Bistability in Apoptosis by Receptor Clustering

Apoptosis is a highly regulated cell death mechanism involved in many physiological processes. A key component of extrinsically activated apoptosis is the death receptor Fas, which, on binding to its cognate ligand FasL, oligomerize to form the death-inducing signaling complex. Motivated by recent experimental data, we propose a mathematical model of death ligand-receptor dynamics where FasL acts as a clustering agent for Fas, which form locally stable signaling platforms through proximity-induced receptor interactions. Significantly, the model exhibits hysteresis, providing an upstream mechanism for bistability and robustness. At low receptor concentrations, the bistability is contingent on the trimerism of FasL. Moreover, irreversible bistability, representing a committed cell death decision, emerges at high concentrations, which may be achieved through receptor pre-association or localization onto membrane lipid rafts. Thus, our model provides a novel theory for these observed biological phenomena within the unified context of bistability. Importantly, as Fas interactions initiate the extrinsic apoptotic pathway, our model also suggests a mechanism by which cells may function as bistable life/death switches independently of any such dynamics in their downstream components. Our results highlight the role of death receptors in deciding cell fate and add to the signal processing capabilities attributed to receptor clustering.Comment: Accepted by PLoS Comput Bio

Real-Time Dynamics of Ca2+, Caspase-3/7, and Morphological Changes in Retinal Ganglion Cell Apoptosis under Elevated Pressure

Quantitative information on the dynamics of multiple molecular processes in individual live cells under controlled stress is central to the understanding of the cell behavior of interest and the establishment of reliable models. Here, the dynamics of the apoptosis regulator intracellular Ca2+, apoptosis effector caspase-3/7, and morphological changes, as well as temporal correlation between them at the single cell level, are examined in retinal gangling cell line (differentiated RGC-5 cells) undergoing apoptosis at elevated hydrostatic pressure using a custom-designed imaging platform that allows long-term real-time simultaneous imaging of morphological and molecular-level physiological changes in large numbers of live cells (beyond the field-of-view of typical microscopy) under controlled hydrostatic pressure. This examination revealed intracellular Ca2+ elevation with transient single or multiple peaks of less than 0.5 hour duration appearing at the early stages (typically less than 5 hours after the onset of 100 mmHg pressure) followed by gradual caspase-3/7 activation at late stages (typically later than 5 hours). The data reveal a strong temporal correlation between the Ca2+ peak occurrence and morphological changes of neurite retraction and cell body shrinkage. This suggests that Ca2+ elevation, through its impact on ion channel activity and water efflux, is likely responsible for the onset of apoptotic morphological changes. Moreover, the data show a significant cell-to-cell variation in the onset of caspase-3/7 activation, an inevitable consequence of the stochastic nature of the underlying biochemical reactions not captured by conventional assays based on population-averaged cellular responses. This real-time imaging study provides, for the first time, statistically significant data on simultaneous multiple molecular level changes to enable refinements and testing of models of the dynamics of mitochondria-mediated apoptosis. Further, the platform developed and the approach has direct significance to the study of a variety of signaling pathway phenomena

Understanding dynamics using sensitivity analysis: caveat and solution

<p>Abstract</p> <p>Background</p> <p>Parametric sensitivity analysis (PSA) has become one of the most commonly used tools in computational systems biology, in which the sensitivity coefficients are used to study the parametric dependence of biological models. As many of these models describe dynamical behaviour of biological systems, the PSA has subsequently been used to elucidate important cellular processes that regulate this dynamics. However, in this paper, we show that the PSA coefficients are not suitable in inferring the mechanisms by which dynamical behaviour arises and in fact it can even lead to incorrect conclusions.</p> <p>Results</p> <p>A careful interpretation of parametric perturbations used in the PSA is presented here to explain the issue of using this analysis in inferring dynamics. In short, the PSA coefficients quantify the integrated change in the system behaviour due to persistent parametric perturbations, and thus the dynamical information of when a parameter perturbation matters is lost. To get around this issue, we present a new sensitivity analysis based on impulse perturbations on system parameters, which is named impulse parametric sensitivity analysis (iPSA). The inability of PSA and the efficacy of iPSA in revealing mechanistic information of a dynamical system are illustrated using two examples involving switch activation.</p> <p>Conclusions</p> <p>The interpretation of the PSA coefficients of dynamical systems should take into account the persistent nature of parametric perturbations involved in the derivation of this analysis. The application of PSA to identify the controlling mechanism of dynamical behaviour can be misleading. By using impulse perturbations, introduced at different times, the iPSA provides the necessary information to understand how dynamics is achieved, i.e. which parameters are essential and when they become important.</p

Global Analysis of Dynamical Decision-Making Models through Local Computation around the Hidden Saddle

Bistable dynamical switches are frequently encountered in mathematical modeling of biological systems because binary decisions are at the core of many cellular processes. Bistable switches present two stable steady-states, each of them corresponding to a distinct decision. In response to a transient signal, the system can flip back and forth between these two stable steady-states, switching between both decisions. Understanding which parameters and states affect this switch between stable states may shed light on the mechanisms underlying the decision-making process. Yet, answering such a question involves analyzing the global dynamical (i.e., transient) behavior of a nonlinear, possibly high dimensional model. In this paper, we show how a local analysis at a particular equilibrium point of bistable systems is highly relevant to understand the global properties of the switching system. The local analysis is performed at the saddle point, an often disregarded equilibrium point of bistable models but which is shown to be a key ruler of the decision-making process. Results are illustrated on three previously published models of biological switches: two models of apoptosis, the programmed cell death and one model of long-term potentiation, a phenomenon underlying synaptic plasticity

Calcium Signals Driven by Single Channel Noise

Usually, the occurrence of random cell behavior is appointed to small copy numbers of molecules involved in the stochastic process. Recently, we demonstrated for a variety of cell types that intracellular Ca2+ oscillations are sequences of random spikes despite the involvement of many molecules in spike generation. This randomness arises from the stochastic state transitions of individual Ca2+ release channels and does not average out due to the existence of steep concentration gradients. The system is hierarchical due to the structural levels channel - channel cluster - cell and a corresponding strength of coupling. Concentration gradients introduce microdomains which couple channels of a cluster strongly. But they couple clusters only weakly; too weak to establish deterministic behavior on cell level. Here, we present a multi-scale modelling concept for stochastic hierarchical systems. It simulates active molecules individually as Markov chains and their coupling by deterministic diffusion. Thus, we are able to follow the consequences of random single molecule state changes up to the signal on cell level. To demonstrate the potential of the method, we simulate a variety of experiments. Comparisons of simulated and experimental data of spontaneous oscillations in astrocytes emphasize the role of spatial concentration gradients in Ca2+ signalling. Analysis of extensive simulations indicates that frequency encoding described by the relation between average and standard deviation of interspike intervals is surprisingly robust. This robustness is a property of the random spiking mechanism and not a result of control

Progress in Diamond Detector Development

Detectors based on Chemical Vapor Deposition (CVD) diamond have been used successfully in Luminosity and Beam Condition Monitors (BCM) in the highest radiation areas of the LHC. Future experiments at CERN will accumulate an order of magnitude larger fluence. As a result, an enormous effort is underway to identify detector materials that can operate under fluences of 1 · 1016 n cm−2 and 1 · 1017 n cm−2. Diamond is one candidate due to its large displacement energy that enhances its radiation tolerance. Over the last 30 years the RD42 collaboration has constructed diamond detectors in CVD diamond with a planar geometry and with a 3D geometry to extend the material's radiation tolerance. The 3D cells in these detectors have a size of 50 µm×50 µm with columns of 2.6 µm in diameter and 100 µm×150 µm with columns of 4.6 µm in diameter. Here we present the latest beam test results from planar and 3D diamond pixel detectors