Parameter estimation in ordinary differential equations (ODEs) has manifold applications not only in physics but also in the life sciences. When estimating the ODE parameters from experimentally observed data, the modeler is frequently concerned with the question of parameter identifiability. The source of parameter nonidentifiability is tightly related to Lie group symmetries. In the present work, we establish a direct search algorithm for the determination of admitted Lie group symmetries. We clarify the relationship between admitted symmetries and parameter nonidentifiability. The proposed algorithm is applied to illustrative toy models as well as a data-based ODE model of the NFκB signaling pathway. We find that besides translations and scaling transformations also higher-order transformations play a role. Enabled by the knowledge about the explicit underlying symmetry transformations, we show how models with nonidentifiable parameters can still be employed to make reliable predictions.

Neural circuits typically consist of many different types of neurons, and one faces a challenge in disentangling their individual contributions in measured neural activity. Classification of cells into inhibitory and excitatory neurons and localization of neurons on the basis of extracellular recordings are frequently employed procedures. Current approaches, however, need a lot of human intervention, which makes them slow, biased, and unreliable. In light of recent advances in deep learning techniques and exploiting the availability of neuron models with quasi-realistic three-dimensional morphology and physiological properties, we present a framework for automatized and objective classification and localization of cells based on the spatiotemporal profiles of the extracellular action potentials recorded by multielectrode arrays. We train convolutional neural networks on simulated signals from a large set of cell models and show that our framework can predict the position of neurons with high accuracy, more precisely than current state-of-the-art methods. Our method is also able to classify whether a neuron is excitatory or inhibitory with very high accuracy, substantially improving on commonly used clustering techniques. Furthermore, our new method seems to have the potential to separate certain subtypes of excitatory and inhibitory neurons. The possibility of automatically localizing and classifying all neurons recorded with large high-density extracellular electrodes contributes to a more accurate and more reliable mapping of neural circuits. NEW & NOTEWORTHY We propose a novel approach to localize and classify neurons from their extracellularly recorded action potentials with a combination of biophysically detailed neuron models and deep learning techniques. Applied to simulated data, this new combination of forward modeling and machine learning yields higher performance compared with state-of-the-art localization and classification methods.

Drug-induced liver injury (DILI) has become a major problem for patients and for clinicians, academics and the pharmaceutical industry. To date, existing hepatotoxicity test systems are only poorly predictive and the underlying mechanisms are still unclear. One of the factors known to amplify hepatotoxicity is the tumor necrosis factor alpha (TNFα), especially due to its synergy with commonly used drugs such as diclofenac. However, the exact mechanism of how diclofenac in combination with TNFα induces liver injury remains elusive. Here, we combined time-resolved immunoblotting and live-cell imaging data of HepG2 cells and primary human hepatocytes (PHH) with dynamic pathway modeling using ordinary differential equations (ODEs) to describe the complex structure of TNFα-induced NFκB signal transduction and integrated the perturbations of the pathway caused by diclofenac. The resulting mathematical model was used to systematically identify parameters affected by diclofenac. These analyses showed that more than one regulatory module of TNFα-induced NFκB signal transduction is affected by diclofenac, suggesting that hepatotoxicity is the integrated consequence of multiple changes in hepatocytes and that multiple factors define toxicity thresholds. Applying our mathematical modeling approach to other DILI-causing compounds representing different putative DILI mechanism classes enabled us to quantify their impact on pathway activation, highlighting the potential of the dynamic pathway model as a quantitative tool for the analysis of DILI compounds.

The impact of pressure waves on cells may provide several possible applications in biology and medicine including the direct killing of tumors, drug delivery or gene transfection. In this study we characterize the physical properties of mechanical pressure waves generated by a nanosecond laser pulse in a setup with well-defined cell culture conditions. To systematically characterize the system on the relevant length and time scales (micrometers and nanoseconds) we use photon Doppler velocimetry (PDV) and obtain velocity profiles of the cell culture vessel at the passage of the pressure wave. These profiles serve as input for numerical pressure wave simulations that help to further quantify the pressure conditions on the cellular length scale. On the biological level we demonstrate killing of glioblastoma cells and quantify experimentally the pressure threshold for cell destruction.