) is always USL-limited, because the USL size always exceeds 1 μm. Consequently, facilitation of CO2 transport by AQP1, RhAG, or any other protein is highly unlikely. The conclusion was confirmed by the observation that CO2 permeability of epithelial cell monolayers was always the same whether AQP1 was overexpressed in both the apical and basolateral membranes or not.

Nonlinear Inverse Problems: Theoretical Aspects and Some Industrial Applications

Driven by the needs from applications both in industry and other sciences, the field of inverse problems has undergone a tremendous growth within the last two decades, where recent emphasis has been laid more than before on nonlinear problems. This is documented by the wide current literature on regularization methods for the solution of nonlinear ill-posed problems. Advances in this theory and the development of sophisticated numerical techniques for treating the direct problems allow to address and solve industrial inverse problems on a level of high complexity.

Passive transport across bilayer lipid membranes: Overton continues to rule

According to Overtons rule, membrane permeability (PM) of a molecule increases with its hydrophobicity. Experiments with a series of carboxylic acids now suggest the opposite: the most hydrophilic acid exhibited the highest PM (1).

Moment fitting for parameter inference in repeatedly and partially observed stochastic biological models.

The inference of reaction rate parameters in biochemical network models from time series concentration data is a central task in computational systems biology. Under the assumption of well mixed conditions the network dynamics are typically described by the chemical master equation, the Fokker Planck equation, the linear noise approximation or the macroscopic rate equation. The inverse problem of estimating the parameters of the underlying network model can be approached in deterministic and stochastic ways, and available methods often compare individual or mean concentration traces obtained from experiments with theoretical model predictions when maximizing likelihoods, minimizing regularized least squares functionals, approximating posterior distributions or sequentially processing the data. In this article we assume that the biological reaction network can be observed at least partially and repeatedly over time such that sample moments of species molecule numbers for various time points can be calculated from the data. Based on the chemical master equation we furthermore derive closed systems of parameter dependent nonlinear ordinary differential equations that predict the time evolution of the statistical moments. For inferring the reaction rate parameters we suggest to not only compare the sample mean with the theoretical mean prediction but also to take the residual of higher order moments explicitly into account. Cost functions that involve residuals of higher order moments may form landscapes in the parameter space that have more pronounced curvatures at the minimizer and hence may weaken or even overcome parameter sloppiness and uncertainty. As a consequence both deterministic and stochastic parameter inference algorithms may be improved with respect to accuracy and efficiency. We demonstrate the potential of moment fitting for parameter inference by means of illustrative stochastic biological models from the literature and address topics for future research.

Mean value iterations for nonlinear elliptic Cauchy problems

Summary.We investigate the Cauchy problem for a class of nonlinear elliptic operators with C∞–coefficients at a regular set Ω⊂ℝn. The Cauchy data are given at a manifold Γ⊂∂Ω and our goal is to reconstruct the trace of the H1(Ω) solution of a nonlinear elliptic equation at ∂Ω/Γ. We propose two iterative methods based on the segmenting Mann iteration applied to fixed point equations, which are closely related to the original problem. The first approach consists in obtaining a corresponding linear Cauchy problem and analyzing a linear fixed point equation; a convergence proof is given and convergence rates are obtained. On the second approach a nonlinear fixed point equation is considered and a fully nonlinear iterative method is investigated; some preliminary convergence results are proven and a numerical analysis is provided.

Parameter identification for chemical reaction systems using sparsity enforcing regularization: a case study for the chlorite-iodide reaction.

Complex chemical reactions are commonly described by systems of nonlinear ordinary differential equations. Rate and equilibrium constants of these models are usually not directly accessible and have to be indirectly inferred from experimental observations of the system. As a consequence, parameter identification problems have to be formulated and computationally solved. Because of a limited amount of information and uncertainties in the data, the solutions to such parameter identification problems typically lack uniqueness and stability properties and hence cannot be found in a reliable way by a pure minimization of the data mismatch (i.e., the discrepancy between experimental observations and simulated model output). To overcome these difficulties, so-called regularization methods have to be used. In this article, we suggest a sparsity promoting regularization approach that eliminates unidentifiable model parameters (i.e., parameters of low or no sensitivity to the given data). That way, the model is reduced to a core reaction mechanism with manageable interpretation while still remaining in accordance with the experimental observations. For the computational realization, we utilize the adjoint state technique for an efficient calculation of the gradient of the objective with respect to model parameters as well as uncertain initial and experimental conditions. Illustrations of our approach are given by means of the chlorite-iodide reaction for which reference parameter values are available.

Identification of a Temperature Dependent Heat Conductivity from Single Boundary Measurements

Considering the identification of a temperature dependent conductivity in a quasilinear elliptic heat equation from single boundary measurements, we proof uniqueness in dimensions

Monitoring single-channel water permeability in polarized cells.

n \ge 2

Differentiation between genomic and non-genomic feedback controls yields an HPA axis model featuring Hypercortisolism as an irreversible bistable switch

. Taking noisy data into account, we apply Tikhonov regularization in order to overcome the instabilities. By using a problem-adapted adjoint, we give convergence rates under substantially weaker and more realistic conditions than required by the general theory. Our theory is supported by numerical tests.