Model of calcium oscillations due to negative feedback in olfactory cilia

Nitric oxide modulates NMDA receptor through a negative feedback mechanism and regulates the dynamical behavior of neuronal postsynaptic components

Nitric oxide (NO) is known to be an important regulator of neurological processes in the central nervous system which acts directly on the presynaptic neuron and enhances the release of neurotransmitters like glutamate into the synaptic cleft. Calcium influx activates a cascade of biochemical reactions to influence the production of nitric oxide in the postsynaptic neuron. This has been modeled in the present work as a system of ordinary differential equations, to explore the dynamics of the interacting components and predict the dynamical behavior of the postsynaptic neuron. It has been hypothesized that nitric oxide modulates the NMDA receptor via a feedback mechanism and regulates the dynamic behavior of postsynaptic components. Results obtained by numerical analyses indicate that the biochemical system is stimulus-dependent and shows oscillations of calcium and other components within a limited range of concentration. Some of the parameters such as stimulus strength, extracellular calcium concentration, and rate of nitric oxide feedback are crucial for the dynamics of the components in the postsynaptic neuron.

Analysis of dim-light responses in rod and cone photoreceptors with altered calcium kinetics

Rod and cone photoreceptors in the retina of vertebrates are the primary sensory neurons underlying vision. They convert light into an electrical current using a signal transduction pathway that depends on Ca[Formula: see text] feedback. It is known that manipulating the Ca[Formula: see text] kinetics affects the response shape and the photoreceptor sensitivity, but a precise quantification of these effects remains unclear. We have approached this task in mouse retina by combining numerical simulations with mathematical analysis. We consider a parsimonious phototransduction model that incorporates negative Ca[Formula: see text] feedback onto the synthesis of cyclic GMP, and fast buffering reactions to alter the Ca[Formula: see text] kinetics. We derive analytic results for the photoreceptor functioning in sufficiently dim light conditions depending on the photoreceptor type. We exploit these results to obtain conceptual and quantitative insight into how response waveform and amplitude depend on the underlying biophysical processes and the Ca[Formula: see text] feedback. With a low amount of buffering, the Ca[Formula: see text] concentration changes in proportion to the current, and responses to flashes of light are monophasic. With more buffering, the change in the Ca[Formula: see text] concentration becomes delayed with respect to the current, which gives rise to a damped oscillation and a biphasic waveform. This shows that biphasic responses are not necessarily a manifestation of slow buffering reactions. We obtain analytic approximations for the peak flash amplitude as a function of the light intensity, which shows how the photoreceptor sensitivity depends on the biophysical parameters. Finally, we study how changing the extracellular Ca[Formula: see text] concentration affects the response.

Ca2+-activated Cl- current ensures robust and reliable signal amplification in vertebrate olfactory receptor neurons

Activation of most primary sensory neurons results in transduction currents that are carried by cations. One notable exception is the vertebrate olfactory receptor neuron (ORN), where the transduction current is carried largely by the anion [Formula: see text] However, it remains unclear why ORNs use an anionic current for signal amplification. We have sought to provide clarification on this topic by studying the so far neglected dynamics of [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] in the small space of olfactory cilia during an odorant response. Using computational modeling and simulations we compared the outcomes of signal amplification based on either [Formula: see text] or [Formula: see text] currents. We found that amplification produced by [Formula: see text] influx instead of a [Formula: see text] efflux is problematic for several reasons: First, the [Formula: see text] current amplitude varies greatly, depending on mucosal ion concentration changes. Second, a [Formula: see text] current leads to a large increase in the ciliary [Formula: see text] concentration during an odorant response. This increase inhibits and even reverses [Formula: see text] clearance by [Formula: see text] exchange, which is essential for response termination. Finally, a [Formula: see text] current increases the ciliary osmotic pressure, which could cause swelling to damage the cilia. By contrast, a transduction pathway based on [Formula: see text] efflux circumvents these problems and renders the odorant response robust and reliable.

Multiscale modeling of brain dynamics: from single neurons and networks to mathematical tools

The extreme complexity of the brain naturally requires mathematical modeling approaches on a large variety of scales; the spectrum ranges from single neuron dynamics over the behavior of groups of neurons to neuronal network activity. Thus, the connection between the microscopic scale (single neuron activity) to macroscopic behavior (emergent behavior of the collective dynamics) and vice versa is a key to understand the brain in its complexity. In this work, we attempt a review of a wide range of approaches, ranging from the modeling of single neuron dynamics to machine learning. The models include biophysical as well as data-driven phenomenological models. The discussed models include Hodgkin-Huxley, FitzHugh-Nagumo, coupled oscillators (Kuramoto oscillators, Rössler oscillators, and the Hindmarsh-Rose neuron), Integrate and Fire, networks of neurons, and neural field equations. In addition to the mathematical models, important mathematical methods in multiscale modeling and reconstruction of the causal connectivity are sketched. The methods include linear and nonlinear tools from statistics, data analysis, and time series analysis up to differential equations, dynamical systems, and bifurcation theory, including Granger causal connectivity analysis, phase synchronization connectivity analysis, principal component analysis (PCA), independent component analysis (ICA), and manifold learning algorithms such as ISOMAP, and diffusion maps and equation-free techniques. WIREs Syst Biol Med 2016, 8:438-458. doi: 10.1002/wsbm.1348 For further resources related to this article, please visit the WIREs website.

Mechanisms of regulation of olfactory transduction and adaptation in the olfactory cilium

Olfactory adaptation is a fundamental process for the functioning of the olfactory system, but the underlying mechanisms regulating its occurrence in intact olfactory sensory neurons (OSNs) are not fully understood. In this work, we have combined stochastic computational modeling and a systematic pharmacological study of different signaling pathways to investigate their impact during short-term adaptation (STA). We used odorant stimulation and electroolfactogram (EOG) recordings of the olfactory epithelium treated with pharmacological blockers to study the molecular mechanisms regulating the occurrence of adaptation in OSNs. EOG responses to paired-pulses of odorants showed that inhibition of phosphodiesterases (PDEs) and phosphatases enhanced the levels of STA in the olfactory epithelium, and this effect was mimicked by blocking vesicle exocytosis and reduced by blocking cyclic adenosine monophosphate (cAMP)-dependent protein kinase (PKA) and vesicle endocytosis. These results suggest that G-coupled receptors (GPCRs) cycling is involved with the occurrence of STA. To gain insights on the dynamical aspects of this process, we developed a stochastic computational model. The model consists of the olfactory transduction currents mediated by the cyclic nucleotide gated (CNG) channels and calcium ion (Ca²⁺)-activated chloride (CAC) channels, and the dynamics of their respective ligands, cAMP and Ca²⁺, and it simulates the EOG results obtained under different experimental conditions through changes in the amplitude and duration of cAMP and Ca²⁺ response, two second messengers implicated with STA occurrence. The model reproduced the experimental data for each pharmacological treatment and provided a mechanistic explanation for the action of GPCR cycling in the levels of second messengers modulating the levels of STA. All together, these experimental and theoretical results indicate the existence of a mechanism of regulation of STA by signaling pathways that control GPCR cycling and tune the levels of second messengers in OSNs, and not only by CNG channel desensitization as previously thought.

Disruption of intracellular calcium regulation is integral to aminoglycoside-induced hair cell death

Intracellular Ca(2+) is a key regulator of life or death decisions in cultured neurons and sensory cells. The role of Ca(2+) in these processes is less clear in vivo, as the location of these cells often impedes visualization of intracellular Ca(2+) dynamics. We generated transgenic zebrafish lines that express the genetically encoded Ca(2+) indicator GCaMP in mechanosensory hair cells of the lateral line. These lines allow us to monitor intracellular Ca(2+) dynamics in real time during aminoglycoside-induced hair cell death. After exposure of live larvae to aminoglycosides, dying hair cells undergo a transient increase in intracellular Ca(2+) that occurs shortly after mitochondrial membrane potential collapse. Inhibition of intracellular Ca(2+) elevation through either caged chelators or pharmacological inhibitors of Ca(2+) effectors mitigates toxic effects of aminoglycoside exposure. Conversely, artificial elevation of intracellular Ca(2+) by caged Ca(2+) release agents sensitizes hair cells to the toxic effects of aminoglycosides. These data suggest that alterations in intracellular Ca(2+) homeostasis play an essential role in aminoglycoside-induced hair cell death, and indicate several potential therapeutic targets to stem ototoxicity.

Concordant chemical reaction networks

We describe a large class of chemical reaction networks, those endowed with a subtle structural property called concordance. We show that the class of concordant networks coincides precisely with the class of networks which, when taken with any weakly monotonic kinetics, invariably give rise to kinetic systems that are injective - a quality that, among other things, precludes the possibility of switch-like transitions between distinct positive steady states. We also provide persistence characteristics of concordant networks, instability implications of discordance, and consequences of stronger variants of concordance. Some of our results are in the spirit of recent ones by Banaji and Craciun, but here we do not require that every species suffer a degradation reaction. This is especially important in studying biochemical networks, for which it is rare to have all species degrade.

A dynamical feedback model for adaptation in the olfactory transduction pathway

Olfactory transduction exhibits two distinct types of adaptation, which we denote multipulse and step adaptation. In terms of measured transduction current, multipulse adaptation appears as a decrease in the amplitude of the second of two consecutive responses when the olfactory neuron is stimulated with two brief pulses. Step adaptation occurs in response to a sustained steplike stimulation and is characterized by a return to a steady-state current amplitude close to the prestimulus value, after a transient peak. In this article, we formulate a dynamical model of the olfactory transduction pathway, which includes the kinetics of the CNG channels, the concentration of Ca ions flowing through them, and the Ca-complexes responsible for the regulation. Based on this model, a common dynamical explanation for the two types of adaptation is suggested. We show that both forms of adaptation can be well described using different time constants for the kinetics of Ca ions (faster) and the kinetics of the feedback mechanisms (slower). The model is validated on experimental data collected in voltage-clamp conditions using different techniques and animal species.

SELECTIVITY IMPROVEMENT IN A MODEL OF OLFACTORY RECEPTOR NEURON WITH ADSORPTION-DESORPTION NOISE

In biological olfactory systems, interaction of odorant molecules with olfactory receptor proteins is driven by Brownian motion. As a result, at chemical equilibrium, the total number of bound receptors changes randomly in time. Here we investigate the role of this effect, known in physics as adsorption-desorption noise, in the discriminating ability of olfactory receptor neurons. For this purpose we developed a computer program, which generates the adsorption-desorption process in a model neuron. We compared the processes resulting from two different odorants with different affinities for the receptor proteins. We took into account the threshold at which spikes are triggered and we calculated the neuronal selectivity due to the differences in the threshold-crossing statistics for the processes resulting from both odorants. We conclude that selectivity of the spiking response of the whole neuron is much greater than that of its receptor proteins in the near-threshold range of odorant concentrations.

System identification of Drosophila olfactory sensory neurons

The lack of a deeper understanding of how olfactory sensory neurons (OSNs) encode odors has hindered the progress in understanding the olfactory signal processing in higher brain centers. Here we employ methods of system identification to investigate the encoding of time-varying odor stimuli and their representation for further processing in the spike domain by Drosophila OSNs. In order to apply system identification techniques, we built a novel low-turbulence odor delivery system that allowed us to deliver airborne stimuli in a precise and reproducible fashion. The system provides a 1% tolerance in stimulus reproducibility and an exact control of odor concentration and concentration gradient on a millisecond time scale. Using this novel setup, we recorded and analyzed the in-vivo response of OSNs to a wide range of time-varying odor waveforms. We report for the first time that across trials the response of OR59b OSNs is very precise and reproducible. Further, we empirically show that the response of an OSN depends not only on the concentration, but also on the rate of change of the odor concentration. Moreover, we demonstrate that a two-dimensional (2D) Encoding Manifold in a concentration-concentration gradient space provides a quantitative description of the neuron's response. We then use the white noise system identification methodology to construct one-dimensional (1D) and two-dimensional (2D) Linear-Nonlinear-Poisson (LNP) cascade models of the sensory neuron for a fixed mean odor concentration and fixed contrast. We show that in terms of predicting the intensity rate of the spike train, the 2D LNP model performs on par with the 1D LNP model, with a root mean-square error (RMSE) increase of about 5 to 10%. Surprisingly, we find that for a fixed contrast of the white noise odor waveforms, the nonlinear block of each of the two models changes with the mean input concentration. The shape of the nonlinearities of both the 1D and the 2D LNP model appears to be, for a fixed mean of the odor waveform, independent of the stimulus contrast. This suggests that white noise system identification of Or59b OSNs only depends on the first moment of the odor concentration. Finally, by comparing the 2D Encoding Manifold and the 2D LNP model, we demonstrate that the OSN identification results depend on the particular type of the employed test odor waveforms. This suggests an adaptive neural encoding model for Or59b OSNs that changes its nonlinearity in response to the odor concentration waveforms.

Quantitative analysis of cellular metabolic dissipative, self-organized structures

One of the most important goals of the postgenomic era is understanding the metabolic dynamic processes and the functional structures generated by them. Extensive studies during the last three decades have shown that the dissipative self-organization of the functional enzymatic associations, the catalytic reactions produced during the metabolite channeling, the microcompartmentalization of these metabolic processes and the emergence of dissipative networks are the fundamental elements of the dynamical organization of cell metabolism. Here we present an overview of how mathematical models can be used to address the properties of dissipative metabolic structures at different organizational levels, both for individual enzymatic associations and for enzymatic networks. Recent analyses performed with dissipative metabolic networks have shown that unicellular organisms display a singular global enzymatic structure common to all living cellular organisms, which seems to be an intrinsic property of the functional metabolism as a whole. Mathematical models firmly based on experiments and their corresponding computational approaches are needed to fully grasp the molecular mechanisms of metabolic dynamical processes. They are necessary to enable the quantitative and qualitative analysis of the cellular catalytic reactions and also to help comprehend the conditions under which the structural dynamical phenomena and biological rhythms arise. Understanding the molecular mechanisms responsible for the metabolic dissipative structures is crucial for unraveling the dynamics of cellular life.

Modelling and sensitivity analysis of the reactions involving receptor, G-protein and effector in vertebrate olfactory receptor neurons

A biochemical model of the receptor, G-protein and effector (RGE) interactions during transduction in the cilia of vertebrate olfactory receptor neurons (ORNs) was developed and calibrated to experimental recordings of cAMP levels and the receptor current (RC). The model describes the steps from odorant binding to activation of the effector enzyme which catalyzes the conversion of ATP to cAMP, and shows how odorant stimulation is amplified and delayed by the RGE transduction cascade. A time-dependent sensitivity analysis was performed on the model. The model output-the cAMP production rate-is particularly sensitive to a few, dominant parameters. During odorant stimulation it depends mainly on the initial density of G-proteins and the catalytic constant for cAMP production.

Computational model of the insect pheromone transduction cascade

A biophysical model of receptor potential generation in the male moth olfactory receptor neuron is presented. It takes into account all pre-effector processes—the translocation of pheromone molecules from air to sensillum lymph, their deactivation and interaction with the receptors, and the G-protein and effector enzyme activation—and focuses on the main post-effector processes. These processes involve the production and degradation of second messengers (IP₃ and DAG), the opening and closing of a series of ionic channels (IP₃-gated Ca²⁺ channel, DAG-gated cationic channel, Ca²⁺-gated Cl⁻ channel, and Ca²⁺- and voltage-gated K⁺ channel), and Ca²⁺ extrusion mechanisms. The whole network is regulated by modulators (protein kinase C and Ca²⁺-calmodulin) that exert feedback inhibition on the effector and channels. The evolution in time of these linked chemical species and currents and the resulting membrane potentials in response to single pulse stimulation of various intensities were simulated. The unknown parameter values were fitted by comparison to the amplitude and temporal characteristics (rising and falling times) of the experimentally measured receptor potential at various pheromone doses. The model obtained captures the main features of the dose–response curves: the wide dynamic range of six decades with the same amplitudes as the experimental data, the short rising time, and the long falling time. It also reproduces the second messenger kinetics. It suggests that the two main types of depolarizing ionic channels play different roles at low and high pheromone concentrations; the DAG-gated cationic channel plays the major role for depolarization at low concentrations, and the Ca²⁺-gated Cl⁻ channel plays the major role for depolarization at middle and high concentrations. Several testable predictions are proposed, and future developments are discussed.

All sensory neurons transduce their natural stimulus, whether a molecule, a photon, or a mechanical force, in an electrical current flowing through their sensory membrane via similar molecular and ionic mechanisms. Olfactory receptor neurons (ORNs), whose stimuli are volatile molecules, are no exception, including one of the best known: the exquisitely sensitive ORNs of male moths that detect the sexual pheromone released by conspecific females. We provide a detailed computational model of the intracellular molecular mechanisms at work in this ORN type. We describe qualitatively and quantitatively how the initial event, the interaction of pheromone molecules with specialized receptors at the ORN surface, is amplified through a sequence of linked biochemical and electrical events into a whole cell response, the receptor potential. We detail the respective roles of the upward activating reactions involving a cascade of ionic channels permeable to cations, chloride and potassium, their control by feedback inactivating mechanisms, and the central regulatory role of calcium. This computational model contributes to an integrated understanding of this signalling pathway, provides testable hypotheses, and suggests new experimental approaches.

The electrochemical basis of odor transduction in vertebrate olfactory cilia

Most vertebrate olfactory receptor neurons share a common G-protein-coupled pathway for transducing the binding of odorant into depolarization. The depolarization involves 2 currents: an influx of cations (including Ca2+) through cyclic nucleotide-gated channels and a secondary efflux of Cl- through Ca2+-gated Cl- channels. The relation between stimulus strength and receptor current shows positive cooperativity that is attributed to the channel properties. This cooperativity amplifies the responses to sufficiently strong stimuli but reduces sensitivity and dynamic range. The odor response is transient, and prolonged or repeated stimulation causes adaptation and desensitization. At least 10 mechanisms may contribute to termination of the response; several of these result from an increase in intraciliary Ca2+. It is not known to what extent regulation of ionic concentrations in the cilium depends on the dendrite and soma. Although many of the major mechanisms have been identified, odor transduction is not well understood at a quantitative level.

Olfactory CNG channel desensitization by Ca2+/CaM via the B1b subunit affects response termination but not sensitivity to recurring stimulation

Ca2+/calmodulin-mediated negative feedback is a prototypical regulatory mechanism for Ca2+-permeable ion channels. In olfactory sensory neurons (OSNs), such regulation on the cyclic nucleotide-gated (CNG) channel is considered a major mechanism of OSN adaptation. To determine the role of Ca2+/calmodulin desensitization of the olfactory CNG channel, we introduced a mutation in the channel subunit CNGB1b in mice that rendered the channel resistant to fast desensitization by Ca2+/calmodulin. Contrary to expectations, mutant OSNs showed normal receptor current adaptation to repeated stimulation. Rather, they displayed slower response termination and, consequently, reduced ability to transmit olfactory information to the olfactory bulb. They also displayed reduced response decline during sustained odorant exposure. These results suggest that Ca2+/calmodulin-mediated CNG channel fast desensitization is less important in regulating the sensitivity to recurring stimulation than previously thought and instead functions primarily to terminate OSN responses.

Identification of Cl(Ca) channel distributions in olfactory cilia

Identification of detailed features of neuronal systems is an important challenge in the biosciences today. Transduction of an odor into an electrical signal occurs in the membranes of the cilia. The Cl(Ca) channels that reside in the ciliary membrane are activated by calcium, allow a depolarizing efflux of Cl(-) and are thought to amplify the electrical signal to the brain.In this paper, a mathematical model consisting of partial differential equations is developed to study two different experiments; one involving the interaction of the cyclic-nucleotide-gated (CNG) and Cl(Ca) channels and the other, the diffusion of Ca(2+) into cilia. This work builds on an earlier study (Mathematical modeling of the Cl(Ca) ion channels in frog olfactory cilia. Ph.D. Thesis, University of Cincinnati, Cincinnati, OH, 2006; Math. Comput. Modelling 2006; 43:945-956; Biophys. J. 2006; 91:179-188), which suggested that the CNG channels are clustered at about 0.28 of the length of a cilium from its open end. Closed-form solutions are derived after certain reductions in the model are made. These special solutions provide estimates of the channel distributions. Scientific computation is also used. This preliminary study suggests that the Cl(Ca) ion channels are also clustered at about one-third of the length of a cilium from its open end.

Calcium-signaling networks in olfactory receptor neurons

The olfactory neuroepithelium represents a unique interface between the brain and the external environment. Olfactory function comprises a distinct set of molecular tasks: sensory signal transduction, cytoprotection and adult neurogenesis. A multitude of biochemical studies has revealed the central role of Ca(2+) signaling in the function of olfactory receptor neurons (ORNs). We set out to establish Ca(2+)-dependent signaling networks in ORN cilia by proteomic analysis. We subjected a ciliary membrane preparation to Ca(2+)/calmodulin-affinity chromatography using mild detergent conditions in order to maintain functional protein complexes involved in olfactory Ca(2+) signaling. Thus, calmodulin serves as a valuable tool to gain access to novel Ca(2+)-regulated protein complexes. Tandem mass spectrometry (nanoscale liquid-chromatography-electrospray injection) identified 123 distinct proteins. Ninety-seven proteins (79%) could be assigned to specific olfactory functions, including 32 to sensory signal transduction and 40 to cytoprotection. We point out novel perspectives for research on the Ca(2+)-signaling networks in the olfactory system of the rat.

Olfactory clearance: what time is needed in clinical practice?

Objective:

To determine olfactory adaptation and clearance times for healthy individuals, and to assess the effect of common variables upon these parameters.

Study design and setting:

Fourteen healthy volunteers were recruited for a series of tests. Their initial olfactory threshold levels for phenethyl alcohol were determined. After olfactory exposure to a saturated solution of phenethyl alcohol (i.e. olfactory adaptation), the time taken for subjects to return to their initial olfactory threshold was then recorded (i.e. olfactory clearance). Visual analogue scale scores for subjective variables were also recorded.

Results:

The 14 subjects performed 120 tests in total. Despite consistent linear trends within individuals, olfactory clearance times varied widely within and between individuals. The mean olfactory clearance time for phenethyl alcohol was 170 seconds (range 81–750). Univariate analysis showed a relationship between olfactory clearance times and age (p = 0.031), symptoms (p = 0.029) and mood (p = 0.048).

Conclusions:

When testing a person's sense of smell in a clinical setting, recent exposure to similar smells should be noted, and a period of 15 minutes needs to be allowed before retesting if using phenethyl alcohol. Other variables need not be controlled, but greater clearance time may be needed for older patients.

Response and fluctuations of a two-state signaling module with feedback

We study the stochastic kinetics of a signaling module consisting of a two-state stochastic point process with negative feedback. In the active state, a product is synthesized which increases the active-to-inactive transition rate of the process. We analyze this simple autoregulatory module using a path-integral technique based on the temporal statistics of state flips of the process. We develop a systematic framework to calculate averages, autocorrelations, and response functions by treating the feedback as a weak perturbation. Explicit analytical results are obtained to first order in the feedback strength. Monte Carlo simulations are performed to test the analytical results in the weak feedback limit and to investigate the strong feedback regime. We conclude by relating some of our results to experimental observations in the olfactory and visual sensory systems.

Oscillations and temporal signalling in cells

The development of new techniques to quantitatively measure gene expression in cells has shed light on a number of systems that display oscillations in protein concentration. Here we review the different mechanisms which can produce oscillations in gene expression or protein concentration using a framework of simple mathematical models. We focus on three eukaryotic genetic regulatory networks which show 'ultradian' oscillations, with a time period of the order of hours, and involve, respectively, proteins important for development (Hes1), apoptosis (p53) and immune response (NF-kappaB). We argue that underlying all three is a common design consisting of a negative feedback loop with time delay which is responsible for the oscillatory behaviour.

Switching mechanism for branched biochemical fluxes: Graph-theoretical analysis

A graph-theoretical method is applied to characterize the structure of a simplest switching mechanism of common biochemical importance. This mechanism is based on competition of two coupled substrate-binding pathways for a single substrate. No other regulatory interactions are shown to be needed for the switching phenomenon to be observed. It is shown that switch in branch effluxes is observed as bistability or reciprocal oscillations, depending on the value of steady influx. Frequency of reciprocal efflux oscillations in branches is regulated by steady influx. Therefore, the switching mechanism can function as the coding mechanism in the manner of "influx steady level-efflux frequency". The calculated kinetic equations for the switching mechanism demonstrate very steep transitions in the branch fluxes without using high non-linearity of these equations.

Modelling the early steps of transduction in insect olfactory receptor neurons

Olfactory transduction is a multistep process whose basic function is to convert a low energy reaction, the odorant-receptor interaction that may involve a single odorant molecule, into a whole cell electrical response, the receptor potential, which triggers the firing of one or more action potentials. Although much effort has been devoted to the experimental analysis of transduction in olfactory receptor neurons (ORNS), especially in the favorable moth sex-pheromone receptor neuron, its modelling is less advanced. The model we investigated, which takes into account the translocation of pheromone molecules from air to the extracellular space, their deactivation and their interaction with receptors, focuses on the membrane cascade. It involves the interaction of receptors, G-proteins and effector enzymes, whose reaction rates are limited by lateral diffusion in the membrane. The evolutions in time of these species in response to single pulse stimulation of various intensities were compared to one another and to the experimentally measured electrical response. The results obtained suggest that the receptor-to-effector conversion is fast with respect to the receptor response, that it presents a small amplification factor, contrary to the photoreceptor, and that most of the amplification is achieved in the post-effector processes involving the second messenger and ionic channels.

Fast adaptation in mouse olfactory sensory neurons does not require the activity of phosphodiesterase

Vertebrate olfactory sensory neurons rapidly adapt to repetitive odorant stimuli. Previous studies have shown that the principal molecular mechanisms for odorant adaptation take place after the odorant-induced production of cAMP, and that one important mechanism is the negative feedback modulation by Ca²⁺-calmodulin (Ca²⁺-CaM) of the cyclic nucleotide-gated (CNG) channel. However, the physiological role of the Ca²⁺-dependent activity of phosphodiesterase (PDE) in adaptation has not been investigated yet. We used the whole-cell voltage-clamp technique to record currents in mouse olfactory sensory neurons elicited by photorelease of 8-Br-cAMP, an analogue of cAMP commonly used as a hydrolysis-resistant compound and known to be a potent agonist of the olfactory CNG channel. We measured currents in response to repetitive photoreleases of cAMP or of 8-Br-cAMP and we observed similar adaptation in response to the second stimulus. Control experiments were conducted in the presence of the PDE inhibitor IBMX, confirming that an increase in PDE activity was not involved in the response decrease. Since the total current activated by 8-Br-cAMP, as well as that physiologically induced by odorants, is composed not only of current carried by Na⁺ and Ca²⁺ through CNG channels, but also by a Ca²⁺-activated Cl⁻ current, we performed control experiments in which the reversal potential of Cl⁻ was set, by ion substitution, at the same value of the holding potential, −50 mV. Adaptation was measured also in these conditions of diminished Ca²⁺-activated Cl⁻ current. Furthermore, by producing repetitive increases of ciliary's Ca²⁺ with flash photolysis of caged Ca²⁺, we showed that Ca²⁺-activated Cl⁻ channels do not adapt and that there is no Cl⁻ depletion in the cilia. All together, these results indicate that the activity of ciliary PDE is not required for fast adaptation to repetitive stimuli in mouse olfactory sensory neurons.

Minimal model of spiky oscillations in NF-kappaB signaling

The NF-kappaB signaling system is involved in a variety of cellular processes including immune response, inflammation, and apoptosis. Recent experiments have found oscillations in the nuclear-cytoplasmic translocation of the NF-kappaB transcription factor [Hoffmann, A., et al. (2002) Science 298, ; Nelson, D. E., et al. (2004) Science 306, .] How the cell uses the oscillations to differentiate input conditions and send specific signals to downstream genes is an open problem. We shed light on this issue by examining the small core network driving the oscillations, which we show is designed to produce periodic spikes in nuclear NF-kappaB concentration. The presence of oscillations is extremely robust to variation of parameters, depending mainly on the saturation of the active degradation rate of IkappaB, an inhibitor of NF-kappaB. The oscillations can be used to regulate downstream genes in a variety of ways. In particular, we show that genes to whose operator sites NF-kappaB binds and dissociates fast can respond very sensitively to changes in the input signal, with effective Hill coefficients of >20.

Cyclic nucleotide-gated ion channels in sensory transduction

Cyclic nucleotide-gated (CNG) channels, directly activated by the binding of cyclic nucleotides, were first discovered in retinal rods, cones and olfactory sensory neurons. In the visual and olfactory systems, CNG channels mediate sensory transduction by conducting cationic currents carried primarily by sodium and calcium ions. In olfactory transduction, calcium in combination with calmodulin exerts a negative feedback on CNG channels that is the main molecular mechanism responsible for fast adaptation in olfactory sensory neurons. Six mammalian CNG channel genes are known and some human visual disorders are caused by mutations in retinal rod or cone CNG genes.