Sten Rüdiger

Dynamics of Turing patterns under spatiotemporal forcing

We study, both theoretically and experimentally, the dynamical response of Turing patterns to a spatiotemporal forcing in the form of a traveling-wave modulation of a control parameter. We show that from strictly spatial resonance, it is possible to induce new, generic dynamical behaviors, including temporally modulated traveling waves and localized traveling solitonlike solutions. The latter make contact with the soliton solutions of Coullet [Phys. Rev. Lett. 56, 724 (1986)]] and generalize them. The stability diagram for the different propagating modes in the Lengyel-Epstein model is determined numerically. Direct observations of the predicted solutions in experiments carried out with light modulations in the photosensitive chlorine dioxide-iodine-malonic acid reaction are also reported.

Calcium Domains around Single and Clustered IP3 Receptors and Their Modulation by Buffers

We study Ca(2+) release through single and clustered IP(3) receptor channels on the ER membrane under presence of buffer proteins. Our computational scheme couples reaction-diffusion equations and a Markovian channel model and allows our investigating the effects of buffer proteins on local calcium concentrations and channel gating. We find transient and stationary elevations of calcium concentrations around active channels and show how they determine release amplitude. Transient calcium domains occur after closing of isolated channels and constitute an important part of the channels feedback. They cause repeated openings (bursts) and mediate increased release due to Ca(2+) buffering by immobile proteins. Stationary domains occur during prolonged activity of clustered channels, where the spatial proximity of IP(3)Rs produces a distinct [Ca(2+)] scale (0.5-10 microM), which is smaller than channel pore concentrations (>100 microM) but larger than transient levels. While immobile buffer affects transient levels only, mobile buffers in general reduce both transient and stationary domains, giving rise to Ca(2+) evacuation and biphasic modulation of release amplitude. Our findings explain recent experiments in oocytes and provide a general framework for the understanding of calcium signals.

Bifurcations and chaos in single-roll natural convection with low Prandtl number

Convective flows of a small Prandtl number fluid contained in a two-dimensional cavity subject to a lateral thermal gradient are numerically studied by using different techniques. The aspect ratio (length to height) is kept at around 2. This value is found optimal to make the flow most unstable while keeping the basic single-roll structure. Two cases of thermal boundary conditions on the horizontal plates are considered: perfectly conducting and adiabatic. For increasing Rayleigh numbers we find a transition from steady flow to periodic oscillations through a supercritical Hopf bifurcation that maintains the centrosymmetry of the basic circulation. For a Rayleigh number of about ten times that of the Hopf bifurcation the system initiates a complex scenario of bifurcations. In the conductive case these include a quasiperiodic route to chaos. In the adiabatic one the dynamics is dominated by the interaction of two Neimark-Sacker bifurcations of the basic periodic solutions, leading to the stable coexistence...

Modulation of Elementary Calcium Release Mediates a Transition from Puffs to Waves in an IP3R Cluster Model

The oscillating concentration of intracellular calcium is one of the most important examples for collective dynamics in cell biology. Localized releases of calcium through clusters of inositol 1,4,5-trisphosphate receptor channels constitute elementary signals called calcium puffs. Coupling by diffusing calcium leads to global releases and waves, but the exact mechanism of inter-cluster coupling and triggering of waves is unknown. To elucidate the relation of puffs and waves, we here model a cluster of IP3R channels using a gating scheme with variable non-equilibrium IP3 binding. Hybrid stochastic and deterministic simulations show that puffs are not stereotyped events of constant duration but are sensitive to stimulation strength and residual calcium. For increasing IP3 concentration, the release events become modulated at a timescale of minutes, with repetitive wave-like releases interspersed with several puffs. This modulation is consistent with experimental observations we present, including refractoriness and increase of puff frequency during the inter-wave interval. Our results suggest that waves are established by a random but time-modulated appearance of sustained release events, which have a high potential to trigger and synchronize activity throughout the cell.

An investigation of models of the IP3R channel in Xenopus oocyte.

We consider different models of inositol 1,4,5-trisphosphate (IP(3)) receptor (IP(3)R) channels in order to fit nuclear membrane patch clamp data of the stationary open probability, mean open time, and mean close time of channels in the Xenopus oocyte. Our results indicate that rather than to treat the tetrameric IP(3)R as four independent and identical subunits, one should assume sequential binding-unbinding processes of Ca(2+) ions and IP(3) messengers. Our simulations also favor the assumption that a channel opens through a conformational transition from a close state to an active state.

Modeling of the Modulation by Buffers of Ca2+ Release through Clusters of IP3 Receptors

Intracellular Ca(2+) release is a versatile second messenger system. It is modeled here by reaction-diffusion equations for the free Ca(2+) and Ca(2+) buffers, with spatially discrete clusters of stochastic IP(3) receptor channels (IP(3)Rs) controlling the release of Ca(2+) from the endoplasmic reticulum. IP(3)Rs are activated by a small rise of the cytosolic Ca(2+) concentration and inhibited by large concentrations. Buffering of cytosolic Ca(2+) shapes global Ca(2+) transients. Here we use a model to investigate the effect of buffers with slow and fast reaction rates on single release spikes. We find that, depending on their diffusion coefficient, fast buffers can either decouple clusters or delay inhibition. Slow buffers have little effect on Ca(2+) release, but affect the time course of the signals from the fluorescent Ca(2+) indicator mainly by competing for Ca(2+). At low [IP(3)], fast buffers suppress fluorescence signals, slow buffers increase the contrast between bulk signals and signals at open clusters, and large concentrations of buffers, either fast or slow, decouple clusters.

Ryanodine Receptor Activation Induces Long-Term Plasticity of Spine Calcium Dynamics

A key feature of signalling in dendritic spines is the synapse-specific transduction of short electrical signals into biochemical responses. Ca2+ is a major upstream effector in this transduction cascade, serving both as a depolarising electrical charge carrier at the membrane and an intracellular second messenger. Upon action potential firing, the majority of spines are subject to global back-propagating action potential (bAP) Ca2+ transients. These transients translate neuronal suprathreshold activation into intracellular biochemical events. Using a combination of electrophysiology, two-photon Ca2+ imaging, and modelling, we demonstrate that bAPs are electrochemically coupled to Ca2+ release from intracellular stores via ryanodine receptors (RyRs). We describe a new function mediated by spine RyRs: the activity-dependent long-term enhancement of the bAP-Ca2+ transient. Spines regulate bAP Ca2+ influx independent of each other, as bAP-Ca2+ transient enhancement is compartmentalized and independent of the dendritic Ca2+ transient. Furthermore, this functional state change depends exclusively on bAPs travelling antidromically into dendrites and spines. Induction, but not expression, of bAP-Ca2+ transient enhancement is a spine-specific function of the RyR. We demonstrate that RyRs can form specific Ca2+ signalling nanodomains within single spines. Functionally, RyR mediated Ca2+ release in these nanodomains induces a new form of Ca2+ transient plasticity that constitutes a spine specific storage mechanism of neuronal suprathreshold activity patterns.

Accurate Langevin approaches to simulate Markovian channel dynamics.

The stochasticity of ion-channels dynamic is significant for physiological processes on neuronal cell membranes. Microscopic simulations of the ion-channel gating with Markov chains can be considered to be an accurate standard. However, such Markovian simulations are computationally demanding for membrane areas of physiologically relevant sizes, which makes the noise-approximating or Langevin equation methods advantageous in many cases. In this review, we discuss the Langevin-like approaches, including the channel-based and simplified subunit-based stochastic differential equations proposed by Fox and Lu, and the effective Langevin approaches in which colored noise is added to deterministic differential equations. In the framework of Fox and Lus classical models, several variants of numerical algorithms, which have been recently developed to improve accuracy as well as efficiency, are also discussed. Through the comparison of different simulation algorithms of ion-channel noise with the standard Markovian simulation, we aim to reveal the extent to which the existing Langevin-like methods approximate results using Markovian methods. Open questions for future studies are also discussed.

Degree Correlations Optimize Neuronal Network Sensitivity to Sub-Threshold Stimuli

Information processing in the brain crucially depends on the topology of the neuronal connections. We investigate how the topology influences the response of a population of leaky integrate-and-fire neurons to a stimulus. We devise a method to calculate firing rates from a self-consistent system of equations taking into account the degree distribution and degree correlations in the network. We show that assortative degree correlations strongly improve the sensitivity for weak stimuli and propose that such networks possess an advantage in signal processing. We moreover find that there exists an optimum in assortativity at an intermediate level leading to a maximum in input/output mutual information.

Frequency and Relative Prevalence of Calcium Blips and Puffs in a Model of Small IP3R Clusters

In this work, we model the local calcium release from clusters with a few inositol 1,4,5-trisphosphate receptor (IP3R) channels, focusing on the stochastic process in which an open channel either triggers other channels to open (as a puff) or fails to cause any channel to open (as a blip). We show that there are linear relations for the interevent interval (including blips and puffs) and the first event latency against the inverse cluster size. However, nonlinearity is found for the interpuff interval and the first puff latency against the inverse cluster size. Furthermore, the simulations indicate that the blip fraction among all release events and the blip frequency are increasing with larger basal [Ca(2+)], with blips in turn giving a growing contribution to basal [Ca(2+)]. This result suggests that blips are not just lapses to trigger puffs, but they may also possess a biological function to contribute to the initiation of calcium waves by a preceding increase of basal [Ca(2+)] in cells that have small IP3R clusters.