## Workshop 3: Signal Transduction I: Calcium Dynamics, Phototransduction, and Olfaction

### Organizers

Michael Sanderson
Physiology, University of Massachusetts
James Sneyd
Mathematics, The University of Auckland

In this workshop, we shall study mathematical models for the processes whereby a cell converts an external signal into a signal of a different kind, with particular emphasis upon those transduction mechanisms that rely on the dynamic control of the intracellular calcium concentration. For instance, in response to an external signal such as a neurotransmitter or a hormone, many cell types exhibit oscillations in the concentration of intracellular free calcium, oscillations which themselves control a variety of intracellular processes, including secretion, gene expression, cell movement, or wound repair. In muscle cells, the release of calcium from the sarcoplasmic reticulum controls muscle contraction, while in photoreceptors calcium forms an important negative feedback loop that controls adaptation. In neurosecretory cells, oscillations of the cytoplasmic calcium concentration lead to hormone secretion. Thus, calcium is an integral part of many different transduction processes. It aids in the conversion of an electrical signal to a force (muscle cells), it aids in the conversion of a light signal to an electrical signal (photoreceptors), and it aids in the conversion of one hormonal signal to another hormonal signal or an electrical signal to a hormonal signal (neurosecretory cells).

Mathematical tools: ODEs, PDEs, bifurcation theory, nonlinear traveling waves, excitability, stochastic models, perturbation theory

### Accepted Speakers

Barry Ache
Whitney Laboratory, University of Florida
Genevieve Dupont
Faculte des Sciences, CP231, Universite Libre de Bruxelles
Martin Falcke
Hahn Meitner Institute
Stuart Firestein
Biological Sciences, Columbia University
David Friel
Department of Neurosciences, Case Western Reserve University
Thomas Hoefer
Humboldt University Berlin, Institute of Biology/Theoretical Biophysics
Steve Kleene
Cell Biology/Neurobiology/Anatomy, University of Cincinnati
Leslie Loew
University of Connecticut Health Center, University of Connecticut
Hugh Matthews
Physiological Laboratory, University of Cambridge
Baruch Minke
Ian Parker
Neurobiology and Behavior, University of California, Irvine
Ed Pugh
Department of Psychology, University of Pennsylvania
Johannes Reisert
Neuroscience, Johns Hopkins University
Michael Sanderson
Physiology, University of Massachusetts
Stefan Schuster
Department of Bioninformatics, Max Delbruck Centre for Molecular Medicine
Trevor Shuttleworth
Pharmacology and Physiology, University of Rochester
Andrew Thomas
Pharmacology and Physiology, New Jersey Medical School of UMDNJ
Dan Tranchina
Courant Institute, New York University
Monday, January 26, 2004
Time Session
09:15 AM
10:00 AM
Trevor Shuttleworth - Calcium Entry and Calcium Signaling - Different Routes, Different Roles

An enhanced entry of extracellular Ca2+ is essentially a universal component of receptor-activated Ca2+ signals in cells. Until recently, it was generally assumed that this always involved the well-known, and apparently ubiquitous, capacitative mechanism of entry. In this, the activation of Ca2+ entry results solely from the depletion of intracellular Ca2+ stores. The channels responsible are generically described as store-operated Ca2+ channels (SOC channels), and the most thoroughly studied of these is the Ca2+-release activated Ca2+ channel (CRAC channel). However, in recent years, evidence has accumulated demonstrating an additional noncapacitative mode of receptor-activated Ca2+ entry involving a distinct arachidonic acid-regulated Ca2+ channel (ARC channel). The ARC channels and the SOC/CRAC channels co-exist in cells, but they are not simply alternative, mutually redundant, routes of entry - they are differentially activated at different agonist concentrations in a unique and coordinated fashion, and have distinct roles in the control of the resulting Ca2+ signals. In particular, it is the ARC channels that provide the predominant mode of Ca2+ entry at the low agonist concentrations that give rise to oscillatory Ca2+ signals, and its effect is to modulate oscillation frequency. In addition, the fact that the SOC channels and ARC channels represent spatially distinct entities activated at different agonist concentrations has potential implications for the specific activation of distinct targets within the cell. (Supported by NIH grant GM 40457).

10:45 AM
11:30 AM
Thomas Hoefer - Mathematical Modeling of Calcium Signaling and IP3 Metabolism: Implications for Calcium Oscillations and Waves

The regulation of the second messengers IP3 and calcium is closely linked: IP3 activates calcium release from the endoplasmic reticulum, while calcium ions can exert both positive and negative feedback on IP3 metabolism by activating phospholipase C and IP3 3-kinase, respectively. The generation of calcium oscillations and waves has been much-studied theoretically for conditions of constant IP3 concentration. We developed mathematical models of the IP3/calcium signal ing network which extend the previous models by inclusion of IP3 dynamics. Carrying out stability and bifurcation analyses alongside numerical simulations, we found that calcium regulation of IP3 metabolism profoundly affects both oscillations and wave propagation. Inclusion of IP3 3-kinase is shown to result in a hitherto unidentified mechanism for the generation of oscillations which gives rise to a wide frequency range, as it is observed in a number of cell types. A similarly extended frequency range for oscillations can also be supported by positive feedback via calcium activation of PLC. Moreover, the PLC-mediated feedback has implications for calcium waves, as it provides an additional mechanism of partial or complete signal regeneration in wave propagation. These findings raise the question whether it is possible to identify if significant negative or positive feedback of IP3 is present in a cell. We show that the response of calcium oscillations to the ectopic expression of IP3 buffer, which has recently become feasible experimentally, depends on the type of feedback involved in the oscillator.

Stimulating collaborations with Christian Giaume (College de France), Andrew Thomas and Larry Gaspers (University of Medicine and Dentistry of New Jersey) are gratefully acknowledged.

02:00 PM
02:45 PM
Ian Parker - Calcium Buffers and Binding Proteins with Differing Kinetics Differentially Shape IP3-Evoked Calcium Signals

Cellular calcium buffers shape cytosolic calcium signals by regulating the availability and diffusional mobility of free calcium ions. Most experimental and theoretical studies of these effects have concentrated on signals arising from a fixed 'pulse' of calcium - for example, calcium entry through voltage-gated channels. A more complex case involves intracellular calcium liberation through inositol trisphosphate (IP3) receptors, which are themselves regulated by calcium. Thus, cytosolic buffers are expected to influence the successive cycles of diffusion and calcium-induced calcium release that act both between within clusters of IP3 receptors (to generate local 'puffs'), and between adjacent clusters (to generate global calcium waves).

We studied such interactions in Xenopus oocytes, using confocal line-scan microscopy together with photo-release of IP3. Intracellular injections of buffers with 'slow' calcium-binding kinetics (EGTA and parvalbumin) speeded the decay of calcium signals (Fig. 1A) and 'balkanized' IP3-evoked calcium waves into discrete puffs. Contrastingly, equivalent concentrations 'fast' buffers (BAPTA and calretinin) slowed IP3-evoked calcium responses (Fig. 1B) and promoted 'globalization' of spatially uniform calcium signals. These observations likely reflect buffer actions on calcium feedback at IP3 receptors, since the effects of EGTA and BAPTA on calcium signals evoked by influx through expressed N-type voltage gated channels were markedly less pronounced. Moreover, they point to the importance of buffer kinetics in shaping IP3-evoked calcium signals; likely because fast buffers can influence calcium feedback between individual IP3R within a cluster, whereas slow buffers are able to modulate only cluster-cluster interactions.

We propose that cell-specific expression of calcium binding proteins with distinct kinetics may shape the time course and spatial distribution of IP3-evoked calcium signals for specific physiological roles.

Supported by NIH GM 48071 and GM 58329

Work done in collaboration with Sheila L. Dargan and Beat Schwaller.

03:15 PM
04:00 PM
Stefan Schuster - Bifurcation Analysis of Calcium Oscillations

The transition from a stationary regime to oscillations in the intracellular calcium concentration can occur in different ways. The mathematical tool to analyse this is bifurcation analysis. Calcium oscillations can emerge both by local bifurcations (e.g. supercritical and subcritical Hopf bifurcations) and global bifurcations (e.g. homoclinic and infinite-period bifurcations). The meaning of these terms is explained. Since calcium oscillations are relaxation oscillations (due to the presence of slow and fast processes), so-called canard orbits may arise near local bifurcation points. This means that quasi-harmonic oscillations with a very small amplitude grow very fast to become pulsed oscillations. The jump-like growth in amplitude, which also occurs in global bifurcations, may be of physiological advantage because "misinterpretation" of the signal is avoided. Near homoclinic and infinite-period bifurcations, the oscillations period can reach arbitrarily high values. This is interesting in the light of frequency encoding. These phenomona are illustrated by selected models of calcium oscillations.

04:00 PM
04:20 PM
Pablo d'Alcantara - Modeling Synaptic Ca2+ Dynamics in Hippocampal Dendritic Spines

Synaptic plasticity is triggered by transient changes in Ca2+ concentration ([Ca2+]) within dendritic spines. This in turn induces molecular alterations including changes in the number and opening probability of various ion channels in the spine membrane that result in potentiation or depression of synaptic transmission. While the mechanisms induced by [Ca2+] variation are being elucidated, how the Ca2+ dynamics is governed remains mysterious. Ca2+ dynamic is influenced by sources and sinks in the spines, such as Ca2+ channels and pumps, but also by Ca2+ buffers and the spatiotemporal effects of diffusion. Here we investigate Ca2+ dynamics in dendritic spines duringback-propagating action potentials (BAPs). During depolarisation, voltage sensitive Ca2+ channels (VSCCs) are activated leading to a [Ca2+] increase. Using confocal laser scanning microscopy, we image BAP-induced Ca2+ transients in dendritic spines of CA1 hippocampal neurons in rat organotypic slices. Analysis of these transients under different conditions-including dye saturation, optical fluctuation analysis, and altered dye concentrations-enable us to estimate the increase and decay in [Ca2+], the number and open probability of VSCCs, and the endogenous Ca2+ buffering capacity. Our model predicts that, according both to our data and to previously published data, much bigger [Ca2+] elevations should be observed, from which we infer the operation of unknown Ca2+ sink mechanisms. We show that additional Ca2+ buffering could account for smaller [Ca2+] transients. However, we also show that, if spatiotemporal diffusion of Ca2+ is taken into account, very large [Ca2+] elevations can occur in microdomains although average transients in the spine are small. By combining experiments with physiology-based models, we can investigate the minimum elements required to explain published experimental observations, thereby clarifying the contribution of various molecular mechanisms to synaptic function and plasticity.

04:20 PM
04:40 PM
Gregory Smith - Stochastic Automata Network Models of Instantaneously-Coupled Intracellular Calcium Channels

Although there is consensus that Ca2+ puffs arise from the cooperative action of multiple IP3 receptors (IP3Rs), the precise relationship between single-channel kinetics and the collective phenomena of stochastic Ca2+ excitability is not well understood. Here we present a memory-efficient method by which mathematical models for IP3-sensitive Ca2+ release sites can be derived from Markov models of IP3R single-channel gating that include Ca2+ activation (IP3R-2 like), Ca2+ inactivation, or both (IP3R-1 like). Such models are essentially stochastic automata networks (SANs) that involve a large number of so-called 'functional transitions,' that is, the transition probabilities of the infinitesimal generator matrix (or Q-matrix) of one automata (i.e, an individual channel) may depend on the local [Ca2+] and thus the state of the other channels. We present an iterative method for calculating hitting times that leads to a directly estimate of various puff statistics (e.g., puff duration and inter-puff-interval) from a SAN descriptor.

Tuesday, January 27, 2004
Time Session
09:00 AM
09:45 AM
David Friel - Insights into Calcium Dynamics Obtained Using Approaches Inspired by Studies of Membrane Potential Dynamics in Excitable Cells

Ionized free Ca2+ is a ubiquitous signaling ion that serves as both an important charge carrier and a chemical intermediate that links a variety of physiological stimuli to their intracellular effectors. One of the most important steps in Ca2+ signaling is generation of the Ca2+ signal itself. This signal, which expresses the coordinated activity of multiple Ca2+ regulatory systems operating in different subcellular compartments, serves as the critical intermediate in the physiological control of all Ca2+-sensitive processes within cells. What defines this signal? How does it vary with stimulus strength? How is it influenced by the properties of individual Ca2+ channels, pumps, exchangers and binding proteins that may, during the life of a cell, undergo dramatic changes in expression level or modulatory state? What is the functional impact of mutations of the genes encoding proteins that participate in Ca2+ regulation? Answers to these fundamental questions have been elusive, largely because the system properties of cellular Ca2+ regulation are poorly understood. This is due, in large part, to a lack of quantitative functional descriptions of Ca2+ transporters that operate together in intact cells. I will describe an approach to obtaining this information that exploits basic mechanistic similarities between Ca2+ signaling and signaling through changes in membrane potential, and draws upon previous biophysical studies of membrane excitability. Along with a novel combination of experimental techniques, this approach has made it possible to obtain quantitative characterizations of intracellular Ca2+ transport and buffering systems in intact neurons. These characterizations, in turn, provide clear explanations of a number of puzzling properties of stimulus-evoked changes in neuronal Ca concentration, and reveal the existence of signaling regimes analogous to those found in excitable cells expressing multiple populations of voltage-gated ion channels.

03:15 PM
04:00 PM
Leslie Loew - Morphological Control of Intracellular Calcium Signals

The Virtual Cell computational framework provides a general approach to modeling complex biochemical pathways in the context of actual cellular geometry. Applications of the Virtual Cell to InsP3-mediated calcium signaling will be presented, highlighting how the interplay between theoretical modeling and experimental approaches provides a powerful tool in understanding complex biochemical processes. My colleagues and I combined a quantitative uncaging technique for generating controlled amounts of InsP3 within live cells, measurements of intracellular calcium dynamics, and modeling with the Virtual Cell software system, to determine the time-dependent concentrations of InsP3 in single cells. This technology was applied to the construction of a spatial model of bradykinin-induced calcium waves in differentiated N1E115 neuroblastoma. Using a comprehensive set of experimentally determined image and biochemical data as inputs to the model, we were able to generate simulations that reproduced the experimentally observed calcium waves in these cells. The model also enabled us to visualize the spatiotemporal behavior of InsP3 and gain an understanding of how the neuronal cell geometry controls the overall process. As additional examples of morphological control for very different spatial scales, I will describe the calcium signals following fertilization of frog eggs and how the unique morphology of dendritic spines can control InsP3 signals underlying long term depression.

04:00 PM
04:20 PM
Antonio Politi - The Role of the Inositol-1,4,5-Trisphosphate Dynamics in Shaping Calcium Signals

In non-excitable cells agonist stimulation can induce, via production of inositol-1,4,5- trisphosphate (IP3), transient increases in cytoplasmic calcium so called calcium oscillations. Several mechanisms contribute to the generation and termination of these transients (e.g. calcium induced calcium release, calcium sequestration, inactivation of the IP3 receptors). Among these the calcium dependence of the IP3 metabolism is thought to be involved. Calcium affects the production, by activating phospholipase C (PLC), and the degradation, by activating IP3 3-kinase (IP3K), of IP3. Although there are indications that IP3 oscillates concomitantly to calcium, the role of these oscillations in shaping the calcium signal is still unclear.

Starting from models that show calcium oscillations for constant IP3 levels (e.g. models including CICR and slow inactivation of the IP3R's by calcium), I included the calcium activation of PLC and IP3K (representing an indirect positive and negative feedback of calcium on itself, respectively). The presence of one of the feedbacks greatly increases the stimulatory range where one observes oscillations. Long period oscillations (> 5min) as well as short period oscillations (< 30 sec) are found. The analysis shows that the dynamics of IP3 can be very important in controlling the long period of the oscillations. To determine which of the feedbacks is the most predominant I simulated the expression of an IP3 buffer. In experiments the expression of the IP3 receptor ligand binding domain can strongly modify or stop the calcium oscillations (L.D. Gaspers, A.P. Thomas communication). I studied how IP3 buffer can abolish oscillations. Furthermore the effects of IP3 buffer on the characteristics of the calcium spikes, the period of the oscillations and the propagation of calcium waves have been investigated. Comparing the theoretical with the experimental results indicates that first at least one of the feedbacks is present in the studied cells, and second that the positive feedback of calcium on IP3 (via PLC) is the predominant one. This feedback turns out to be crucial for shaping the calcium signal.

I thank A.P. Thomas and L.D. Gaspers from the New Jersey Medical School for the stimulating discussions.

04:20 PM
04:40 PM
J.F. Dufour - IP3R Isoforms in Liver Pathophysiology

Inositol 1,4,5-trisphosphate (IP3) links activation of receptors at the plasma membane by extracellular agonists to the release of Ca2+ from the internal stores. IP3 binds to its receptor (IP3R) which is a Ca2+ channel gated by IP3 and cytoplasmic Ca2+ (Dufour JBC;1997). Local changes in the free cytoplasmic Ca2+ concentration regulate many enzymes and many aspects of the cellular economy, from metabolism and secretion to gene expression and cell proliferation. The IP3R exists in three isoforms with specific properties. We studied the expression of these isoforms during liver cirrhosis and regeneration. Methods. Cirrhosis was induced in rats by chronic exposure to CCl4/Phenobarbital (C/P) or by bile duct ligation (BDL), hepatic regeneration by 2/3 hepatectomy. Real time quantitative PCR (TaqMana) and Western blots with specific antibodies measured the expression at the mRNA and protein level. We used the 2-hybrid assay to search for interactions of the IP3R with itslef. Results. IP3R isoform 2 represented the predominant isoform (70%) in normal liver and was localized by immunohisto-chemistry near the bile canaliculus. The expression of the isoform 3, which was very low in normal liver, increased many times after induction of liver cirrhosis by C/P and BDL and appeared localized by immunohistochemistry in cholangiocytes. In the hours following 2/3 hepatectomy the isoform 1 increased and the isoform 2 decreased leading to a transient inversion in the predominant isoform in the hours preceding the first round of cellular division. We determined that the IP3R can interact with itself at the level of its C-terminal part and that this interaction is isoform-independent. The same C-terminal domain interacted also in the context of this assay with the C-terminal part of the Ca2+ entry channel Trp-4. Conclusion. The C-terminal part of the IP3R plays probably an important role in the formation and regulation of the tetrameric Ca2+ channel. It may also be the molecular interface between Ca2+ release from the stores and Ca2+ entry through the plasma membrane. The expression of the IP3R is tightly regulated at the isoform level during liver cirrhosis and regeneration.

Wednesday, January 28, 2004
Time Session
09:00 AM
09:45 AM
Martin Falcke - Fluktuations, Spatial Structure and Stability in Intracellular Ca2+ Dynamics

The fundamental role of fluctuations arising from the control of the IP3 receptor channel by calcium and IP3 became obvious in recent years. Fluctuations induce spatial and temporal structures in systems with deterministic dynamic regimes not able to produce these structures without fluctuations. I will present essential results from stochastic modelling. These results ensue questions concerning the dynamic regime of determinsitic models. Simulations of release through single clusters demonstrates the concentration gradients of four orders of magnitude around releasing channel clusters. These gradients are essential in understanding stability properties of determinsitic models of calcium dynamics. A determinsitic, spatially discrete model demonstrates the essential role of diffusion in local stability. I will discuss consequences of these basic results for future modelling and the interpretation of experimental findings.

10:15 AM
11:00 AM
Andrew Thomas - Interacting Feedback Loops in Generation of IP-3 Dependent Calcium Oscillations

Since the first observations showing that hormones coupled to the formation of inositol 1,4,5-trisphospate (IP3) elicit oscillations of cytosolic calcium, there has been much speculation on the mechanism underlying these calcium dynamics. As the properties of the IP3-receptor (IP3R) were elucidated, it became clear that positive and negative feedback effects of Ca2+ directly on the IP3R could yield oscillatory calcium signaling. However, there are a number of other potential sites of calcium feedback in the IP3-dependent calcium-signaling pathway, particularly through alterations in the generation and elimination of IP3. We have utilized GFP-pleckstrin homology domain fusion proteins to monitor intracellular changes in IP3, and a molecular buffer of IP3 based on the ligand binding domain of the IP3R fused to GFP, which serves as an IP3 buffer in the physiologically relevant range. These tools have allowed us to investigate how IP3 dynamics might participate in calcium oscillations. In particular, we suggest that IP3 oscillations may interact with the intrinsic calcium regulation of the IP3R to yield coupled oscillators. This type of system has the potential to enrich the properties of calcium oscillations, and extend the dynamic range of frequency-modulation in Ca2+ signaling. A third level of feedback control of calcium oscillations occurs through the calcium uptake and release properties of mitochondria, which can modify calcium-feedback regulation of the IP3R by virtue of their close proximity to ER calcium release sites. The complex interplay between different feedback loops in the generation of IP3-dependent calcium oscillations, together with the spatial organization of the underlying components, gives rise to diverse patterns of calcium signaling that are tailored to regulate a wide variety of different processes.

Work done in collaboration with Lawrence D. Gaspers, Paul Burnett, Thomas Hofer, and Antonio Politit.

11:00 AM
11:20 AM
Karl-Ernst Kaissling - Olfactory Transduction in Moths Antennae: Perireceptor and Receptor Events

Olfactory transduction comprises intracellular processes but also the extracellular 'perireceptor events'. The latter include the adsorptive uptake of odorant molecules (here the moth female pheromone) from the air space by the surface of the olfactory organ (here the male moths antenna), their diffusion towards the olfactory receptor cell, and a network of extracellular chemical reactions. The odorant reacts with odorant-binding proteins, receptor molecules of the receptor cell, and odorant-degrading enzymes. We discuss the structure of the pheromone-binding protein recently analysed by X-ray1 and NMR2, and its possible functions as carrier and scavenger of the pheromone.

We developed a quantitative mathematical model (computerized by J. Thorson, Oxford) of the network reactions based on experimental data from several laboratories3. From these studies we conclude that the receptor potential, the first electrical response of the receptor cell, reflects the kinetics of the network rather than the one of intracellular transducer processes. The model allows for the moth Antheraea polyphemus to estimate the density of pheromone receptor molecules on the receptor cell membrane of 6,000/mu m2 and a dissociation constant of the pheromone-receptor complex of 40 muM.

1. Sandler, B.H., Nikonova, L., Leal, W.S., & Clardy, J. (2000). Chemistry & Biology, 7, 143-151.

2. Horst, R., Damberger, F., Luginb?hl, P., G?ntert, P., Peng, G., Nikonova, L., et al. (2001). PNAS, 98, 14374-14379.

3. Kaissling, K.E. (2001). Chemical Senses, 26, 125-150.

11:20 AM
11:40 AM
Marko Marhl - Flexibility and Robustness of Ca2+ Oscillations

Flexibility and robustness are important properties of biological systems. These properties are here investigated in a model for simple and complex intracellular calcium oscillations. Flexibility and robustness characterize responses of a system to various external perturbations, such as deterministic pulses or periodic signals, as well as noise. Here, the influence of external periodic forcing is studied. The main point of the study is to compare responses of the system in a chaotic regime with those obtained in a regular periodic regime. We show that the response to external signals in terms of the range of synchronization does not depend on the complexity of Ca2+ oscillations but on the local divergence. Parts of attractors with close to zero local divergence are highly susceptible to external perturbations, thus facilitating signal detection and transduction, whereas highly negative local divergence areas characterize extremely robust regions that are virtually impossible to modify even with strong external signals. The results of the study are applicable for studying cell coupling, robustness to white noise and give an explanation of the constructive and destructive role of noise in the sense of stochastic resonance.

02:00 PM
02:45 PM
Stuart Firestein - Making Sense of Scents

The mammalian olfactory organ is arguably the best chemical detector on the planet. The first step in olfactory detection and discrimination is the interaction between an odor compound and a protein receptor on the membrane of specialized olfactory neurons in the nose. These receptors, each one encoded by a gene, are members of a superfamily of similar receptors that also play important roles in the brain and in other bodily functions. As a group they are known as G-Protein Coupled Receptors (GPCRs) and have many similar structural, genetic and functional features. The odor receptors are the most remarkable sub-group of this family in that they are encoded by more than 1000 genes in rodents, and as many as 350 in humans. This is an order of magnitude greater than the total of all other GPCRs.

Two approaches to understanding how this large family of receptors act in concert to produce neural signals leading to complex perceptions have been pursued. Pharmacological investigation of the binding properties of ORs has allowed us to define molecular receptive fields and begin to appreciate the immense complexity of combinatorial encoding schemes. In parallel whole genome analysis has revealed an underlying organization of the enormous OR family of genes. Combining pharmacology and genomics provides insights into how the brain perceives a world of innumerable and complex chemical odors.

03:15 PM
04:00 PM
Baruch Minke - The TRP Ca2+ Channel and Signal Transduction

The Transient Receptor Potential (TRP) proteins constitute a large and diverse family of channel proteins, which is conserved through evolution. TRP channel proteins have critical functions in many tissues and cell types, but their gating mechanism is an enigma. I'll report on two important new properties of Drosophila TRP and TRP-like (TRPL) channels. We found that TRPL is translocated back and forth between the signaling membrane and an intracellular compartment by a light-regulated mechanism. A high level of rhabdomeral TRPL characteristic of dark-raised flies is functionally manifested in the properties of the light induced current and thus represents a novel mechanism to fine-tune visual responses. We also gained a new insight on the activation mechanism of the TRP and TRPL channels by which both Ca2+ and protein dephosphorylation are required for channel activation. ATP depletion or inhibition of protein kinase C activated the TRP channels, while photo-release of caged ATP or application of phorbol ester antagonized channels openings in the dark. Furthermore, Mg2+-dependent stable phosphorylation event or protein phosphatase inhibition abolished activation of the TRP and TRPL channels. While a high reduction of cellular Ca2+ abolished channel activation, subsequent application of Ca2+ combined with ATP depletion induced a robust dark current that was reminiscent of light responses. The results suggest that the combined action of Ca2+ and protein dephosphorylation activate the TRP and TRPL channels, while protein phosphorylation by PKC antagonized channels openings. The link of TRP gating to the metabolic state of cells makes cells expressing TRP extremely vulnerable to metabolic stress via a mechanism that may underlie retinal degeneration and neuronal cell death in mammals upon reduction in oxygen pressure in the tissue.

04:00 PM
04:20 PM
Donald Gill - Regulation of TRPC Channel Function by Diacylglycerol and Protein Kinase C

The mechanism of receptor-induced activation of the ubiquitously expressed family of mammalian TRPC channels has been the focus of intense study. Primarily responding to phospholipase C (PLC)-coupled receptors, the channels are reported to receive modulatory input from diacylglycerol, endoplasmic reticulum (ER) inositol 1,4,5-trisphoshate receptors (InsP3R), and ER Ca2+ stores. Analysis of TRPC5 channels transfected within DT40 B cells and deletion mutants thereof, revealed efficient activation in response to PLC- or PLC-? activation which was independent of InsP3Rs or the content of stores. In both HEK293 cells and DT40 cells, TRPC5 and TRPC3 channel responses to PLC-activation were highly analogous, but only TRPC3 and not TRPC5 channels responded to addition of the permeant diacylglycerol (DAG) analogue, 1-oleoyl-2-acetyl-sn-glycerol (OAG). However, OAG application or elevated endogenous DAG resulting from either DAG-lipase or DAG-kinase inhibition, completely prevented TRPC5 or TRPC4 activation. This inhibitory action of DAG on TRPC5 and TRPC4 channels was clearly mediated by protein kinase C (PKC), in distinction to the stimulatory action of DAG on TRPC3 which is established to be PKC-independent. PKC activation totally blocked TRPC3 channel activation in response to OAG, and the activation was restored by PKC-blockade. PKC-inhibition resulted in decreased TRPC3 channel deactivation. Store-operated Ca2+ entry in response to PLC-coupled receptor activation was substantially reduced by OAG or DAG-lipase inhibition in a PKC-dependent manner. However, store-operated Ca2+ entry in response to the pump blocker, thapsigargin, was unaffected by PKC. The results reveal that each TRPC subtype is strongly inhibited by DAG-induced PKC activation reflecting a likely universal feed-back control on TRPCs, and that DAG-mediated PKC-independent activation of TRPC channels is highly subtype specific. The profound yet distinct control by PKC and DAG on the activation of TRPC channel subtypes is likely the basis of a spectrum of regulatory phenotypes of expressed TRPC channels.

Work done in collaboration with Fei Zheng and Kartik Venkatachalam.

Thursday, January 29, 2004
Time Session
09:00 AM
09:45 AM
Dan Tranchina - Calcium Seems to Do Everything, but Things Are Seldom What They Seem in Phototransduction

There have been numerous twists and turns in the road to understanding vertebrate phototransduction over the years. The phototransduction field has been characterized by great controversy surrounding numerous confusing and seemingly incompatible experimental results. Calcium has been at the heart of controversy on multiple occasions, including a recent one. In the dark, there is a circulating current across the rod membrane, which flows inward through channels in the outer segment and flows outward across the inner segment membrane. The modulation of the voltage across the rod membrane in response to light is a consequence of the reduction of this dark (light-sensitive) current. When rhodopsin absorbs a photon it is converted into an activated enzyme (R*) that initiates a cascade of biochemical reactions. These reactions lead to change in the concentration of an internal transmitter that gates the light-sensitive current. For many years the phototransduction community was divided between those who thought that this transmitter was calcium ions and those who thought it was cyclic-GMP (cGMP), until twenty years ago when definitive experimental evidence showed that the transmitter is cGMP. Other roles were found for calcium. Two salient features of rods are their ability to adapt to changes in ambient light level by adjusting the sensitivity and kinetics of their responses; and their remarkably reproducible responses to single photons. Calcium ions have been implicated in both these phenomena. A major outstanding problem in sensory physiology has been to understand how the rod's ingle-photon response (SPR) manages to have such little variation in amplitude and kinetics, despite the fact that it is mediated by the activity of a single molecule of activated rhodopsin (R*). Once R* is produced, it activates G-protein; G-protein activates phosphodiesterase; phosphodiesterase hydrolyzes cGMP; the cGMP concentration drops, resulting in closure of some of the light-sensitive channels; the reduction of inward current causes the rod membrane voltage to become hyperpolarized. The sequence of events following the activation of rhodopsin continues until R* is inactivated. The regularity of the single-photon response implies that the lifetime of R* is controlled with high precision-or does it? Closure of the light-sensitive channels blocks the entry of calcium, but it is still pumped out of the rod by a calcium exchanger. Therefore, the concentration of calcium is controlled by light, and it can serve as a feedback messenger to control sensitivity and the lifetime of R*. I will discuss the experimental evidence and mathematical theory for the role calcium in SPR reproducibility. Although evidence to support the calcium hypothesis seemed compelling, other experimental results and mathematical theory cast grave doubt on this hypothesis. Evidence on both sides can now be understood with the aid of a detailed stochastic biochemical kinetic model for rod phototransduction.

Work done in collaboration with Russ Hamer and Spero Nicholas.

11:00 AM
11:20 AM
Daniel Dougherty - Mechanistic Mathematical Models for Signal Transduction in Olfactory Receptor Neurons

We construct simple mathematical models for the G-protein coupled transduction machinery of olfactory receptor neurons. The models all include descriptions of ligand-receptor interaction, intracellular signaling via the second messenger cAMP, and effector ion channel activity, although they differ in how calcium-dependent feedback inhibition is incorporated. These models were parameterized with respect to voltage-clamped current recordings from single cells exposed to three different odorants over a family of concentrations (Firestein, Picco, and Menini, 1993). We investigate how differences in odorant identity are captured in the model parameterizations, and test mechanisms to account for adaptation under repetitive or prolonged stimulation.

Work done in collaboration with Alice Yew and Geraldine Wright.

11:20 AM
11:40 AM
Maarten Kamermans - Ephaptic Communication in the Retina and Beyond

Generally, two modes of fast communication between neurons are considered; Ca-dependent neurotransmitter release and electrical coupling via gap-junctions. There is, however, evidence for a third type of fast communication: ephaptic communication. Ephaptic comes from the Greek word Ephapse which means "to touch". In this type of communication, the extracellular potential instead of the intracellular potential is modulated. In the retina we have found evidence that horizontal cells project back to photoreceptors via an ephaptic mechanism (Kamermans et al., Science, 2001). In this talk Iwill present the evidence for ephaptic communication n the retina and, I will discuss the likelihood that this type of communication is a general phenomenon instead of being restricted to the retina.

02:00 PM
02:45 PM
Barry Ache - Cellular Mechanisms of Olfactory Signal Transduction

Odors are detected by primary olfactory neurons whose job it is to not only detect odor signals but also transduce them into electrical signals for downstream processing in the central nervous system. The role of cyclic nucleotide signaling in olfactory transduction in vertebrates is well established. G-protein-coupled odorant receptors activate olfactory receptor neurons by targeting olfactory-specific cyclic nucleotide gated ion channels that transiently increase intracellular calcium in the cells. Recently, we found that blocking phosphatidylinositol 3-kinase (PI3K)-dependent phosphoinositide signaling increases odorant-evoked, cyclic nucleotide-dependent elevation of intracellular calcium in acutely dissociated rat olfactory receptor neurons, and does so in an odorant-specific manner. We argue that phosphoinositide signaling can inhibit cyclic nucleotide-dependent excitation of the cells, and that the interaction of these two signaling pathways is important in odorant coding by mediating opponent inputs into the receptor cell.

Friday, January 30, 2004
Time Session
09:00 AM
09:45 AM
Steve Kleene - Signal-to-Noise Issues in Olfactory Transduction

When the olfactory system detects a very weak stimulus, it somehow discriminates it from false signals due to random fluctuations in the transduction cascade. At least two mechanisms have been found to facilitate this discrimination. First, the neuron maintains a small, optimal concentration of cAMP at rest. cAMP gates the primary transduction channels in the olfactory cilia. Because of non-linearities in the response to cAMP, a weak odorous stimulus can produce the greatest depolarization in a neuron that already contains 0.1-0.3 muM cAMP. The second mechanism is a high-gain, low-noise amplification of the weak signal. A pair of receptor currents underlying vertebrate olfactory transduction constitutes such an amplifier. Calcium enters the cilium through the cAMP-gated channels. Calcium can in turn gate chloride channels, activating a secondary depolarizing receptor current. Because the chloride channels have a small unitary conductance, they amplify the primary current while introducing little additional noise.

10:15 AM
11:00 AM
Jean-Pierre Rospars - From Stimulus Intensity to Spike Trains in Frog Olfatory Receptor Neurons: In Vivo and in Computo Approaches

Olfactory stimuli are complex chemical signals whose composition varies quantitatively and qualitatively in space and time. Olfactory receptor neurons (ORNs) can monitor these variations and convey raw data to the brain from which biologically meaningful information can be extracted. The primary purpose of this work is to investigate quantitatively how the intensitive properties of odors, measured by their odorant concentration in the air, are encoded in the spike trains delivered by ORNs. To this end, we studied ORN responses in the frog olfactory epithelium to four volatile compounds, anisole, camphor, isoamyl acetate and limonene, which are strongly and distinctively odorous for humans.

All four odorants were applied as square pulses of 2-s duration at increasing concentrations. So, only the time variable was kept identical through all experiments. The neural activity was recorded one neuron at a time with extracellular electrodes from an intact epithelium in order to minimize the modifications due to experimental conditions [3, 4]. The spike train yielded by each stimulation was characterized by its latency, length (number of spikes), duration and median frequency. These variables were studied at the single neuron, neuron population and ciliary membrane levels.

At the single neuron level, the dose-response plots for the four variables were fitted to specific functions (negative exponential, alpha and half-Hill functions). The location along the concentration axis (e.g. thresholds), width (dynamic ranges) and heights (maximum latency, duration or frequency) of the fitted curves were evaluated for each plot.

At the neuron population level, the curves are extremely diverse. Both their dose characteristics (e.g. at threshold, at maximum response) and response characteristics (e.g. minimum latency, maximum frequency) were found to follow lognormal statistical distributions. Lognormal histograms are asymmetric with peaks close to the origin and long tails. The histogram of dynamic ranges in spike frequency is the most asymmetric, so that a significant fraction of neurons presents a much wider range than their one-decade peak, confirming the short dynamic range of the typical ORN but revealing the presence of a significant proportion of ORNs with a behavior very different from the average. From these histograms, response properties of the whole neuron population can be inferred. In general, thresholds, dynamic ranges and maximum responses are independent, which prevcnts their global categorization and can serve as a support for the qualitative coding of odorants.

Some of the response characteristics can be interpreted in terms of molecular events (deactivation of odorant molecules, odorant-receptor interaction, transduction cascade) using a chemo-electrical model of the ORN [1] and its environment [2] based on known mucus biochemical and neuron morpho-electrical data. From this model both dose-conductance curves and the apparent dissociation equilibrium constants of odorant-receptor interaction were determined, as well as their statistical distributions in the neuron population. The values found are in broad agreement with independent determinations.

References

1. Rospars, J.P., L?nsk?, P., Tuckwell, H.C., & Vermeulen, A. (1996). Coding of odor intensity in a steady-state deterministic model of an olfactory receptor cell neuron. Journal of Computational Neuroscience, 3, 51-72.

2. Rospars, J.P., Krivan, V., & Lansky, P. (2000a). Perireceptor and receptor events in olfaction. Comparison of concentration and flux detectors: a modeling study. Chemical Senses, 25, 293-311.

3. Rospars, J.P., L?nsk?, P., Duchamp-Viret, P., & Duchamp, A. (2000b). Spiking frequency vs. odorant concentration in olfactory receptor neurons. BioSystems, 58, 133-141.

4. Rospars, J.P., L?nsk?, P., Duchamp-Viret, P., & Duchamp, A. (2003). Relation between stimulus and response in frog olfactory receptor neurons in vivo. European Journal of Neuroscience, 18, 1135-1154.

Work done in collaboration with Petr L?nsk?, Andr? Duchamp, and Patricia Duchamp-Viret.

11:00 AM
11:45 AM
Johannes Reisert - The Ca-Activated Cl Channel and its Control in Rat Olfactory Receptor Neurons

Odorants activate sensory transduction in olfactory receptor neurons (ORNs) via a cAMP signalling cascade, which results in the opening of non-selective, cyclic nucleotide-gated (CNG) channels. The consequent Ca2+ influx through CNG channels activates Cl channels, which serve to amplify the transduction signal. We investigate here the functional interplay of the CNG channel with the Cl channel by using inside-out membrane patches excised from ORN dendritic knobs/cilia. The Cl channels on an excised patch could be activated by Ca2+ flux through the CNG channels which were opened by cytoplasmic application of cAMP. The magnitude of the Cl current depended on the strength of Ca-buffering in the bath solution, suggesting that the CNG and Cl channels were probably not organized as constituents of a local transducisome complex. Likewise, Cl channels and the Na/Ca exchanger, which extrudes Ca2+, appear to be spatially segregated. Based on the theory of buffered Ca2+ diffusion, we determined the Ca2+ diffusion coefficient and calculated that the CNG and Cl channel densities on the membrane were ca. 8 and 62 mu m 2, respectively. These densities, together with the Ca2+ diffusion coefficient, demonstrate that a given Cl channel is activated by Ca2+ originating from multiple CNG channels, thus allowing low-noise amplification of the olfactory receptor current.

Work done in collaboration with Paul J. Bauer1, King-Wai Yau, and Stephan Frings.

Name Email Affiliation
Ache, Barry bwa@whitney.ufl.edu Whitney Laboratory, University of Florida
Altobelli, Joseph jaltobel@kent.edu Department of Mathematics, Kent State University
Anderson, Jeffrey jeffma78@hotmail.com Biomedical Mathematics, Kent State University
Antolin Silva, Salome saymds2@hermes.cam.ac.uk Department of Physiology, Trinity Hall College
Best, Janet jbest@mbi.osu.edu Mathematics, The Ohio State University
Borisyuk, Alla borisyuk@mbi.osu.edu Mathematical Biosciences Institute, The Ohio State University
Cracium, Gheorghe craciun@math.wisc.edu Dept. of Mathematics, University of Wisconsin-Madison
d'Alcantara, Pablo pablo.dalcantara@nimr.mrc.ac.uk Department of Neurophysiology, Nat'l Inst. for Medical Research, MRC
Danthi, Sanjay danthi.1@osu.edu Staff Scientist II, Genzyme Corporation
Dougherty, Daniel dpdoughe@mbi.osu.edu Mathematical Biosciences Institute, The Ohio State University
Dufour, J.F. jdufour@ikp.unibe.ch Clinical Pharmacology, University of Bern
Dupont, Genevieve gdupont@ulb.ac.be Faculte des Sciences, CP231, Universite Libre de Bruxelles
Falcke, Martin falcke@hmi.de Hahn Meitner Institute
Fall, Chris fall@uic.edu Department of Anatomy and Cell Biology, University of Illinois
Firestein, Stuart sjf24@columbia.edu Biological Sciences, Columbia University
Fogarty, Kevin kevin.fogarty@umassmed.edu Department of Physiology, University of Massachusetts
French, Donald french@math.uc.edu Department of Mathematical Sciences, University of Cincinnati
Friel, David ddf2@po.cwru.edu Department of Neurosciences, Case Western Reserve University
Gill, Donald dgill@umaryland.edu Biochemistry & Molecular Biology, College of Business and Management
Goel, Pranay goelpra@helix.nih.gov NIDDK, Indian Institute of Science Education and Research
Gruenstein, Eric eric.gruenstein@uc.edu Molecular Genetics & Biochemistry , University of Cincinnati
Guo, Yixin yixin@math.drexel.edu Department of Mathematics, The Ohio State University
He, Li-Ping Lhe001@umaryland.edu Biochemistry & Molecular Biology, College of Business and Management
Hoefer, Thomas thomas.hoefer@rz.hu-berlin.de Humboldt University Berlin, Institute of Biology/Theoretical Biophysics
Holcman, David holcman@phy.ucsf.edu Department of Physiology, University of San Francisco
Kaissling, Karl-Ernst Kaissling@mpi-seewiesen.mpg.de Verhaltensphysiologie, Max Planck Institute for Colloids and Interfaces
Kamermans, Maarten m.kamermans@ioi.knaw.nl Netherlands Ophthalmic Research Inst., Royal Netherlands Academy of Arts & Science
Kang, Minchul mckang@dtc.umn.edu Department of Mathematics, University of Minnesota
Kao, Lie-Jane ljkao@mbi.osu.edu Department of Industrial Engineering, Da-Yeh University
Kleene, Steve steve@syrano.acb.uc.edu Cell Biology/Neurobiology/Anatomy, University of Cincinnati
Lancia, Giuseppe lancia@dimi.uniud.it Mathematics, Istituto Nazionale di Alta Matematica Francesco Severi'' (INdAM)
Li, Yue-Xian yxli@math.ubc.ca Mathematica Department, University of British Columbia
Lifshitz, Lawrence lawrence.lifshitz@umassmed.edu Biomedical Imaging Group, University of Massachusetts
Lim, Sookkyung limsk@math.uc.edu Mathematical Biosciences Institute, The Ohio State University
Loew, Leslie les@volt.uchc.edu University of Connecticut Health Center, University of Connecticut
Lolas, Georgios mpokos@hotmail.com Mathematical Biosciences Institute, The Ohio State University
Marhl, Marko marko.marhl@uni-mb.si Dept. of Physics, Faculty of Education, University of Maribor
Matthews, Hugh hrm1@cam.ac.uk Physiological Laboratory, University of Cambridge
Minke, Baruch minke@md.huji.ac.il Physiology, Hebrew University-Hadassah Medical School
Nadkarni, Suhita Physics and Astronomy, Ohio University
Parker, Ian iparker@uci.edu Neurobiology and Behavior, University of California, Irvine
Politi, Antonio antonio.politi@rz.hu-berlin.de Theoretical Biophysics, Humboldt University of Berlin
Pugh, Ed pugh@mail.med.upenn.edu Department of Psychology, University of Pennsylvania
Reisert, Johannes jreisert@jhmi.edu Neuroscience, Johns Hopkins University
Rejniak, Katarzyna rejniak@mbi.osu.edu Mathematical Biosciences Institute, The Ohio State University
Rosol, Thomas rosol.1@osu.edu Veterinary Biosciences, The Ohio State University
Rospars, Jean-Pierre Jean-Pierre.Rospars@versailles.inra.fr Unite Phytopharmacie et Mediateurs chimiques, INRA
Sadee, Wolfgang wolfgang.sadee@osumc.edu Internal Medicine, College of Medicine (OSUMC), The Ohio State University
Sanderson, Michael michael.sanderson@umassmed.edu Physiology, University of Massachusetts
Schuster, Stefan schuster@minet.uni-jena.de Department of Bioninformatics, Max Delbruck Centre for Molecular Medicine
Shuttleworth, Trevor trevor_shuttleworth@urmc.rochester.edu Pharmacology and Physiology, University of Rochester
Smith, Gregory greg@as.wm.edu Department of Applied Science, College of William and Mary
Sneyd, James sneyd@mbi.osu.edu Mathematics, The University of Auckland
Soto, Gabriel gabys@math.bu.edu Center for BioDynamics, Boston University
Stone, Emily stone@math.usu.edu Mathematics and Statistics, Utah State University
Terman, David terman@math.ohio-state.edu Mathemathics Department, The Ohio State University
Thomas, Andrew thomasap@umdnj.edu Pharmacology and Physiology, New Jersey Medical School of UMDNJ
Timofeeva, Yulia yulia.timofeeva@nottingham.ac.uk Mathematical Sciences, Loughborough University
Tranchina, Dan dt2@nyu.edu Courant Institute, New York University
Tsai, Chih-Chiang tsaijc@mbi.osu.edu Department of Mathematics, National Taiwan Normal University
Tsaneva-Atanasova , Krasimira K.Tsaneva-Atanasova@bristol.ac.uk Mathematical Biosciences Institute, The Ohio State University
Ullah, Ghanim Physics and Astronomy, Ohio University
Wechselberger, Martin wm@mbi.osu.edu Mathematical Biosciences Insitute, The Ohio State University
Wright, Geraldine wright.572@osu.edu School of Biology, Newcastle University
Xiao, Rui xiao.36@osu.edu Center of Molecular Neurobiology, The Ohio State University
Yule, David david_yule@urmc.rochester.edu Department of Pharmacology & Physiology, University of Rochester
Cellular Mechanisms of Olfactory Signal Transduction

Odors are detected by primary olfactory neurons whose job it is to not only detect odor signals but also transduce them into electrical signals for downstream processing in the central nervous system. The role of cyclic nucleotide signaling in olfactory transduction in vertebrates is well established. G-protein-coupled odorant receptors activate olfactory receptor neurons by targeting olfactory-specific cyclic nucleotide gated ion channels that transiently increase intracellular calcium in the cells. Recently, we found that blocking phosphatidylinositol 3-kinase (PI3K)-dependent phosphoinositide signaling increases odorant-evoked, cyclic nucleotide-dependent elevation of intracellular calcium in acutely dissociated rat olfactory receptor neurons, and does so in an odorant-specific manner. We argue that phosphoinositide signaling can inhibit cyclic nucleotide-dependent excitation of the cells, and that the interaction of these two signaling pathways is important in odorant coding by mediating opponent inputs into the receptor cell.

Modeling Synaptic Ca2+ Dynamics in Hippocampal Dendritic Spines

Synaptic plasticity is triggered by transient changes in Ca2+ concentration ([Ca2+]) within dendritic spines. This in turn induces molecular alterations including changes in the number and opening probability of various ion channels in the spine membrane that result in potentiation or depression of synaptic transmission. While the mechanisms induced by [Ca2+] variation are being elucidated, how the Ca2+ dynamics is governed remains mysterious. Ca2+ dynamic is influenced by sources and sinks in the spines, such as Ca2+ channels and pumps, but also by Ca2+ buffers and the spatiotemporal effects of diffusion. Here we investigate Ca2+ dynamics in dendritic spines duringback-propagating action potentials (BAPs). During depolarisation, voltage sensitive Ca2+ channels (VSCCs) are activated leading to a [Ca2+] increase. Using confocal laser scanning microscopy, we image BAP-induced Ca2+ transients in dendritic spines of CA1 hippocampal neurons in rat organotypic slices. Analysis of these transients under different conditions-including dye saturation, optical fluctuation analysis, and altered dye concentrations-enable us to estimate the increase and decay in [Ca2+], the number and open probability of VSCCs, and the endogenous Ca2+ buffering capacity. Our model predicts that, according both to our data and to previously published data, much bigger [Ca2+] elevations should be observed, from which we infer the operation of unknown Ca2+ sink mechanisms. We show that additional Ca2+ buffering could account for smaller [Ca2+] transients. However, we also show that, if spatiotemporal diffusion of Ca2+ is taken into account, very large [Ca2+] elevations can occur in microdomains although average transients in the spine are small. By combining experiments with physiology-based models, we can investigate the minimum elements required to explain published experimental observations, thereby clarifying the contribution of various molecular mechanisms to synaptic function and plasticity.

Mechanistic Mathematical Models for Signal Transduction in Olfactory Receptor Neurons

We construct simple mathematical models for the G-protein coupled transduction machinery of olfactory receptor neurons. The models all include descriptions of ligand-receptor interaction, intracellular signaling via the second messenger cAMP, and effector ion channel activity, although they differ in how calcium-dependent feedback inhibition is incorporated. These models were parameterized with respect to voltage-clamped current recordings from single cells exposed to three different odorants over a family of concentrations (Firestein, Picco, and Menini, 1993). We investigate how differences in odorant identity are captured in the model parameterizations, and test mechanisms to account for adaptation under repetitive or prolonged stimulation.

Work done in collaboration with Alice Yew and Geraldine Wright.

IP3R Isoforms in Liver Pathophysiology

Inositol 1,4,5-trisphosphate (IP3) links activation of receptors at the plasma membane by extracellular agonists to the release of Ca2+ from the internal stores. IP3 binds to its receptor (IP3R) which is a Ca2+ channel gated by IP3 and cytoplasmic Ca2+ (Dufour JBC;1997). Local changes in the free cytoplasmic Ca2+ concentration regulate many enzymes and many aspects of the cellular economy, from metabolism and secretion to gene expression and cell proliferation. The IP3R exists in three isoforms with specific properties. We studied the expression of these isoforms during liver cirrhosis and regeneration. Methods. Cirrhosis was induced in rats by chronic exposure to CCl4/Phenobarbital (C/P) or by bile duct ligation (BDL), hepatic regeneration by 2/3 hepatectomy. Real time quantitative PCR (TaqMana) and Western blots with specific antibodies measured the expression at the mRNA and protein level. We used the 2-hybrid assay to search for interactions of the IP3R with itslef. Results. IP3R isoform 2 represented the predominant isoform (70%) in normal liver and was localized by immunohisto-chemistry near the bile canaliculus. The expression of the isoform 3, which was very low in normal liver, increased many times after induction of liver cirrhosis by C/P and BDL and appeared localized by immunohistochemistry in cholangiocytes. In the hours following 2/3 hepatectomy the isoform 1 increased and the isoform 2 decreased leading to a transient inversion in the predominant isoform in the hours preceding the first round of cellular division. We determined that the IP3R can interact with itself at the level of its C-terminal part and that this interaction is isoform-independent. The same C-terminal domain interacted also in the context of this assay with the C-terminal part of the Ca2+ entry channel Trp-4. Conclusion. The C-terminal part of the IP3R plays probably an important role in the formation and regulation of the tetrameric Ca2+ channel. It may also be the molecular interface between Ca2+ release from the stores and Ca2+ entry through the plasma membrane. The expression of the IP3R is tightly regulated at the isoform level during liver cirrhosis and regeneration.

Fluktuations, Spatial Structure and Stability in Intracellular Ca2+ Dynamics

The fundamental role of fluctuations arising from the control of the IP3 receptor channel by calcium and IP3 became obvious in recent years. Fluctuations induce spatial and temporal structures in systems with deterministic dynamic regimes not able to produce these structures without fluctuations. I will present essential results from stochastic modelling. These results ensue questions concerning the dynamic regime of determinsitic models. Simulations of release through single clusters demonstrates the concentration gradients of four orders of magnitude around releasing channel clusters. These gradients are essential in understanding stability properties of determinsitic models of calcium dynamics. A determinsitic, spatially discrete model demonstrates the essential role of diffusion in local stability. I will discuss consequences of these basic results for future modelling and the interpretation of experimental findings.

Making Sense of Scents

The mammalian olfactory organ is arguably the best chemical detector on the planet. The first step in olfactory detection and discrimination is the interaction between an odor compound and a protein receptor on the membrane of specialized olfactory neurons in the nose. These receptors, each one encoded by a gene, are members of a superfamily of similar receptors that also play important roles in the brain and in other bodily functions. As a group they are known as G-Protein Coupled Receptors (GPCRs) and have many similar structural, genetic and functional features. The odor receptors are the most remarkable sub-group of this family in that they are encoded by more than 1000 genes in rodents, and as many as 350 in humans. This is an order of magnitude greater than the total of all other GPCRs.

Two approaches to understanding how this large family of receptors act in concert to produce neural signals leading to complex perceptions have been pursued. Pharmacological investigation of the binding properties of ORs has allowed us to define molecular receptive fields and begin to appreciate the immense complexity of combinatorial encoding schemes. In parallel whole genome analysis has revealed an underlying organization of the enormous OR family of genes. Combining pharmacology and genomics provides insights into how the brain perceives a world of innumerable and complex chemical odors.

Insights into Calcium Dynamics Obtained Using Approaches Inspired by Studies of Membrane Potential Dynamics in Excitable Cells

Ionized free Ca2+ is a ubiquitous signaling ion that serves as both an important charge carrier and a chemical intermediate that links a variety of physiological stimuli to their intracellular effectors. One of the most important steps in Ca2+ signaling is generation of the Ca2+ signal itself. This signal, which expresses the coordinated activity of multiple Ca2+ regulatory systems operating in different subcellular compartments, serves as the critical intermediate in the physiological control of all Ca2+-sensitive processes within cells. What defines this signal? How does it vary with stimulus strength? How is it influenced by the properties of individual Ca2+ channels, pumps, exchangers and binding proteins that may, during the life of a cell, undergo dramatic changes in expression level or modulatory state? What is the functional impact of mutations of the genes encoding proteins that participate in Ca2+ regulation? Answers to these fundamental questions have been elusive, largely because the system properties of cellular Ca2+ regulation are poorly understood. This is due, in large part, to a lack of quantitative functional descriptions of Ca2+ transporters that operate together in intact cells. I will describe an approach to obtaining this information that exploits basic mechanistic similarities between Ca2+ signaling and signaling through changes in membrane potential, and draws upon previous biophysical studies of membrane excitability. Along with a novel combination of experimental techniques, this approach has made it possible to obtain quantitative characterizations of intracellular Ca2+ transport and buffering systems in intact neurons. These characterizations, in turn, provide clear explanations of a number of puzzling properties of stimulus-evoked changes in neuronal Ca concentration, and reveal the existence of signaling regimes analogous to those found in excitable cells expressing multiple populations of voltage-gated ion channels.

Regulation of TRPC Channel Function by Diacylglycerol and Protein Kinase C

The mechanism of receptor-induced activation of the ubiquitously expressed family of mammalian TRPC channels has been the focus of intense study. Primarily responding to phospholipase C (PLC)-coupled receptors, the channels are reported to receive modulatory input from diacylglycerol, endoplasmic reticulum (ER) inositol 1,4,5-trisphoshate receptors (InsP3R), and ER Ca2+ stores. Analysis of TRPC5 channels transfected within DT40 B cells and deletion mutants thereof, revealed efficient activation in response to PLC- or PLC-? activation which was independent of InsP3Rs or the content of stores. In both HEK293 cells and DT40 cells, TRPC5 and TRPC3 channel responses to PLC-activation were highly analogous, but only TRPC3 and not TRPC5 channels responded to addition of the permeant diacylglycerol (DAG) analogue, 1-oleoyl-2-acetyl-sn-glycerol (OAG). However, OAG application or elevated endogenous DAG resulting from either DAG-lipase or DAG-kinase inhibition, completely prevented TRPC5 or TRPC4 activation. This inhibitory action of DAG on TRPC5 and TRPC4 channels was clearly mediated by protein kinase C (PKC), in distinction to the stimulatory action of DAG on TRPC3 which is established to be PKC-independent. PKC activation totally blocked TRPC3 channel activation in response to OAG, and the activation was restored by PKC-blockade. PKC-inhibition resulted in decreased TRPC3 channel deactivation. Store-operated Ca2+ entry in response to PLC-coupled receptor activation was substantially reduced by OAG or DAG-lipase inhibition in a PKC-dependent manner. However, store-operated Ca2+ entry in response to the pump blocker, thapsigargin, was unaffected by PKC. The results reveal that each TRPC subtype is strongly inhibited by DAG-induced PKC activation reflecting a likely universal feed-back control on TRPCs, and that DAG-mediated PKC-independent activation of TRPC channels is highly subtype specific. The profound yet distinct control by PKC and DAG on the activation of TRPC channel subtypes is likely the basis of a spectrum of regulatory phenotypes of expressed TRPC channels.

Work done in collaboration with Fei Zheng and Kartik Venkatachalam.

Mathematical Modeling of Calcium Signaling and IP3 Metabolism: Implications for Calcium Oscillations and Waves

The regulation of the second messengers IP3 and calcium is closely linked: IP3 activates calcium release from the endoplasmic reticulum, while calcium ions can exert both positive and negative feedback on IP3 metabolism by activating phospholipase C and IP3 3-kinase, respectively. The generation of calcium oscillations and waves has been much-studied theoretically for conditions of constant IP3 concentration. We developed mathematical models of the IP3/calcium signal ing network which extend the previous models by inclusion of IP3 dynamics. Carrying out stability and bifurcation analyses alongside numerical simulations, we found that calcium regulation of IP3 metabolism profoundly affects both oscillations and wave propagation. Inclusion of IP3 3-kinase is shown to result in a hitherto unidentified mechanism for the generation of oscillations which gives rise to a wide frequency range, as it is observed in a number of cell types. A similarly extended frequency range for oscillations can also be supported by positive feedback via calcium activation of PLC. Moreover, the PLC-mediated feedback has implications for calcium waves, as it provides an additional mechanism of partial or complete signal regeneration in wave propagation. These findings raise the question whether it is possible to identify if significant negative or positive feedback of IP3 is present in a cell. We show that the response of calcium oscillations to the ectopic expression of IP3 buffer, which has recently become feasible experimentally, depends on the type of feedback involved in the oscillator.

Stimulating collaborations with Christian Giaume (College de France), Andrew Thomas and Larry Gaspers (University of Medicine and Dentistry of New Jersey) are gratefully acknowledged.

Olfactory Transduction in Moths Antennae: Perireceptor and Receptor Events

Olfactory transduction comprises intracellular processes but also the extracellular 'perireceptor events'. The latter include the adsorptive uptake of odorant molecules (here the moth female pheromone) from the air space by the surface of the olfactory organ (here the male moths antenna), their diffusion towards the olfactory receptor cell, and a network of extracellular chemical reactions. The odorant reacts with odorant-binding proteins, receptor molecules of the receptor cell, and odorant-degrading enzymes. We discuss the structure of the pheromone-binding protein recently analysed by X-ray1 and NMR2, and its possible functions as carrier and scavenger of the pheromone.

We developed a quantitative mathematical model (computerized by J. Thorson, Oxford) of the network reactions based on experimental data from several laboratories3. From these studies we conclude that the receptor potential, the first electrical response of the receptor cell, reflects the kinetics of the network rather than the one of intracellular transducer processes. The model allows for the moth Antheraea polyphemus to estimate the density of pheromone receptor molecules on the receptor cell membrane of 6,000/mu m2 and a dissociation constant of the pheromone-receptor complex of 40 muM.

1. Sandler, B.H., Nikonova, L., Leal, W.S., & Clardy, J. (2000). Chemistry & Biology, 7, 143-151.

2. Horst, R., Damberger, F., Luginb?hl, P., G?ntert, P., Peng, G., Nikonova, L., et al. (2001). PNAS, 98, 14374-14379.

3. Kaissling, K.E. (2001). Chemical Senses, 26, 125-150.

Ephaptic Communication in the Retina and Beyond

Generally, two modes of fast communication between neurons are considered; Ca-dependent neurotransmitter release and electrical coupling via gap-junctions. There is, however, evidence for a third type of fast communication: ephaptic communication. Ephaptic comes from the Greek word Ephapse which means "to touch". In this type of communication, the extracellular potential instead of the intracellular potential is modulated. In the retina we have found evidence that horizontal cells project back to photoreceptors via an ephaptic mechanism (Kamermans et al., Science, 2001). In this talk Iwill present the evidence for ephaptic communication n the retina and, I will discuss the likelihood that this type of communication is a general phenomenon instead of being restricted to the retina.

Signal-to-Noise Issues in Olfactory Transduction

When the olfactory system detects a very weak stimulus, it somehow discriminates it from false signals due to random fluctuations in the transduction cascade. At least two mechanisms have been found to facilitate this discrimination. First, the neuron maintains a small, optimal concentration of cAMP at rest. cAMP gates the primary transduction channels in the olfactory cilia. Because of non-linearities in the response to cAMP, a weak odorous stimulus can produce the greatest depolarization in a neuron that already contains 0.1-0.3 muM cAMP. The second mechanism is a high-gain, low-noise amplification of the weak signal. A pair of receptor currents underlying vertebrate olfactory transduction constitutes such an amplifier. Calcium enters the cilium through the cAMP-gated channels. Calcium can in turn gate chloride channels, activating a secondary depolarizing receptor current. Because the chloride channels have a small unitary conductance, they amplify the primary current while introducing little additional noise.

Morphological Control of Intracellular Calcium Signals

The Virtual Cell computational framework provides a general approach to modeling complex biochemical pathways in the context of actual cellular geometry. Applications of the Virtual Cell to InsP3-mediated calcium signaling will be presented, highlighting how the interplay between theoretical modeling and experimental approaches provides a powerful tool in understanding complex biochemical processes. My colleagues and I combined a quantitative uncaging technique for generating controlled amounts of InsP3 within live cells, measurements of intracellular calcium dynamics, and modeling with the Virtual Cell software system, to determine the time-dependent concentrations of InsP3 in single cells. This technology was applied to the construction of a spatial model of bradykinin-induced calcium waves in differentiated N1E115 neuroblastoma. Using a comprehensive set of experimentally determined image and biochemical data as inputs to the model, we were able to generate simulations that reproduced the experimentally observed calcium waves in these cells. The model also enabled us to visualize the spatiotemporal behavior of InsP3 and gain an understanding of how the neuronal cell geometry controls the overall process. As additional examples of morphological control for very different spatial scales, I will describe the calcium signals following fertilization of frog eggs and how the unique morphology of dendritic spines can control InsP3 signals underlying long term depression.

Flexibility and Robustness of Ca2+ Oscillations

Flexibility and robustness are important properties of biological systems. These properties are here investigated in a model for simple and complex intracellular calcium oscillations. Flexibility and robustness characterize responses of a system to various external perturbations, such as deterministic pulses or periodic signals, as well as noise. Here, the influence of external periodic forcing is studied. The main point of the study is to compare responses of the system in a chaotic regime with those obtained in a regular periodic regime. We show that the response to external signals in terms of the range of synchronization does not depend on the complexity of Ca2+ oscillations but on the local divergence. Parts of attractors with close to zero local divergence are highly susceptible to external perturbations, thus facilitating signal detection and transduction, whereas highly negative local divergence areas characterize extremely robust regions that are virtually impossible to modify even with strong external signals. The results of the study are applicable for studying cell coupling, robustness to white noise and give an explanation of the constructive and destructive role of noise in the sense of stochastic resonance.

The TRP Ca2+ Channel and Signal Transduction

The Transient Receptor Potential (TRP) proteins constitute a large and diverse family of channel proteins, which is conserved through evolution. TRP channel proteins have critical functions in many tissues and cell types, but their gating mechanism is an enigma. I'll report on two important new properties of Drosophila TRP and TRP-like (TRPL) channels. We found that TRPL is translocated back and forth between the signaling membrane and an intracellular compartment by a light-regulated mechanism. A high level of rhabdomeral TRPL characteristic of dark-raised flies is functionally manifested in the properties of the light induced current and thus represents a novel mechanism to fine-tune visual responses. We also gained a new insight on the activation mechanism of the TRP and TRPL channels by which both Ca2+ and protein dephosphorylation are required for channel activation. ATP depletion or inhibition of protein kinase C activated the TRP channels, while photo-release of caged ATP or application of phorbol ester antagonized channels openings in the dark. Furthermore, Mg2+-dependent stable phosphorylation event or protein phosphatase inhibition abolished activation of the TRP and TRPL channels. While a high reduction of cellular Ca2+ abolished channel activation, subsequent application of Ca2+ combined with ATP depletion induced a robust dark current that was reminiscent of light responses. The results suggest that the combined action of Ca2+ and protein dephosphorylation activate the TRP and TRPL channels, while protein phosphorylation by PKC antagonized channels openings. The link of TRP gating to the metabolic state of cells makes cells expressing TRP extremely vulnerable to metabolic stress via a mechanism that may underlie retinal degeneration and neuronal cell death in mammals upon reduction in oxygen pressure in the tissue.

Calcium Buffers and Binding Proteins with Differing Kinetics Differentially Shape IP3-Evoked Calcium Signals

Cellular calcium buffers shape cytosolic calcium signals by regulating the availability and diffusional mobility of free calcium ions. Most experimental and theoretical studies of these effects have concentrated on signals arising from a fixed 'pulse' of calcium - for example, calcium entry through voltage-gated channels. A more complex case involves intracellular calcium liberation through inositol trisphosphate (IP3) receptors, which are themselves regulated by calcium. Thus, cytosolic buffers are expected to influence the successive cycles of diffusion and calcium-induced calcium release that act both between within clusters of IP3 receptors (to generate local 'puffs'), and between adjacent clusters (to generate global calcium waves).

We studied such interactions in Xenopus oocytes, using confocal line-scan microscopy together with photo-release of IP3. Intracellular injections of buffers with 'slow' calcium-binding kinetics (EGTA and parvalbumin) speeded the decay of calcium signals (Fig. 1A) and 'balkanized' IP3-evoked calcium waves into discrete puffs. Contrastingly, equivalent concentrations 'fast' buffers (BAPTA and calretinin) slowed IP3-evoked calcium responses (Fig. 1B) and promoted 'globalization' of spatially uniform calcium signals. These observations likely reflect buffer actions on calcium feedback at IP3 receptors, since the effects of EGTA and BAPTA on calcium signals evoked by influx through expressed N-type voltage gated channels were markedly less pronounced. Moreover, they point to the importance of buffer kinetics in shaping IP3-evoked calcium signals; likely because fast buffers can influence calcium feedback between individual IP3R within a cluster, whereas slow buffers are able to modulate only cluster-cluster interactions.

We propose that cell-specific expression of calcium binding proteins with distinct kinetics may shape the time course and spatial distribution of IP3-evoked calcium signals for specific physiological roles.

Supported by NIH GM 48071 and GM 58329

Work done in collaboration with Sheila L. Dargan and Beat Schwaller.

The Role of the Inositol-1,4,5-Trisphosphate Dynamics in Shaping Calcium Signals

In non-excitable cells agonist stimulation can induce, via production of inositol-1,4,5- trisphosphate (IP3), transient increases in cytoplasmic calcium so called calcium oscillations. Several mechanisms contribute to the generation and termination of these transients (e.g. calcium induced calcium release, calcium sequestration, inactivation of the IP3 receptors). Among these the calcium dependence of the IP3 metabolism is thought to be involved. Calcium affects the production, by activating phospholipase C (PLC), and the degradation, by activating IP3 3-kinase (IP3K), of IP3. Although there are indications that IP3 oscillates concomitantly to calcium, the role of these oscillations in shaping the calcium signal is still unclear.

Starting from models that show calcium oscillations for constant IP3 levels (e.g. models including CICR and slow inactivation of the IP3R's by calcium), I included the calcium activation of PLC and IP3K (representing an indirect positive and negative feedback of calcium on itself, respectively). The presence of one of the feedbacks greatly increases the stimulatory range where one observes oscillations. Long period oscillations (> 5min) as well as short period oscillations (< 30 sec) are found. The analysis shows that the dynamics of IP3 can be very important in controlling the long period of the oscillations. To determine which of the feedbacks is the most predominant I simulated the expression of an IP3 buffer. In experiments the expression of the IP3 receptor ligand binding domain can strongly modify or stop the calcium oscillations (L.D. Gaspers, A.P. Thomas communication). I studied how IP3 buffer can abolish oscillations. Furthermore the effects of IP3 buffer on the characteristics of the calcium spikes, the period of the oscillations and the propagation of calcium waves have been investigated. Comparing the theoretical with the experimental results indicates that first at least one of the feedbacks is present in the studied cells, and second that the positive feedback of calcium on IP3 (via PLC) is the predominant one. This feedback turns out to be crucial for shaping the calcium signal.

I thank A.P. Thomas and L.D. Gaspers from the New Jersey Medical School for the stimulating discussions.

The Ca-Activated Cl Channel and its Control in Rat Olfactory Receptor Neurons

Odorants activate sensory transduction in olfactory receptor neurons (ORNs) via a cAMP signalling cascade, which results in the opening of non-selective, cyclic nucleotide-gated (CNG) channels. The consequent Ca2+ influx through CNG channels activates Cl channels, which serve to amplify the transduction signal. We investigate here the functional interplay of the CNG channel with the Cl channel by using inside-out membrane patches excised from ORN dendritic knobs/cilia. The Cl channels on an excised patch could be activated by Ca2+ flux through the CNG channels which were opened by cytoplasmic application of cAMP. The magnitude of the Cl current depended on the strength of Ca-buffering in the bath solution, suggesting that the CNG and Cl channels were probably not organized as constituents of a local transducisome complex. Likewise, Cl channels and the Na/Ca exchanger, which extrudes Ca2+, appear to be spatially segregated. Based on the theory of buffered Ca2+ diffusion, we determined the Ca2+ diffusion coefficient and calculated that the CNG and Cl channel densities on the membrane were ca. 8 and 62 mu m 2, respectively. These densities, together with the Ca2+ diffusion coefficient, demonstrate that a given Cl channel is activated by Ca2+ originating from multiple CNG channels, thus allowing low-noise amplification of the olfactory receptor current.

Work done in collaboration with Paul J. Bauer1, King-Wai Yau, and Stephan Frings.

From Stimulus Intensity to Spike Trains in Frog Olfatory Receptor Neurons: In Vivo and in Computo Approaches

Olfactory stimuli are complex chemical signals whose composition varies quantitatively and qualitatively in space and time. Olfactory receptor neurons (ORNs) can monitor these variations and convey raw data to the brain from which biologically meaningful information can be extracted. The primary purpose of this work is to investigate quantitatively how the intensitive properties of odors, measured by their odorant concentration in the air, are encoded in the spike trains delivered by ORNs. To this end, we studied ORN responses in the frog olfactory epithelium to four volatile compounds, anisole, camphor, isoamyl acetate and limonene, which are strongly and distinctively odorous for humans.

All four odorants were applied as square pulses of 2-s duration at increasing concentrations. So, only the time variable was kept identical through all experiments. The neural activity was recorded one neuron at a time with extracellular electrodes from an intact epithelium in order to minimize the modifications due to experimental conditions [3, 4]. The spike train yielded by each stimulation was characterized by its latency, length (number of spikes), duration and median frequency. These variables were studied at the single neuron, neuron population and ciliary membrane levels.

At the single neuron level, the dose-response plots for the four variables were fitted to specific functions (negative exponential, alpha and half-Hill functions). The location along the concentration axis (e.g. thresholds), width (dynamic ranges) and heights (maximum latency, duration or frequency) of the fitted curves were evaluated for each plot.

At the neuron population level, the curves are extremely diverse. Both their dose characteristics (e.g. at threshold, at maximum response) and response characteristics (e.g. minimum latency, maximum frequency) were found to follow lognormal statistical distributions. Lognormal histograms are asymmetric with peaks close to the origin and long tails. The histogram of dynamic ranges in spike frequency is the most asymmetric, so that a significant fraction of neurons presents a much wider range than their one-decade peak, confirming the short dynamic range of the typical ORN but revealing the presence of a significant proportion of ORNs with a behavior very different from the average. From these histograms, response properties of the whole neuron population can be inferred. In general, thresholds, dynamic ranges and maximum responses are independent, which prevcnts their global categorization and can serve as a support for the qualitative coding of odorants.

Some of the response characteristics can be interpreted in terms of molecular events (deactivation of odorant molecules, odorant-receptor interaction, transduction cascade) using a chemo-electrical model of the ORN [1] and its environment [2] based on known mucus biochemical and neuron morpho-electrical data. From this model both dose-conductance curves and the apparent dissociation equilibrium constants of odorant-receptor interaction were determined, as well as their statistical distributions in the neuron population. The values found are in broad agreement with independent determinations.

References

1. Rospars, J.P., L?nsk?, P., Tuckwell, H.C., & Vermeulen, A. (1996). Coding of odor intensity in a steady-state deterministic model of an olfactory receptor cell neuron. Journal of Computational Neuroscience, 3, 51-72.

2. Rospars, J.P., Krivan, V., & Lansky, P. (2000a). Perireceptor and receptor events in olfaction. Comparison of concentration and flux detectors: a modeling study. Chemical Senses, 25, 293-311.

3. Rospars, J.P., L?nsk?, P., Duchamp-Viret, P., & Duchamp, A. (2000b). Spiking frequency vs. odorant concentration in olfactory receptor neurons. BioSystems, 58, 133-141.

4. Rospars, J.P., L?nsk?, P., Duchamp-Viret, P., & Duchamp, A. (2003). Relation between stimulus and response in frog olfactory receptor neurons in vivo. European Journal of Neuroscience, 18, 1135-1154.

Work done in collaboration with Petr L?nsk?, Andr? Duchamp, and Patricia Duchamp-Viret.

Bifurcation Analysis of Calcium Oscillations

The transition from a stationary regime to oscillations in the intracellular calcium concentration can occur in different ways. The mathematical tool to analyse this is bifurcation analysis. Calcium oscillations can emerge both by local bifurcations (e.g. supercritical and subcritical Hopf bifurcations) and global bifurcations (e.g. homoclinic and infinite-period bifurcations). The meaning of these terms is explained. Since calcium oscillations are relaxation oscillations (due to the presence of slow and fast processes), so-called canard orbits may arise near local bifurcation points. This means that quasi-harmonic oscillations with a very small amplitude grow very fast to become pulsed oscillations. The jump-like growth in amplitude, which also occurs in global bifurcations, may be of physiological advantage because "misinterpretation" of the signal is avoided. Near homoclinic and infinite-period bifurcations, the oscillations period can reach arbitrarily high values. This is interesting in the light of frequency encoding. These phenomona are illustrated by selected models of calcium oscillations.

Calcium Entry and Calcium Signaling - Different Routes, Different Roles

An enhanced entry of extracellular Ca2+ is essentially a universal component of receptor-activated Ca2+ signals in cells. Until recently, it was generally assumed that this always involved the well-known, and apparently ubiquitous, capacitative mechanism of entry. In this, the activation of Ca2+ entry results solely from the depletion of intracellular Ca2+ stores. The channels responsible are generically described as store-operated Ca2+ channels (SOC channels), and the most thoroughly studied of these is the Ca2+-release activated Ca2+ channel (CRAC channel). However, in recent years, evidence has accumulated demonstrating an additional noncapacitative mode of receptor-activated Ca2+ entry involving a distinct arachidonic acid-regulated Ca2+ channel (ARC channel). The ARC channels and the SOC/CRAC channels co-exist in cells, but they are not simply alternative, mutually redundant, routes of entry - they are differentially activated at different agonist concentrations in a unique and coordinated fashion, and have distinct roles in the control of the resulting Ca2+ signals. In particular, it is the ARC channels that provide the predominant mode of Ca2+ entry at the low agonist concentrations that give rise to oscillatory Ca2+ signals, and its effect is to modulate oscillation frequency. In addition, the fact that the SOC channels and ARC channels represent spatially distinct entities activated at different agonist concentrations has potential implications for the specific activation of distinct targets within the cell. (Supported by NIH grant GM 40457).

Stochastic Automata Network Models of Instantaneously-Coupled Intracellular Calcium Channels

Although there is consensus that Ca2+ puffs arise from the cooperative action of multiple IP3 receptors (IP3Rs), the precise relationship between single-channel kinetics and the collective phenomena of stochastic Ca2+ excitability is not well understood. Here we present a memory-efficient method by which mathematical models for IP3-sensitive Ca2+ release sites can be derived from Markov models of IP3R single-channel gating that include Ca2+ activation (IP3R-2 like), Ca2+ inactivation, or both (IP3R-1 like). Such models are essentially stochastic automata networks (SANs) that involve a large number of so-called 'functional transitions,' that is, the transition probabilities of the infinitesimal generator matrix (or Q-matrix) of one automata (i.e, an individual channel) may depend on the local [Ca2+] and thus the state of the other channels. We present an iterative method for calculating hitting times that leads to a directly estimate of various puff statistics (e.g., puff duration and inter-puff-interval) from a SAN descriptor.

Interacting Feedback Loops in Generation of IP-3 Dependent Calcium Oscillations

Since the first observations showing that hormones coupled to the formation of inositol 1,4,5-trisphospate (IP3) elicit oscillations of cytosolic calcium, there has been much speculation on the mechanism underlying these calcium dynamics. As the properties of the IP3-receptor (IP3R) were elucidated, it became clear that positive and negative feedback effects of Ca2+ directly on the IP3R could yield oscillatory calcium signaling. However, there are a number of other potential sites of calcium feedback in the IP3-dependent calcium-signaling pathway, particularly through alterations in the generation and elimination of IP3. We have utilized GFP-pleckstrin homology domain fusion proteins to monitor intracellular changes in IP3, and a molecular buffer of IP3 based on the ligand binding domain of the IP3R fused to GFP, which serves as an IP3 buffer in the physiologically relevant range. These tools have allowed us to investigate how IP3 dynamics might participate in calcium oscillations. In particular, we suggest that IP3 oscillations may interact with the intrinsic calcium regulation of the IP3R to yield coupled oscillators. This type of system has the potential to enrich the properties of calcium oscillations, and extend the dynamic range of frequency-modulation in Ca2+ signaling. A third level of feedback control of calcium oscillations occurs through the calcium uptake and release properties of mitochondria, which can modify calcium-feedback regulation of the IP3R by virtue of their close proximity to ER calcium release sites. The complex interplay between different feedback loops in the generation of IP3-dependent calcium oscillations, together with the spatial organization of the underlying components, gives rise to diverse patterns of calcium signaling that are tailored to regulate a wide variety of different processes.

Work done in collaboration with Lawrence D. Gaspers, Paul Burnett, Thomas Hofer, and Antonio Politit.

Calcium Seems to Do Everything, but Things Are Seldom What They Seem in Phototransduction

There have been numerous twists and turns in the road to understanding vertebrate phototransduction over the years. The phototransduction field has been characterized by great controversy surrounding numerous confusing and seemingly incompatible experimental results. Calcium has been at the heart of controversy on multiple occasions, including a recent one. In the dark, there is a circulating current across the rod membrane, which flows inward through channels in the outer segment and flows outward across the inner segment membrane. The modulation of the voltage across the rod membrane in response to light is a consequence of the reduction of this dark (light-sensitive) current. When rhodopsin absorbs a photon it is converted into an activated enzyme (R*) that initiates a cascade of biochemical reactions. These reactions lead to change in the concentration of an internal transmitter that gates the light-sensitive current. For many years the phototransduction community was divided between those who thought that this transmitter was calcium ions and those who thought it was cyclic-GMP (cGMP), until twenty years ago when definitive experimental evidence showed that the transmitter is cGMP. Other roles were found for calcium. Two salient features of rods are their ability to adapt to changes in ambient light level by adjusting the sensitivity and kinetics of their responses; and their remarkably reproducible responses to single photons. Calcium ions have been implicated in both these phenomena. A major outstanding problem in sensory physiology has been to understand how the rod's ingle-photon response (SPR) manages to have such little variation in amplitude and kinetics, despite the fact that it is mediated by the activity of a single molecule of activated rhodopsin (R*). Once R* is produced, it activates G-protein; G-protein activates phosphodiesterase; phosphodiesterase hydrolyzes cGMP; the cGMP concentration drops, resulting in closure of some of the light-sensitive channels; the reduction of inward current causes the rod membrane voltage to become hyperpolarized. The sequence of events following the activation of rhodopsin continues until R* is inactivated. The regularity of the single-photon response implies that the lifetime of R* is controlled with high precision-or does it? Closure of the light-sensitive channels blocks the entry of calcium, but it is still pumped out of the rod by a calcium exchanger. Therefore, the concentration of calcium is controlled by light, and it can serve as a feedback messenger to control sensitivity and the lifetime of R*. I will discuss the experimental evidence and mathematical theory for the role calcium in SPR reproducibility. Although evidence to support the calcium hypothesis seemed compelling, other experimental results and mathematical theory cast grave doubt on this hypothesis. Evidence on both sides can now be understood with the aid of a detailed stochastic biochemical kinetic model for rod phototransduction.

Work done in collaboration with Russ Hamer and Spero Nicholas.

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