Modeling oscillations and waves of cAMP in Dictyostelium discoideum cells

Design patterns of biological cells

Design patterns are generalized solutions to frequently recurring problems. They were initially developed by architects and computer scientists to create a higher level of abstraction for their designs. Here, we extend these concepts to cell biology to lend a new perspective on the evolved designs of cells' underlying reaction networks. We present a catalog of 21 design patterns divided into three categories: creational patterns describe processes that build the cell, structural patterns describe the layouts of reaction networks, and behavioral patterns describe reaction network function. Applying this pattern language to the E. coli central metabolic reaction network, the yeast pheromone response signaling network, and other examples lends new insights into these systems.

The Use of Diffusion Calculations and Monte Carlo Simulations to Understand the Behavior of Cells in Dictyostelium Communities

Microbial communities are the simplest possible model of multicellular tissues, allowing studies of cell-cell interactions to be done with as few extraneous factors as possible. For instance, the eukaryotic microbe Dictyostelium discoideum proliferates as single cells, and when starved, the cells aggregate together and form structures of ~20,000 cells. The cells use a variety of signals to direct their movement, inform each other of their local cell density and whether they are starving, and organize themselves into groups of ~20,000 cells. Mathematical models and computational approaches have been a key check on, and guide of, the experimental work. In this minireview, I will discuss diffusion calculations and Monte Carlo simulations that were used for Dictyostelium studies that offer general paradigms for several aspects of cell-cell communication. For instance, computational work showed that diffusible secreted cell-density sensing (quorum) factors can diffuse away so quickly from a single cell that the local concentration will not build up to incorrectly cause the cell to sense that it is in the presence of a high density of other cells secreting that signal. In another example, computation correctly predicted a mechanism that allows a group of cells to break up into subgroups. These are thus some examples of the power and necessity of computational work in biology.

Two-photon microscopy assessment of the overall energy metabolism alteration of amoeba in hypertonic environment

In this study, a two-photon fluorescence microscopic imaging technique is reported for assessment the effect of dynamic hypertonic environment on the overall energy metabolism alteration and adaptation of soil-living amoeba Dictyostelium discoideum. For that purpose the fluorescence intensity of mitochondrial reduced nicotinamide adenine dinucleotide (NADH) was monitored and quantified in order to evaluate the corresponded metabolic state of monolayer cultured cells. The two-photon excitation of NADH with 720 nm near infrared irradiation produced blue fluorescence emission with maximum wavelength centered at 460 nm. The benefits of reported noninvasive microscopic technique are the significantly less cellular damage and avoiding the excitation of other biomolecules except of NADH. It enabled to acquire data for NADH levels of the observed cells on agar plate specimen and hypertonic nutrition media in a Petri dish. The method demonstrated also good sensitivity, reproducibility and the obtained results revealed that D. discoideum species form aggregation in hypertonic environment within several minutes with aim to survive. The formed aggregate had amorphous shape and it consisted from dozen amoeba cells, which kept their NADH amount in constant level for few hours. The reported imaging method might be applicable in various studies for characterization of metabolic events and assessment of the cell energy balance in hypertonic environment.

Biological Oscillators in Nanonetworks-Opportunities and Challenges

One of the major issues in molecular communication-based nanonetworks is the provision and maintenance of a common time knowledge. To stay true to the definition of molecular communication, biological oscillators are the potential solutions to achieve that goal as they generate oscillations through periodic fluctuations in the concentrations of molecules. Through the lens of a communication systems engineer, the scope of this survey is to explicitly classify, for the first time, existing biological oscillators based on whether they are found in nature or not, to discuss, in a tutorial fashion, the main principles that govern the oscillations in each oscillator, and to analyze oscillator parameters that are most relevant to communication engineer researchers. In addition, the survey highlights and addresses the key open research issues pertaining to several physical aspects of the oscillators and the adoption and implementation of the oscillators to nanonetworks. Moreover, key research directions are discussed.

Basin of Attraction of Solutions with Pattern Formation in Slow-Fast Reaction-Diffusion Systems

This article is devoted to the characterization of the basin of attraction of pattern solutions for some slow-fast reaction-diffusion systems with a symmetric property and an underlying oscillatory reaction part. We characterize some subsets of initial conditions that prevent the dynamical system to evolve asymptotically toward solutions which are homogeneous in space. We also perform numerical simulations that illustrate theoretical results and give rise to symmetric and non-symmetric pattern solutions. We obtain these last solutions by choosing particular random initial conditions.

Regulation of Spatiotemporal Patterns by Biological Variability: General Principles and Applications to Dictyostelium discoideum

Spatiotemporal patterns often emerge from local interactions in a self-organizing fashion. In biology, the resulting patterns are also subject to the influence of the systematic differences between the system’s constituents (biological variability). This regulation of spatiotemporal patterns by biological variability is the topic of our review. We discuss several examples of correlations between cell properties and the self-organized spatiotemporal patterns, together with their relevance for biology. Our guiding, illustrative example will be spiral waves of cAMP in a colony of Dictyostelium discoideum cells. Analogous processes take place in diverse situations (such as cardiac tissue, where spiral waves occur in potentially fatal ventricular fibrillation) so a deeper understanding of this additional layer of self-organized pattern formation would be beneficial to a wide range of applications. One of the most striking differences between pattern-forming systems in physics or chemistry and those in biology is the potential importance of variability. In the former, system components are essentially identical with random fluctuations determining the details of the self-organization process and the resulting patterns. In biology, due to variability, the properties of potentially very few cells can have a driving influence on the resulting asymptotic collective state of the colony. Variability is one means of implementing a few-element control on the collective mode. Regulatory architectures, parameters of signaling cascades, and properties of structure formation processes can be "reverse-engineered" from observed spatiotemporal patterns, as different types of regulation and forms of interactions between the constituents can lead to markedly different correlations. The power of this biology-inspired view of pattern formation lies in building a bridge between two scales: the patterns as a collective state of a very large number of cells on the one hand, and the internal parameters of the single cells on the other.

Pattern formation is abundant in nature—from the rich ornaments of sea shells and the diversity of animal coat patterns to the myriad of fractal structures in biology and pattern-forming colonies of bacteria. Particularly fascinating are patterns changing with time, spatiotemporal patterns, like propagating waves and aggregation streams. Bacteria form large branched and nested aggregation-like patterns to immobilize themselves against water flow. The individual amoeba in Dictyostelium discoideum colonies initiates a transition to a collective multicellular state via a quorum-sensing form of communication—a cAMP signal propagating through the community in the form of spiral waves—and the subsequent chemotactic response of the cells leads to branch-like aggregation streams. The theoretical principle underlying most of these spatial and spatiotemporal patterns is self-organization, in which local interactions lead to patterns as large-scale collective”modes” of the system. Over more than half a century, these patterns have been classified and analyzed according to a”physics paradigm,” investigating such questions as how parameters regulate the transitions among patterns, which (types of) interactions lead to such large-scale patterns, and whether there are "critical parameter values" marking the sharp, spontaneous onset of patterns. A fundamental discovery has been that simple local interaction rules can lead to complex large-scale patterns. The specific pattern "layouts" (i.e., their spatial arrangement and their geometric constraints) have received less attention. However, there is a major difference between patterns in physics and chemistry on the one hand and patterns in biology on the other: in biology, patterns often have an important functional role for the biological system and can be considered to be under evolutionary selection. From this perspective, we can expect that individual biological elements exert some control on the emerging patterns. Here we explore spiral wave patterns as a prominent example to illustrate the regulation of spatiotemporal patterns by biological variability. We propose a new approach to studying spatiotemporal data in biology: analyzing the correlation between the spatial distribution of the constituents’ properties and the features of the spatiotemporal pattern. This general concept is illustrated by simulated patterns and experimental data of a model organism of biological pattern formation, the slime mold Dictyostelium discoideum. We introduce patterns starting from Turing (stripe and spot) patterns, together with target waves and spiral waves. The biological relevance of these patterns is illustrated by snapshots from real and theoretical biological systems. The principles of spiral wave formation are first explored in a stylized cellular automaton model and then reproduced in a model of Dictyostelium signaling. The shaping of spatiotemporal patterns by biological variability (i.e., by a spatial distribution of cell-to-cell differences) is demonstrated, focusing on two Dictyostelium models. Building up on this foundation, we then discuss in more detail how the nonlinearities in biological models translate the distribution of cell properties into pattern events, leaving characteristic geometric signatures.

Cell-to-cell coordination for the spontaneous cAMP oscillation in Dictyostelium

We propose a new cellular dynamics scheme for the spontaneous cAMP oscillations in Dictyostelium discoideum. Our scheme seamlessly integrates both receptor dynamics and G-protein dynamics into our previously developed cellular dynamics scheme. Extensive computer simulation studies based on our new cellular dynamics scheme were conducted in mutant cells to evaluate the molecular network. The validity of our proposed molecular network as well as the controversial PKA-dependent negative feedback mechanism was supported by our simulation studies. Spontaneous cAMP oscillations were not observed in a single mutant cell. However, multicellular states of various mutant cells consistently initiated spontaneous cAMP oscillations. Therefore, cell-to-cell coordination via the cAMP receptor is essential for the robust initiation of spontaneous cAMP oscillations.

Dictyostelium Ric8 is a nonreceptor guanine exchange factor for heterotrimeric G proteins and is important for development and chemotaxis

Heterotrimeric G proteins couple external signals to the activation of intracellular signal transduction pathways. Agonist-stimulated guanine nucleotide exchange activity of G-protein-coupled receptors results in the exchange of G-protein-bound GDP to GTP and the dissociation and activation of the complex into Gα-GTP and a Gβγ dimer. In Dictyostelium, a basal chemotaxis pathway consisting of heterotrimeric and monomeric G proteins is sufficient for chemotaxis. Symmetry breaking and amplification of chemoattractant sensing occurs between heterotrimeric G protein signaling and Ras activation. In a pull-down screen coupled to mass spectrometry, with Gα proteins as bait, we have identified resistant to inhibitors of cholinesterase 8 (Ric8) as a nonreceptor guanine nucleotide exchange factor for Gα-protein. Ric8 is not essential for the initial activation of heterotrimeric G proteins or Ras by uniform chemoattractant; however, it amplifies Gα signaling, which is essential for Ras-mediated symmetry breaking during chemotaxis and development.

Predictability of spatio-temporal patterns in a lattice of coupled FitzHugh-Nagumo oscillators

In many biological systems, variability of the components can be expected to outrank statistical fluctuations in the shaping of self-organized patterns. In pioneering work in the late 1990s, it was hypothesized that a drift of cellular parameters (along a 'developmental path'), together with differences in cell properties ('desynchronization' of cells on the developmental path) can establish self-organized spatio-temporal patterns (in their example, spiral waves of cAMP in a colony of Dictyostelium discoideum cells) starting from a homogeneous state. Here, we embed a generic model of an excitable medium, a lattice of diffusively coupled FitzHugh-Nagumo oscillators, into a developmental-path framework. In this minimal model of spiral wave generation, we can now study the predictability of spatio-temporal patterns from cell properties as a function of desynchronization (or 'spread') of cells along the developmental path and the drift speed of cell properties on the path. As a function of drift speed and desynchronization, we observe systematically different routes towards fully established patterns, as well as strikingly different correlations between cell properties and pattern features. We show that the predictability of spatio-temporal patterns from cell properties contains important information on the pattern formation process as well as on the underlying dynamical system.

The relationship between pulsatile GnRH secretion and cAMP production in immortalized GnRH neurons

In perifused immortalized GnRH neurons (GT1-7), simultaneous measurements of GnRH and cAMP revealed that the secretory profiles for both GnRH and cAMP are pulsatile. An analysis of GnRH and cAMP pulses in 16 independent experiments revealed that 25% of pulses coincide. Inversion of the peak and nadir levels was found in 33% and random relationship between GnRH and cAMP found in 42% of analyzed pulses. The random relation between GnRH and cAMP pulse resets to synchronous after an inverse relation between pulses occurred during the major GnRH release, indicating that GnRH acts as a switching mechanism to synchronize cAMP and GnRH release in perifused GT1-7 neurons. Activation of GnRH receptors with increasing agonist concentrations caused a biphasic change in cAMP levels. Low nanomolar concentrations increased cAMP production, but at high concentrations the initial increase was followed by a rapid decline to below the basal level. Blockade of the GnRH receptors by peptide and nonpeptide antagonists generated monotonic nonpulsatile increases in both GnRH and cAMP production. These findings indicate that cAMP positively regulates GnRH secretion but does not participate in the mechanism of pulsatile GnRH release.

A cAMP signaling model explains the benefit of maintaining two forms of phosphodiesterase in Dictyostelium

Starving Dictyostelium cells respond chemotactically to cell-generated waves of cyclic adenosine -3',5'- monophosphate (cAMP) that guide cell aggregation toward a signaling center. In this process, a large number of cells are recruited, resulting in the formation of aggregation territories that are essential for fruiting body formation. The enzyme PdsA phosphodiesterase (PDE), a crucial component of the signaling system, breaks down the external cAMP and can be either membrane-bound or secreted. The existence of two such forms is unusual in cell biology, and it remains to be determined why they have both been maintained through evolution. Here, using a model of the cAMP signaling system, I show that colonies can successfully organize into aggregates over a wider range of initial cell densities when both forms of PDE are present in an appropriately tuned ratio than when only a single form is present. The model indicates that membrane-bound PDE maintains aggregation-territory integrity in colonies with high initial cell density, whereas the secreted form is important for wave propagation at low cell densities. Thus, the ultimate retention of both forms can increase territory size. These findings have implications for other excitable media, including Ca(2+) propagation in cardiac cells and propagation of electrical excitation in nerve axons, since these systems have similar features of spatial nonuniform "release" and "degradation" of the relevant signals.

Decreased expression of A-kinase anchoring protein 150 in GT1 neurons decreases neuron excitability and frequency of intrinsic gonadotropin-releasing hormone pulses

The frequency of intrinsic pulsatile GnRH secretion from endogenous GnRH neurons and GT1 GnRH cell lines is stimulated by increased intracellular cAMP levels. The downstream molecules comprising the cAMP signaling pathway are organized in microdomains by a family of scaffolding proteins, A-kinase anchoring proteins (AKAPs). These molecules tether protein kinase A, cAMP-specific phosphodiesterases, phosphatases to known substrates. In neurons AKAP150 organizes many of the signaling molecules known to regulate the excitability and intrinsic pulsatile activity of GnRH neurons. AKAP150 was expressed in both the GT1-1 and GT1-7 cells. We determined the role of AKAP150 in coordinating GT1-1 cell excitability and intrinsic GnRH pulsatile secretion by lowering AKAP150 levels with a small interfering RNA (siRNA) adenovirus construct to AKAP150 (Ad-AKAP150-siRNA). Infection with Ad-AKAP150-siRNA specifically decreased AKAP150 mRNA levels by 74% and protein levels by 53% relative to uninfected cells or cells infected with a luciferase control adenovirus siRNA vector. In GT1 cells, spontaneous Ca(2+) oscillations, an index of neuron excitability, are stimulated by increased levels of intracellular cAMP and lowered by decreased levels. The frequency of spontaneous Ca(2+) oscillations in Ad-AKAP150-siRNA-treated GT1-1 cells decreased by 47.2% relative to controls. A dramatic decrease in the number of spontaneous GnRH pulses was also observed after infection with Ad-AKAP150-siRNA. The interpulse interval increased to 143 +/- 20.25 min in Ad-AKAP150-siRNA infected cells from 32.2 +/- 7.3 min in luciferase control adenovirus siRNA vector-infected cells. These data demonstrate an important role of AKAP150 in coordinating signaling events regulating the frequency of intrinsic pulsatile GnRH secretion.

Predicting the distribution of spiral waves from cell properties in a developmental-path model of Dictyostelium pattern formation

The slime mold Dictyostelium discoideum is one of the model systems of biological pattern formation. One of the most successful answers to the challenge of establishing a spiral wave pattern in a colony of homogeneously distributed D. discoideum cells has been the suggestion of a developmental path the cells follow (Lauzeral and coworkers). This is a well-defined change in properties each cell undergoes on a longer time scale than the typical dynamics of the cell. Here we show that this concept leads to an inhomogeneous and systematic spatial distribution of spiral waves, which can be predicted from the distribution of cells on the developmental path. We propose specific experiments for checking whether such systematics are also found in data and thus, indirectly, provide evidence of a developmental path.

The ups and downs of p53: understanding protein dynamics in single cells

Cells living in a complex environment must constantly detect, process and appropriately respond to changing signals. Therefore, all cellular information processing is dynamic in nature. As a consequence, understanding the process of signal transduction often requires detailed quantitative analysis of dynamic behaviours. Here, we focus on the oscillatory dynamics of the tumour suppressor protein p53 as a model for studying protein dynamics in single cells to better understand its regulation and function.

Oscillations and waves of cyclic AMP in Dictyostelium: a prototype for spatio-temporal organization and pulsatile intercellular communication

The amoebae Dictyostelium discoideum aggregate after starvation in a wavelike manner in response to periodic pulses of cyclic AMP (cAMP) secreted by cells which behave as aggregation centers. In addition to autonomous oscillations, the cAMP signaling system that controls aggregation is also capable of excitable behavior, which consists in the transient amplification of suprathreshold pulses of extracellular cAMP. Since the first theoretical model for slime mold aggregation proposed by Keller and Segel in 1970, many theoretical studies have addressed various aspects of the mechanism and function of cAMP signaling in Dictyostelium. This paper presents a brief overview of these developments as well as some reminiscences of the author's collaboration with Lee Segel in modeling the dynamics of cAMP relay and oscillations. Considered in turn are models for cAMP signaling in Dictyostelium, the developmental path followed by the cAMP signaling system after starvation, the frequency encoding of cAMP signals, and the origin of concentric or spiral waves of cAMP.

A model for the pulsatile secretion of gonadotropin-releasing hormone from synchronized hypothalamic neurons

Cultured gonadotropin-releasing hormone (GnRH) neurons have been shown to express GnRH receptors. GnRH binding to its receptors activates three types of G-proteins at increasing doses. These G-proteins selectively activate or inhibit GnRH secretion by regulating the intracellular levels of Ca2+ and cAMP. Based on these recent observations, we build a model in which GnRH plays the roles of a feedback regulator and a diffusible synchronizing agent. We show that this GnRH-regulated GnRH-release mechanism is sufficient for generating pulsatile GnRH release. The model reproduces the observed effects of some key drugs that disturb the GnRH pulse generator in specific ways. Simulations of 100 heterogeneous neurons revealed that the synchronization mediated by a common pool of diffusible GnRH is robust. The population can generate synchronized pulsatile signals even when all the individual GnRH neurons oscillate at different amplitudes and peak at different times. These results suggest that the positive and negative effects of the autocrine regulation by GnRH on GnRH neurons are sufficient and robust in generating GnRH pulses.

Accordion waves in Myxococcus xanthus

Myxococcus xanthus are Gram-negative bacteria that glide on solid surfaces, periodically reversing their direction of movement. When starved, M. xanthus cells organize their movements into waves of cell density that sweep over the colony surface. These waves are unique: Although they appear to interpenetrate, they actually reflect off one another when they collide, so that each wave crest oscillates back and forth with no net displacement. Because the waves reflect the coordinated back and forth oscillations of the individual bacteria, we call them "accordion" waves. The spatial oscillations of individuals are a manifestation of an internal biochemical oscillator, probably involving the Frz chemosensory system. These internal "clocks," each of which is quite variable, are synchronized by collisions between individual cells using a contact-mediated signal-transduction system. The result of collision signaling is that the collective spatial behavior is much less variable than the individual oscillators. In this work, we present experimental observations in which individual cells marked with GFP can be followed in groups of unlabeled cells in monolayer cultures. These data, together with an agent-based computational model demonstrate that the only properties required to explain the ripple patterns are an asymmetric biochemical limit cycle that controls direction reversals and asymmetric contact-induced signaling between cells: Head-to-head signaling is stronger than head-to-tail signaling. Together, the experimental and computational data provide new insights into how populations of interacting oscillators can synchronize and organize spatially to produce morphogenetic patterns that may have parallels in higher organisms.

"Live memory" of the cell, the other hereditary memory of living systems

We propose to designate by the term "live memory" of the cell, the cytoplasmic memory. This phenomenon consists of non-genetic memory, but nevertheless includes transmission function, which may be "hereditary" via the ovum, from mother cell to daughter cell, or simply within the same cell from instant t to instant t+1. To understand this notion of "live memory", its role and interactions with DNA must be resituated; indeed, operational information belongs as much to the cell body and to its cytoplasmic regulatory protein components and other endogenous or exogenous ligands as it does to the DNA database. We will see in Section 2, using examples from recent experiments in biology, the principal roles of "live memory" in relation to the four aspects of cellular identity, memory of form, hereditary transmission and also working memory.

In a mirror dimly: tracing the movements of molecules in living cells

The random movement of molecules (diffusion) is fundamental to most cellular processes, including enzymatic reactions, signalling, protein-protein interaction, as well as domain and pattern formation. Despite playing a central role, diffusion is, to a large extent, under-appreciated in the cell biology community. One reason for this is that diffusion is rather challenging to study in living cells. This article is intended to explain, at least in part, how we can go about studying diffusion of molecules in living cells, why it is important and how it provides us with important clues about biological systems. As the title 'In a mirror dimly' suggests, we do this by monitoring faint light emitted by fluorescent probes or proteins using advanced optics (e.g. mirrors) and electronics. The data are then fitted and interpreted with mathematical and physical models, providing a glimpse into the world of molecules.

The Ups and Downs of Modeling the Cell Cycle

We discuss the impact of mathematical modeling on our understanding of the cell cycle. Although existing, detailed models confirm that the known interactions in the cell cycle can produce oscillations and predict behaviors such as hysteresis, they contain many parameters and are poorly constrained by data which are almost all qualitative. Questions about the basic architecture of the oscillator may be more amenable to modeling approaches that ignore molecular details. These include asking how the various elaborations of the basic oscillator affect the robustness of the system and how cells monitor their size and use this information to control the cell cycle.

Control analysis for autonomously oscillating biochemical networks

It has hitherto not been possible to analyze the control of oscillatory dynamic cellular processes in other than qualitative ways. The control coefficients, used in metabolic control analyses of steady states, cannot be applied directly to dynamic systems. We here illustrate a way out of this limitation that uses Fourier transforms to convert the time domain into the stationary frequency domain, and then analyses the control of limit cycle oscillations. In addition to the already known summation theorems for frequency and amplitude, we reveal summation theorems that apply to the control of average value, waveform, and phase differences of the oscillations. The approach is made fully operational in an analysis of yeast glycolytic oscillations. It follows an experimental approach, sampling from the model output and using discrete Fourier transforms of this data set. It quantifies the control of various aspects of the oscillations by the external glucose concentration and by various internal molecular processes. We show that the control of various oscillatory properties is distributed over the system enzymes in ways that differ among those properties. The models that are described in this paper can be accessed on http://jjj.biochem.sun.ac.za.

Resetting wave forms in dictyostelium territories

The mechanism by which spiral wave patterns appear in populations of Dictyostelium was probed experimentally by external chemical perturbation. Spiral waves, which often arise from the breakup of circular waves driven by pacemakers, typically entrain those pacemakers. We studied these processes by resetting the waves with a spatially uniform pulse of extrinsic cyclic AMP. A pattern of spirals reappeared if resetting was early in the signaling stage, but only targets emerged following late resetting, in a manner analogous to cardiac defibrillation. This supports recent hypotheses that wave pattern selection naturally occurs by slow temporal variation of the excitability of the cells.

Regulation of gonadotropin-releasing hormone release by cyclic AMP signalling pathways

The frequency and amplitude of gonadotropin-releasing hormone (GnRH) pulses are tightly regulated for the maintenance of reproductive cycles. Pulsatile GnRH release was shown to be an intrinsic property of murine GT1 GnRH neurons, and primate placodal GnRH neurons. GT1 neurons show spontaneous action potentials that are associated with Ca2+ oscillations and hormone secretion. Increased cyclic AMP (cAMP) levels in GT1 neurons appear to stimulate GnRH release by activation of cAMP-gated cation (CNG) channels. Activation of the CNG channels correlated with increased neuron excitability and Ca2+ oscillations. Activation of protein kinase A is not necessary for cAMP-induced stimulation of GnRH secretion, but appears to activate negative feedback pathways. Potential negative feedback pathways may decrease cAMP levels by inhibiting adenylyl cyclase V, and activating the phosphodiesterase, PDE4D3. These stimulatory and inhibitory cAMP-signalling pathways appear to regulate the excitability of the GT1 neurons, and may constitute a biological clock timing the pulsatile release of GnRH.

From simple to complex oscillatory behavior in metabolic and genetic control networks

We present an overview of mechanisms responsible for simple or complex oscillatory behavior in metabolic and genetic control networks. Besides simple periodic behavior corresponding to the evolution toward a limit cycle we consider complex modes of oscillatory behavior such as complex periodic oscillations of the bursting type and chaos. Multiple attractors are also discussed, e.g., the coexistence between a stable steady state and a stable limit cycle (hard excitation), or the coexistence between two simultaneously stable limit cycles (birhythmicity). We discuss mechanisms responsible for the transition from simple to complex oscillatory behavior by means of a number of models serving as selected examples. The models were originally proposed to account for simple periodic oscillations observed experimentally at the cellular level in a variety of biological systems. In a second stage, these models were modified to allow for complex oscillatory phenomena such as bursting, birhythmicity, or chaos. We consider successively (1) models based on enzyme regulation, proposed for glycolytic oscillations and for the control of successive phases of the cell cycle, respectively; (2) a model for intracellular Ca(2+) oscillations based on transport regulation; (3) a model for oscillations of cyclic AMP based on receptor desensitization in Dictyostelium cells; and (4) a model based on genetic regulation for circadian rhythms in Drosophila. Two main classes of mechanism leading from simple to complex oscillatory behavior are identified, namely (i) the interplay between two endogenous oscillatory mechanisms, which can take multiple forms, overt or more subtle, depending on whether the two oscillators each involve their own regulatory feedback loop or share a common feedback loop while differing by some related process, and (ii) self-modulation of the oscillator through feedback from the system's output on one of the parameters controlling oscillatory behavior. However, the latter mechanism may also be viewed as involving the interplay between two feedback processes, each of which might be capable of producing oscillations. Although our discussion primarily focuses on the case of autonomous oscillatory behavior, we also consider the case of nonautonomous complex oscillations in a model for circadian oscillations subjected to periodic forcing by a light-dark cycle and show that the occurrence of entrainment versus chaos in these conditions markedly depends on the wave form of periodic forcing. (c) 2001 American Institute of Physics.

Role of the cAMP signaling pathway in the regulation of gonadotropin-releasing hormone secretion in GT1 cells

We studied the signaling pathways coupling gonadotropin-releasing hormone (GnRH) secretion to elevations in cAMP levels in the GT1 GnRH-secreting neuronal cell line. We hypothesized that increased cAMP could be acting directly by means of cyclic nucleotide-gated (CNG) cation channels or indirectly by means of activation of cAMP-dependent protein kinase (PKA). We showed that GT1 cells express the three CNG subunits present in olfactory neurons (CNG2, -4.3, and -5) and exhibit functional cAMP-gated cation channels. Activation of PKA does not appear to be necessary for the stimulation of GnRH release by increased levels of cAMP. In fact, pharmacological inhibition of PKA activity caused an increase in the basal secretion of GnRH. Consistent with this observation activation PKA inhibited adenylyl cyclase activity, presumably by inhibiting adenylyl cyclase V expressed in the cells. Therefore, the stimulation of GnRH release by elevations in cAMP appears to be the result of depolarization of the neurons initiated by increased cation conductance by cAMP-gated cation channels. Activation of PKA may constitute a negative-feedback mechanisms for lowering cAMP levels. We hypothesize that these mechanisms could result in oscillations in cAMP levels, providing a biochemical basis for timing the pulsatile release of GnRH.