Uncovering bifurcation patterns in cortical synapses

Individual cortical synapses are known to exhibit a very complex short-time dynamic behaviour in response to simple “naturalistic” stimulation. We describe a computational study of the experimentally obtained excitatory post-synaptic potential trains of individual cortical synapses. By adopting a new nonlinear modelling scheme we construct robust and repeatable models of the underlying dynamics. These models suggest that cortical synapses exhibit a wide range of either periodic or chaotic dynamics. For stimulus at a fixed rate our models predict that the response of the individual synapse will vary from a fixed point to periodic and chaotic, depending on the frequency of stimulus. Dynamics for individual synapses vary widely, suggesting that the individual behaviour of synapses is highly tuned and that the dynamic behaviour of even a small network of synapse-coupled neurons could be extremely varied.     

Timing regulation in a network reduced from voltage-gated equations to a one-dimensional map

 We discuss a method by which the dynamics of a network of neurons, coupled by mutual inhibition, can be reduced to a one-dimensional map. This network consists of a pair of neurons, one of which is an endogenous burster, and the other excitable but not bursting in the absence of phasic input. The latter cell has more than one slow process. The reduction uses the standard separation of slow/fast processes; it also uses information about how the dynamics on the slow manifold evolve after a finite amount of slow time. From this reduction we obtain a one-dimensional map dependent on the parameters of the original biophysical equations. In some parameter regimes, one can deduce that the original equations have solutions in which the active phase of the originally excitable cell is constant from burst to burst, while in other parameter regimes it is not. The existence or absence of this kind of regulation corresponds to qualitatively different dynamics in the one-dimensional map. The computations associated with the reduction and the analysis of the dynamics includes the use of coordinates that parameterize by time along trajectories, and “singular Poincaré maps” that combine information about flows along a slow manifold with information about jumps between branches of the slow manifold. Received: 19 May 1997 / Revised version: 6 April 1998     

Can inverse density dependence at small spatial scales produce dynamic instability in animal populations?

All else being equal, inversely density-dependent (IDD) mortality destabilizes population dynamics. However, stability has not been investigated for cases in which multiple types of density dependence act simultaneously. To determine whether IDD mortality can destabilize populations that are otherwise regulated by directly density-dependent (DDD) mortality, I used scale transition approximations to model populations with IDD mortality at smaller “aggregation” scales and DDD mortality at larger “landscape” scales, a pattern observed in some reef fish and insect populations. I evaluated dynamic stability for a range of demographic parameter values, including the degree of compensation in DDD mortality and the degree of spatial aggregation, which together determine the relative importance of DDD and IDD processes. When aggregation-scale survival was a monotonically increasing function of density (a “dilution” effect), dynamics were stable except for extremely high levels of aggregation combined with either undercompensatory landscape-scale density dependence or certain values of adult fecundity. When aggregation-scale survival was a unimodal function of density (representing both “dilution” and predator “detection” effects), instability occurred with lower levels of aggregation and also depended on the values of fecundity, survivorship, detection effect, and DDD compensation parameters. These results suggest that only in extreme circumstances will IDD mortality destabilize dynamics when DDD mortality is also present, so IDD processes may not affect the stability of many populations in which they are observed. Model results were evaluated in the context of reef fish, but a similar framework may be appropriate for a diverse range of species that experience opposing patterns of density dependence across spatial scales.     

Measuring and quantifying dynamic visual signals in jumping spiders

Animals emit visual signals that involve simultaneous, sequential movements of appendages that unfold with varying dynamics in time and space. Algorithms have been recently reported (e.g. Peters et al. in Anim Behav 64:131–146, 2002) that enable quantitative characterization of movements as optical flow patterns. For decades, acoustical signals have been rendered by techniques that decompose sound into amplitude, time, and spectral components. Using an optic-flow algorithm we examined visual courtship behaviours of jumping spiders and depict their complex visual signals as “speed waveform”, “speed surface”, and “speed waterfall” plots analogous to acoustic waveforms, spectrograms, and waterfall plots, respectively. In addition, these “speed profiles” are compatible with analytical techniques developed for auditory analysis. Using examples from the jumping spider Habronattus pugillis we show that we can statistically differentiate displays of different “sky island” populations supporting previous work on diversification. We also examined visual displays from the jumping spider Habronattus dossenus and show that distinct seismic components of vibratory displays are produced concurrently with statistically distinct motion signals. Given that dynamic visual signals are common, from insects to birds to mammals, we propose that optical-flow algorithms and the analyses described here will be useful for many researchers.Damian O. Elias and Bruce R. Land contributed equallyAn erratum to this article can be found at     

Weevils and camellias in a Darwin’s race: model system for the study of eco-evolutionary interactions between species

Organisms are surrounded by their predators, parasites, hosts, and mutualists, being involved in reciprocal adaptation processes with such “biotic environment”. The concept of “coevolution”, therefore, provides a basis for the comprehensive understanding of evolutionary and ecological dynamics in biological communities and ecosystems. Recent studies have shown that coevolutionary processes are spatially heterogeneous and that traits mediating interspecific interactions can evolve rapidly in natural communities. Here, I discuss factors promoting the geographic differentiation of coevolutionary interactions, the spatial scales of the geographic structuring, and the pace of coevolutionary changes, reviewing findings in the arms race coevolution involving a long-mouthed weevil and its host camellia plant. Evolutionary, ecological, and population genetic studies on the system illuminated that viewpoints from the aspect of “coevolving biosphere” were important for predicting how ongoing anthropogenic change in global environment alter the spatiotemporal dynamics of biological communities.     

Activator-induced dynamic disorder and molecular memory in human two-pore domain hTREK1 K+ channel

Ion channels are fundamental molecules in the nervous system that catalyze the flux of ions across the cell membrane. Ion channel flux activity is comparable to the catalytic activity of enzyme molecules. Saturating concentrations of substrate induce “dynamic disorder” in the kinetic rate processes of single-enzyme molecules and consequently, develop correlative “memory” of the previous history of activities. Similarly, binding of ions as substrate alone or in presence of agonists affects the catalytic turnover of single-ion channels. Here, we investigated the possible existence of dynamic disorder and molecular memory in the single human-TREK1-channel due to binding of substrate/agonist using the excised inside–out patch-clamp technique. Our results suggest that the single-hTREK1-channel behaves as a typical Michaelis–Menten enzyme molecule with a high-affinity binding site for K⁺ ion as substrate. But, in contrast to enzyme, dynamic disorder in single-hTREK1-channel was not induced by substrate K⁺ binding, but required allosteric modification of the channel molecule by the agonist, trichloroethanol. In addition, interaction of trichloroethanol with hTREK1 induced strong correlation in the waiting time and flux intensity, exemplified by distinct mode-switching between high and low flux activities. This suggested the induction of molecular memory in the channel molecule by the agonist, which persisted for several decades in time. Our mathematical modeling studies identified the kinetic rate processes associated with dynamic disorder. It further revealed the presence of multiple populations of distinct conformations that contributed to the “heterogeneity” and consequently, to the molecular memory phenomenon that we observed.     

Regulation of Long-Term Plasticity Induction by the Channel and C-Terminal Domains of GluN2 Subunits

Conventional long-term potentiation (LTP) and long-term depression (LTD) are induced by different patterns of synaptic stimulation, but both forms of synaptic modification require calcium influx through NMDA receptors (NMDARs). A prevailing model (the “calcium hypothesis”) suggests that high postsynaptic calcium elevation results in LTP, whereas moderate elevations give rise to LTD. Recently, additional evidence has come to suggest that differential activation of NMDAR subunits also factors in determining which type of plasticity is induced. While the growing amount of data suggest that activation of NMDARs containing specific GluN2 subunits plays an important role in the induction of plasticity, it remains less clear which subunit is tied to which form of plasticity. Additionally, it remains to be determined which properties of the subunits confer upon them the ability to differentially induce long-term plasticity. This review highlights recent studies suggesting differential roles for the subunits, as well as findings that begin to shed light on how two similar subunits may be linked to the induction of opposing forms of plasticity.     

Novel method for the quantification of inorganic polyphosphate (iPoP) in <Emphasis Type="Italic">Saccharomyces cerevisiae</Emphasis> shows dependence of iPoP content on the growth phase

Inorganic polyphosphate (iPoP)—linear chains of up to hundreds of phosphate residues—is ubiquitous in nature and appears to be involved in many different cellular processes. In Saccharomyces cerevisiae, iPoP has been detected in high concentrations, especially after transfer of phosphate-deprived cells to a high-phosphate medium. Here, the dynamics of iPoP synthesis in yeast as a function of the growth phase as well as glucose and phosphate availability have been investigated. To address this question, a simple, fast and novel method for the quantification of iPoP from yeast was developed. Both the iPoP content during growth and the iPoP “overplus” were highest towards the end of the exponential phase, when glucose became limiting. Accumulation of iPoP during growth required excess of free phosphate, while the iPoP “overplus” was only observed after the shift from low- to high-phosphate medium. The newly developed iPoP quantification method and the knowledge about the dynamics of iPoP content during growth made it possible to define specific growth conditions for the analysis of iPoP levels. These experimental procedures will be essential for the large-scale analysis of various mutant strains or the comparison of different growth conditions.     

The neuronal dynamics underlying cognitive flexibility in set shifting tasks

The ability to switch attention from one aspect of an object to another or in other words to switch the “attentional set” as investigated in tasks like the “Wisconsin Card Sorting Test” is commonly referred to as cognitive flexibility. In this work we present a biophysically detailed neurodynamical model which illustrates the neuronal base of the processes related to this cognitive flexibility. For this purpose we conducted behavioral experiments which allow the combined evaluation of different aspects of set shifting tasks: uninstructed set shifts as investigated in Wisconsin-like tasks, effects of stimulus congruency as investigated in Stroop-like tasks and the contribution of working memory as investigated in “Delayed-Match-to-Sample” tasks. The work describes how general experimental findings are usable to design the architecture of a biophysical detailed though minimalistic model with a high orientation on neurobiological findings and how, in turn, the simulations support experimental investigations. The resulting model is able to account for experimental and individual response times and error rates and enables the switch of attention as a system inherent model feature: The switching process suggested by the model is based on the memorization of the visual stimuli and does not require any synaptic learning. The operation of the model thus demonstrates with at least a high probability the neuronal dynamics underlying a key component of human behavior: the ability to adapt behavior according to context requirements—cognitive flexibility. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users. Action Editor: Peter Dayan     

Mixed mode oscillations as a mechanism for pseudo-plateau bursting

We combine bifurcation analysis with the theory of canard-induced mixed mode oscillations to investigate the dynamics of a novel form of bursting. This bursting oscillation, which arises from a model of the electrical activity of a pituitary cell, is characterized by small impulses or spikes riding on top of an elevated voltage plateau. Oscillations with these characteristics have been called “pseudo-plateau bursting”. Unlike standard bursting, the subsystem of fast variables does not possess a stable branch of periodic spiking solutions, and in the case studied here the standard fast/slow analysis provides little information about the underlying dynamics. We demonstrate that the bursting is actually a canard-induced mixed mode oscillation, and use canard theory to characterize the dynamics of the oscillation. We also use bifurcation analysis of the full system of equations to extend the results of the singular analysis to the physiological regime. This demonstrates that the combination of these two analysis techniques can be a powerful tool for understanding the pseudo-plateau bursting oscillations that arise in electrically excitable pituitary cells and isolated pancreatic β-cells.     

The Skok legacy and beyond: Molecular mechanisms of slow synaptic excitation in sympathetic ganglia

Vladimir Skok and his colleagues did much of the pioneering work on fast excitatory synaptic transmission in sympathetic ganglia and on nicotinic acetylcholine receptors that mediate fast transmission. I and my colleagues (including Alex Selyanko, one of Vladimir’s protégés) have studied the additional process of slow synaptic excitation that is mediated by the action of acetylcholine on muscarinic receptors. This results primarily from the closure of “M-channels,” a subset of voltage-gated potassium channels composed of Kv7.2 and Kv7.3 channel subunits. These channels require membrane phosphatidylinositol-4,5-bisphosphate (PIP₂) for their opening, and their closure by muscarinic receptor activation is now thought to result from the reduction in PIP₂ levels that follows receptor-induced PIP₂ hydrolysis. The dynamics of these two forms of synaptic excitation are compared. Neirofiziologiya/Neurophysiology, Vol. 39, Nos. 4/5, pp. 284–289, July–October, 2007.     

A Phantom Bursting Mechanism for Episodic Bursting

We describe a novel dynamic mechanism for episodic or compound bursting oscillations, in which bursts of electrical impulses are clustered together into episodes, separated by long silent phases. We demonstrate the mechanism for episodic bursting using a minimal mathematical model for “phantom bursting.” Depending on the location in parameter space, this model can produce fast, medium, or slow bursting, or in the present case, fast, slow, and episodic bursting. The episodic bursting is modestly robust to noise and to parameter variation, and the effect that noise has on the episodic bursting pattern is quite different from that of an alternate episodic burst mechanism in which the slow envelope is produced by metabolic oscillations. This mechanism could account for episodic bursting produced in endocrine cells or neurons, such as pancreatic islets or gonadotropin releasing neurons of the hypothalamus.     

An intracellular Ca2+ subsystem as a biologically plausible source of intrinsic conditional bistability in a network model of working memory

We have developed a firing rate network model for working memory that combines Mexican-hat-like synaptic coupling with intrinsic or cellular dynamics that are conditionally bistable. While our approach is in the spirit of Camperi and Wang (1998) we include a specific and plausible mechanism for the cellular bistability. Modulatory neurotransmitters are known to activate second messenger signaling systems, and our model includes an intracellular Ca²⁺ handling subsystem whose dynamics depend upon the level of the second messenger inositol 1,4,5 trisphosphate (IP3). This Ca²⁺ subsystem endows individual units with conditional intrinsic bistability for a range of IP3. The full “hybrid” network sustains IP3-dependent persistent (“bump”) activity in response to a brief transient stimulus. The bump response in our hybrid model, like that of Camperi-Wang, is resistant to noise – its position does not drift with time. Action Editor: Upinder Bhalla     

The structure of social behaviour inTheropithecus gelada

Through the use of principal components analysis of the correlation matrix between excentricity quotients of intra- and inter-individual transitions between pairs of the 22 most frequent behaviour elements of male and female gelada baboons observed in captivity, the total variance could be described in terms of a low number of causal factors. In intra-individual sequences the five factors requested of the analysis explain 74 per cent of the total variance. The following intra-individual groupings were found: (I) “autostimulation”, (II) “intensive social” versus “groom”, (III) “male sexual”, (IV) “attack” versus “sexual presentation”, and (V) “greeting” versus “threat”. In inter-individual transitions, the five factors explain 68 per cent of the variance. The following communicative sets were found: (1) “female-sexual releasing”, (2) “greeting and approaching releasing” versus “groom releasing”, (3) “austostimulation releasing” versus “male-sexual releasing”, (4) “fight releasing”, and (5) “conflict”. Mimetic induction of same acts or acts within one particular intra-individual set was frequent.     

The cancer cell’s “power plants” as promising therapeutic targets: An overview

This introductory article to the review series entitled “The Cancer Cell’s Power Plants as Promising Therapeutic Targets” is written while more than 20 million people suffer from cancer. It summarizes strategies to destroy or prevent cancers by targeting their energy production factories, i.e., “power plants.” All nucleated animal/human cells have two types of power plants, i.e., systems that make the “high energy” compound ATP from ADP and P _i . One type is “glycolysis,” the other the “mitochondria.” In contrast to most normal cells where the mitochondria are the major ATP producers (>90%) in fueling growth, human cancers detected via Positron Emission Tomography (PET) rely on both types of power plants. In such cancers, glycolysis may contribute nearly half the ATP even in the presence of oxygen (“Warburg effect”). Based solely on cell energetics, this presents a challenge to identify curative agents that destroy only cancer cells as they must destroy both of their power plants causing “necrotic cell death” and leave normal cells alone. One such agent, 3-bromopyruvate (3-BrPA), a lactic acid analog, has been shown to inhibit both glycolytic and mitochondrial ATP production in rapidly growing cancers (Ko et al., Cancer Letts., 173, 83–91, 2001), leave normal cells alone, and eradicate advanced cancers (19 of 19) in a rodent model (Ko et al., Biochem. Biophys. Res. Commun., 324, 269–275, 2004). A second approach is to induce only cancer cells to undergo “apoptotic cell death.” Here, mitochondria release cell death inducing factors (e.g., cytochrome c). In a third approach, cancer cells are induced to die by both apoptotic and necrotic events. In summary, much effort is being focused on identifying agents that induce “necrotic,” “apoptotic” or apoptotic plus necrotic cell death only in cancer cells. Regardless how death is inflicted, every cancer cell must die, be it fast or slow.     

Dynamics of protein evolution

Protein sequences of the SWISS-PROT data bank were analysed by fractal techniques and harmonic analysis. In both cases, the results show the presence of self-affinity, a kind of self-similarity, in the sequences. Self-similarity is a sign of fractality and fractality is a consequence of a chaotic dynamical process. The evolution of the protein sequences is modelled as a dynamical system. The abundance of the fractal form in biology and creation of fractal forms as a result of “chaos” is already established. It may be noted that the word “chaos” here implies that most predictable processes can also become unpredictable under certain conditions, and that the most unpredictable processes are not as unpredictable as they are expected to be. In evolutionary dynamics, this allows scope for mutations and variations in otherwise predictable situations, potentially leading to increased diversity. Part of this work was presented at the National Symposium on Evolution of Life.     

Compact internal representation of dynamic situations: neural network implementing the causality principle

Animals for survival in complex, time-evolving environments can estimate in a “single parallel run” the fitness of different alternatives. Understanding of how the brain makes an effective compact internal representation (CIR) of such dynamic situations is a challenging problem. We propose an artificial neural network capable of creating CIRs of dynamic situations describing the behavior of a mobile agent in an environment with moving obstacles. The network exploits in a mental world model the principle of causality, which enables reduction of the time-dependent structure of real situations to compact static patterns. It is achieved through two concurrent processes. First, a wavefront representing the agent’s virtual present interacts with mobile and immobile obstacles forming static effective obstacles in the network space. The dynamics of the corresponding neurons in the virtual past is frozen. Then the diffusion-like process relaxes the remaining neurons to a stable steady state, i.e., a CIR is given by a single point in the multidimensional phase space. Such CIRs can be unfolded into real space for execution of motor actions, which allows a flexible task-dependent path planning in realistic time-evolving environments. Besides, the proposed network can also work as a part of “autonomous thinking”, i.e., some mental situations can be supplied for evaluation without direct motor execution. Finally we hypothesize the existence of a specific neuronal population responsible for detection of possible time-space coincidences of the animal and moving obstacles.     

Determination of corneal gel dynamics

From observations of the dynamics of light scattered by the cornea, intensity autocorrelation func-tions that revealed two independent diffusion coefficients, D (fast) = 2.4±0.2×10^–7 cm²/s and D (slow) = 9.4±1.3× 10^–9 cm²/s, were obtained. The diffusion coefficients were found to be statistically independent of the position and depth on the lateral surface of the cornea from which the scattered light was sampled. The slow diffusion coefficients obtained from light sampled from within cross-sections of the cornea were, however, measurably different. Diffusion coefficients obtained independently from observations of the kinetics of corneal swelling for comparison were found to be several orders of magnitude greater than those obtained from light scattering. The large disparity in the diffusion coefficients obtained from the two independent methods invoked the possibility that the lamellar layers within the cornea behave as individual gel sheets. Irrespective of this additional hypothesis, divergent behavior in the measured total scattered light intensities and diffusion coefficients upon varying external conditions, such as temperature or pressure (stretching), was observed. Namely, a slowing down of the dynamic modes accompanied by increased “static” scattered light intensities was observed. Although the slowing down of the dynamic modes is possibly indicative of the reduced affinity of protein binding to the gel matrix that “softens” the gel, the divergent behavior in the scattered light intensities and diffusion coefficients is, however, more characteristic of a phase transition. In addition, the divergent behavior in the scattered light intensities and diffusion coefficients was reversible up to a critical temperature (∼55 °C) or stretching (∼16%). Received: 18 March 1998 / Revised version: 4 February 1999 / Accepted: 4 February 1999     

Interplay of the magnitude and time-course of postsynaptic Ca<Superscript>2 + </Superscript> concentration in producing spike timing-dependent plasticity

Synaptic strength can be modified by the relative timing of pre- and postsynaptic activity, a phenomenon termed spike timing-dependent plasticity (STDP). Studies of neurons in the hippocampus and in other regions have found that when presynaptic activity occurs within a narrow time window, typically 10 or 20 ms, before postsynaptic activity, long-term potentiation (LTP) is induced, while if presynaptic activity occurs within a similar time window after postsynaptic activity, long-term depression (LTD) results. The mechanisms underlying these modifications are not completely understood, although there is strong evidence that the postsynaptic Ca ^2 + concentration plays a central role. Some previous modeling of STDP has focused on the dynamics of the postsynaptic Ca ^2 + concentration, while other work has studied biophysical mechanisms of how a synapse can exist in, and switch between, different states corresponding to LTP and LTD. Building on previous work in these two areas we have developed the first low level STDP model of a tristable biochemical system that incorporates induction and maintenance of both LTP and LTD. Our model is able to explain the STDP observed in hippocampal neurons in response to pre- and postsynaptic pulse pairs, using only parameters derived from previous work and without the need for parameter fine-tuning. Our results also give insight into how and why the time course of the postsynaptic Ca ^2 + concentration can lead to either LTP or LTD, and suggest that voltage dependent calcium channels play a key role.     

3D and 4D imaging of immune cells in vitro and in vivo

Analyzing the dynamics of cellular immune responses, although performed for decades in immunologic research, has seen an enormous increase in the number of studies using this approach since the development of intravital 2-photon microscopy. Meanwhile, new insights into the dynamics of cellular immunity are being published on a daily basis. This review gives a short overview of the currently most widely used techniques, both on the microscopy side as well as on the experimental part. Difficulties and promises will be discussed. Finally, a personal selection of the most interesting findings of the first 6 years of intravital 2-photon microscopy for immunological questions will be given. The overall aim is to get the reader interested into this fascinating way of investigating the immune response by means of “dynamic histology”. This already has and will continue to broaden our view on how immune cells work in real life.