In vitro detection of adrenocorticotropic hormone levels by fluorescence correlation spectroscopy immunoassay for mathematical modeling of glucocorticoid-mediated feedback mechanisms

Performing quantitative, highly sensitive measurements at a single molecule level is often necessary to address specific issues related to complex molecular and biochemical systems. For that purpose, we present a technique exploiting both the flexibility of immunoassays as well as the low operating costs and high throughput rates of the fluorescence correlation spectroscopy (FCS) method. That way we have established a quantitative measurement technique providing accurate and flexibly time resolved data of single molecules. Nanomolar changes in adrenocorticotropic hormone (ACTH) levels have been detected in a short time-frame that are caused by fast feedback actions in AtT-20 anterior pituitary glands in vitro. Especially with respect to clinical diagnostic or mathematical modeling this improved FCS setup may be of high relevance in order to accurately quantify the amounts of peptide hormones—such as ACTH—as well as signaling molecules, transcription factors, etc., being involved in intra- and extracellular reaction networks

Different pathways for activation and deactivation in CaV1.2: a minimal gating model

Point mutations in pore-lining S6 segments of CaV1.2 shift the voltage dependence of activation into the hyperpolarizing direction and significantly decelerate current activation and deactivation. Here, we analyze theses changes in channel gating in terms of a circular four-state model accounting for an activation R–A–O and a deactivation O–D–R pathway. Transitions between resting-closed (R) and activated-closed (A) states (rate constants x(V) and y(V)) and open (O) and deactivated-open (D) states (u(V) and w(V)) describe voltage-dependent sensor movements. Voltage-independent pore openings and closures during activation (A–O) and deactivation (D–R) are described by rate constants α and β, and γ and δ, respectively. Rate constants were determined for 16-channel constructs assuming that pore mutations in IIS6 do not affect the activating transition of the voltage-sensing machinery (x(V) and y(V)). Estimated model parameters of 15 CaV1.2 constructs well describe the activation and deactivation processes. Voltage dependence of the “pore-releasing” sensor movement ((x(V)) was much weaker than the voltage dependence of “pore-locking” sensor movement (y(V)). Our data suggest that changes in membrane voltage are more efficient in closing than in opening CaV1.2. The model failed to reproduce current kinetics of mutation A780P that was, however, accurately fitted with individually adjusted x(V) and y(V). We speculate that structural changes induced by a proline substitution in this position may disturb the voltage-sensing domain

Inference for stochastic chemical kinetics using moment equations and system size expansion

Quantitative mechanistic models are valuable tools for disentangling biochemical pathways and for achieving a comprehensive understanding of biological systems. However, to be quantitative the parameters of these models have to be estimated from experimental data. In the presence of significant stochastic fluctuations this is a challenging task as stochastic simulations are usually too time-consuming and a macroscopic description using reaction rate equations (RREs) is no longer accurate. In this manuscript, we therefore consider moment-closure approximation (MA) and the system size expansion (SSE), which approximate the statistical moments of stochastic processes and tend to be more precise than macroscopic descriptions. We introduce gradient-based parameter optimization methods and uncertainty analysis methods for MA and SSE. Efficiency and reliability of the methods are assessed using simulation examples as well as by an application to data for Epo-induced JAK/STAT signaling. The application revealed that even if merely population-average data are available, MA and SSE improve parameter identifiability in comparison to RRE. Furthermore, the simulation examples revealed that the resulting estimates are more reliable for an intermediate volume regime. In this regime the estimation error is reduced and we propose methods to determine the regime boundaries. These results illustrate that inference using MA and SSE is feasible and possesses a high sensitivity

Early Afterdepolarizations with Growing Amplitudes via Delayed Subcritical Hopf Bifurcations and Unstable Manifolds of Saddle Foci in Cardiac Action Potential Dynamics.

Early afterdepolarizations (EADs) are pathological oscillations in cardiac action potentials during the repolarization phase and may be caused by drug side effects, ion channel disease or oxidative stress. The most widely observed EAD pattern is characterized by oscillations with growing amplitudes. So far, its occurence has been explained in terms of a supercritical Hopf bifurcation in the fast subsystem of the action potential dynamics from which stable limit cycles with growing amplitudes emerge. The novel contribution of this article is the introduction of two alternative explanations of EAD genesis with growing amplitudes that do not involve stable limit cycles in fast subsystems. In particular, we demonstrate that EAD patterns with growing amplitudes may alternatively arise due to a delayed subcritical Hopf bifurcation or an unstable manifold of a saddle focus fixed point in the full fast-slow system modelling the action potential. Our work extends the list of possible dynamical EAD mechanisms and may contribute to a classification of drug effects in preclinical cardiotoxicity testing

Moment Fitting for Parameter Inference in Repeatedly and Partially Observed Stochastic Biological Models

<div><p>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.</p> </div

Generation of astrocytes from embryonic stem cells

Human exposure to chemicals by environmental pollution, food or drug constituents has been linked to developmental neurotoxicity (DNT) in epidemiological studies. In vitro models open up new possibilities to study toxicity on a molecular level, which is expected to improve human risk assessment. A starting point for the development of these models may be pluripotent stem cells as they can replicate development of an embryo in vitro.In this thesis, I discuss how DNT can be modelled in vitro using stem cell derived, differentiating neural cultures. Transcriptional profiling is suggested as a sensitive endpoint to detect toxic effects of substances. For this purpose, we developed comprehensive lists of marker genes for cells of different developmental stages within developing neural cultures. These were used to describe the effect of chemicals on embryonic stem cells (ESC) that differentiate to neurons.Until now, in vitro neurotoxicology has mainly focussed on neurons, the primary effector cells of the brain. However, other cells, such as astrocytes also play a role in generation of toxicity in the brain, either by causing an overshooting inflammatory response upon activation by pathogens or toxicants, or by metabolic activation of xenobiotics. At the start of this thesis, no protocols that described the generation of pure and functional astrocytes from ESC were known. Therefore, I developed two methods for the differentiation of mouse embryonic stem cell derived astrocytes (MEDA).The first method aimed at producing subtypes of astrocytes to study possible differences in astrocyte subpopulations. It relies on a 2-step protocol and yielded mixed subpopulations of astrocytes. While most cells (81 ± 16%) express the astrocyte marker S100β, only a subpopulation of these MEDA (31 ± 18 %) was positive for the standard astrocyte marker GFAP.With the second protocol, homogeneous astrocyte populations were obtained in very short time. ESC were first differentiated into pure populations of neural precursor cells. These precursor cells were then differentiated within 3-5 days to GFAP-positive MEDA. The fast transition into astrocytes makes them ideally suited for studies of developmental toxicity, as drugs interfering with astrocyte development can be picked up quickly.Both types of stem cell derived astrocytes were characterised in depth as to their inflammatory competence, metabolic activity, and their ability to provide trophic support to developing neuronal cultures. They were also compared to primary astrocytes isolated from mouse brain. To our knowledge, this work comprised the first functional characterisation of astrocyte subpopulations, and we found that GFAP-negative astrocytes contribute to inflammatory responses, and are able to support neurons in the same way as their GFAP-positive counterparts. In co-cultures with neurons, we found that MEDA were able to prolong neuronal survival. Furthermore, when plated on astrocytes, neurons grew at low cell-densities allowing single cell analysis of individual neurons. We propose that MEDA are an adequate alternative to primary isolated astrocytes.The new cell models generated during the course of this thesis are expected to be useful for research on brain disease and the development of novel test systems to detect (developmental) neurotoxicity.<br /

Cardiac AP and Distortion by EADs.

<p>Green curve shows simulation of cardiac action potential with depolarization due to superthreshold stimulation and normal repolarization back to resting potential. Red curve shows an AP distorted by early afterdepolarizations with growing amplitudes.</p

Iterative minimization for inference of the dimerisation process parameters.

<p>Iterative minimization of the cost functions (7) and (8) using the MATLAB trust region algorithm with default settings and and initial guess . The gradient information both for (7) and (8) was provided by means of the adjoint method in order to avoid error-prone finite differencing. (A) Plot of the value of the cost function (7) at the iterate . The optimization algorithm terminates after (outer) iteration steps and yields the minimizer . (B) Using the cost function (8) instead of (7), the algorithm already terminates after (outer) iteration steps and yields the minimizer . (C,E) Plots of the relative errors , show that convergence to the true parameter vector is obtained (up to a negligible error in ) if (7) is chosen as objective function. (D,F) Parameter convergence is also obtained if (8) is chosen instead of (7). However, parameter convergence is much faster in this case.</p

Iterative minimization for inference of the model parameters.

<p>Iterative minimization of the cost functions (9) and (10) using the MATLAB trust region algorithm with default settings, the initial guess , , and the adjoint method for providing the gradient information. (A) Plot of the value of the cost function at the iterate . The optimization algorithm terminates after (outer) iteration steps and yields the minimizer . (B) Plot of the relative errors of in showing a huge deviation from the true parameter in the second and fourth components. (C) Plot of the value of the cost function at the iterate . The optimization algorithm terminates after only (outer) iteration steps and yields the minimizer . (D) The quality of the parameter estimate has significantly improved in comparison to .</p