Encoding with bursting, subthreshold oscillations, and noise in mammalian cold receptors

Characterizing the aggregated encoding method utilizing bursts activated by a VCSEL-neuron with a feedback structure

The rapid advancement of photonic technologies has facilitated the development of photonic neurons that emulate neuronal functionalities akin to those observed in the human brain. Neuronal bursts frequently occur in behaviors where information is encoded and transmitted. Here, we present the demonstration of the bursting response activated by an artificial photonic neuron. This neuron utilizes a single vertical-cavity surface-emitting laser (VCSEL) and encodes multiple stimuli effectively by varying the spike count during a burst based on the polarization competition in the VCSEL. By virtue of the modulated optical injection in the VCSEL employed to trigger the spiking response, we activate bursts output in the VCSEL with a feedback structure in this scheme. The bursting response activated by the VCSEL-neuron exhibits neural signal characteristics, promising an excitation threshold and the refractory period. Significantly, this marks the inaugural implementation of a controllable integrated encoding scheme predicated on bursts within photonic neurons. There are two remarkable merits; on the one hand, the interspike interval of bursts is distinctly diminished, amounting to merely one twenty-fourth compared to that observed in optoelectronic oscillators. Moreover, the interspike period of bursts is about 70.8% shorter than the period of spikes activated by a VCSEL neuron without optical feedback. Our results may shed light on the analogy between optical and biological neurons and open the door to fast burst encoding-based optical systems with a speed several orders of magnitude faster than their biological counterparts.

Cold-Temperature Coding with Bursting and Spiking Based on TRP Channel Dynamics in Drosophila Larva Sensory Neurons

Temperature sensation involves thermosensitive TRP (thermoTRP) and non-TRP channels. Drosophila larval Class III (CIII) neurons serve as the primary cold nociceptors and express a suite of thermoTRP channels implicated in noxious cold sensation. How CIII neurons code temperature remains unclear. We combined computational and electrophysiological methods to address this question. In electrophysiological experiments, we identified two basic cold-evoked patterns of CIII neurons: bursting and spiking. In response to a fast temperature drop to noxious cold, CIII neurons distinctly mark different phases of the stimulus. Bursts frequently occurred along with the fast temperature drop, forming a peak in the spiking rate and likely coding the high rate of the temperature change. Single spikes dominated at a steady temperature and exhibited frequency adaptation following the peak. When temperature decreased slowly to the same value, mainly spiking activity was observed, with bursts occurring sporadically throughout the stimulation. The spike and the burst frequencies positively correlated with the rate of the temperature drop. Using a computational model, we explain the distinction in the occurrence of the two CIII cold-evoked patterns bursting and spiking using the dynamics of a thermoTRP current. A two-parameter activity map (Temperature, constant TRP current conductance) marks parameters that support silent, spiking, and bursting regimes. Projecting on the map the instantaneous TRP conductance, governed by activation and inactivation processes, reflects temperature coding responses as a path across silent, spiking, or bursting domains on the map. The map sheds light on how various parameter sets for TRP kinetics represent various types of cold-evoked responses. Together, our results indicate that bursting detects the high rate of temperature change, whereas tonic spiking could reflect both the rate of change and magnitude of steady cold temperature.

Ion-tunable antiambipolarity in mixed ion-electron conducting polymers enables biorealistic organic electrochemical neurons

Biointegrated neuromorphic hardware holds promise for new protocols to record/regulate signalling in biological systems. Making such artificial neural circuits successful requires minimal device/circuit complexity and ion-based operating mechanisms akin to those found in biology. Artificial spiking neurons, based on silicon-based complementary metal-oxide semiconductors or negative differential resistance device circuits, can emulate several neural features but are complicated to fabricate, not biocompatible and lack ion-/chemical-based modulation features. Here we report a biorealistic conductance-based organic electrochemical neuron (c-OECN) using a mixed ion-electron conducting ladder-type polymer with stable ion-tunable antiambipolarity. The latter is used to emulate the activation/inactivation of sodium channels and delayed activation of potassium channels of biological neurons. These c-OECNs can spike at bioplausible frequencies nearing 100 Hz, emulate most critical biological neural features, demonstrate stochastic spiking and enable neurotransmitter-/amino acid-/ion-based spiking modulation, which is then used to stimulate biological nerves in vivo. These combined features are impossible to achieve using previous technologies.

Subthreshold Oscillating Waves in Neural Tissue Propagate by Volume Conduction and Generate Interference

Subthreshold neural oscillations have been observed in several brain regions and can influence the timing of neural spikes. However, the spatial extent and function of these spontaneous oscillations remain unclear. To study the mechanisms underlying these oscillations, we use optogenetic stimulation to generate oscillating waves in the longitudinal hippocampal slice expressing optopatch proteins. We found that optogenetic stimulation can generate two types of neural activity: suprathreshold neural spikes and subthreshold oscillating waves. Both waves could propagate bidirectionally at similar speeds and go through a transection of the tissue. The propagating speed is independent of the oscillating frequency but increases with increasing amplitudes of the waves. The endogenous electric fields generated by oscillating waves are about 0.6 mV/mm along the dendrites and about 0.3 mV/mm along the cell layer. We also observed that these oscillating waves could interfere with each other. Optical stimulation applied simultaneously at each slice end generated a larger wave in the middle of the tissue (constructive interference) or destructive interference with laser signals in opposite phase. However, the suprathreshold neural spikes were annihilated when they collided. Finally, the waves were not affected by the NMDA blocker (APV) and still propagated in the presence of tetrodotoxin (TTX) but at a significantly lower amplitude. The role of these subthreshold waves in neural function is unknown, but the results show that at low amplitude, the subthreshold propagating waves lack a refractory period allowing a novel analog form of preprocessing of neural activity by interference independent of synaptic transmission.

The voltage and spiking responses of subthreshold resonant neurons to structured and fluctuating inputs: persistence and loss of resonance and variability

We systematically investigate the response of neurons to oscillatory currents and synaptic-like inputs and we extend our investigation to non-structured synaptic-like spiking inputs with more realistic distributions of presynaptic spike times. We use two types of chirp-like inputs consisting of (i) a sequence of cycles with discretely increasing frequencies over time, and (ii) a sequence having the same cycles arranged in an arbitrary order. We develop and use a number of frequency-dependent voltage response metrics to capture the different aspects of the voltage response, including the standard impedance (Z) and the peak-to-trough amplitude envelope ([Formula: see text]) profiles. We show that Z-resonant cells (cells that exhibit subthreshold resonance in response to sinusoidal inputs) also show [Formula: see text]-resonance in response to sinusoidal inputs, but generally do not (or do it very mildly) in response to square-wave and synaptic-like inputs. In the latter cases the resonant response using Z is not predictive of the preferred frequencies at which the neurons spike when the input amplitude is increased above subthreshold levels. We also show that responses to conductance-based synaptic-like inputs are attenuated as compared to the response to current-based synaptic-like inputs, thus providing an explanation to previous experimental results. These response patterns were strongly dependent on the intrinsic properties of the participating neurons, in particular whether the unperturbed Z-resonant cells had a stable node or a focus. In addition, we show that variability emerges in response to chirp-like inputs with arbitrarily ordered patterns where all signals (trials) in a given protocol have the same frequency content and the only source of uncertainty is the subset of all possible permutations of cycles chosen for a given protocol. This variability is the result of the multiple different ways in which the autonomous transient dynamics is activated across cycles in each signal (different cycle orderings) and across trials. We extend our results to include high-rate Poisson distributed current- and conductance-based synaptic inputs and compare them with similar results using additive Gaussian white noise. We show that the responses to both Poisson-distributed synaptic inputs are attenuated with respect to the responses to Gaussian white noise. For cells that exhibit oscillatory responses to Gaussian white noise (band-pass filters), the response to conductance-based synaptic inputs are low-pass filters, while the response to current-based synaptic inputs may remain band-pass filters, consistent with experimental findings. Our results shed light on the mechanisms of communication of oscillatory activity among neurons in a network via subthreshold oscillations and resonance and the generation of network resonance.

White-noise-induced double coherence resonances in reduced Hodgkin-Huxley neuron model near subcritical Hopf bifurcation

Coherence resonance (CR) describes a counterintuitive phenomenon in which the optimal oscillatory responses in nonlinear systems are shaped by a suitable noise amplitude. This phenomenon has been observed in neural systems. In this research, the generation of double coherence resonances (DCRs) due to white noise is investigated in a three-dimensional reduced Hodgkin-Huxley neuron model with multiple-timescale feature. We show that additive white noise can induce DCRs from the resting state near a subcritical Hopf bifurcation. The appearance of DCRs is related to the changes of the firing pattern aroused by the increases of the noise amplitude. The underlying dynamical mechanisms for the appearance of the DCRs and the changes of the firing pattern are interpreted using the phase space analysis and the dynamics of the stable focus-node near the subcritical Hopf bifurcation. We find that the multiple-timescale dynamics is essential for generating the DCRs and different firing patterns. The results not only present a case in which noise can induce DCRs near a Hopf bifurcation but also provide its dynamical mechanism, which enriches the phenomena in nonlinear dynamics and provides further understanding on the roles of noise in neural systems with multiple-timescale feature.

Transient and Steady-State Properties of Drosophila Sensory Neurons Coding Noxious Cold Temperature

Coding noxious cold signals, such as the magnitude and rate of temperature change, play essential roles in the survival of organisms. We combined electrophysiological and computational neuroscience methods to investigate the neural dynamics of Drosophila larva cold-sensing Class III (CIII) neurons. In response to a fast temperature change (-2 to -6°C/s) from room temperature to noxious cold, the CIII neurons exhibited a pronounced peak of a spiking rate with subsequent relaxation to a steady-state spiking. The magnitude of the peak was higher for a higher rate of temperature decrease, while slow temperature decrease (-0.1°C/s) evoked no distinct peak of the spiking rate. The rate of the steady-state spiking depended on the magnitude of the final temperature and was higher at lower temperatures. For each neuron, we characterized this dependence by estimating the temperature of the half activation of the spiking rate by curve fitting neuron's spiking rate responses to a Boltzmann function. We found that neurons had a temperature of the half activation distributed over a wide temperature range. We also found that CIII neurons responded to decrease rather than increase in temperature. There was a significant difference in spiking activity between fast and slow returns from noxious cold to room temperature: The CIII neurons usually stopped activity abruptly in the case of the fast return and continued spiking for some time in the case of the slow return. We developed a biophysical model of CIII neurons using a generalized description of transient receptor potential (TRP) current kinetics with temperature-dependent activation and Ca²⁺-dependent inactivation. This model recapitulated the key features of the spiking rate responses found in experiments and suggested mechanisms explaining the transient and steady-state activity of the CIII neurons at different cold temperatures and rates of their decrease and increase. We conclude that CIII neurons encode at least three types of cold sensory information: the rate of temperature decrease by a peak of the firing rate, the magnitude of cold temperature by the rate of steady spiking activity, and direction of temperature change by spiking activity augmentation or suppression corresponding to temperature decrease and increase, respectively.

Biological plausibility and stochasticity in scalable VO2 active memristor neurons

Neuromorphic networks of artificial neurons and synapses can solve computationally hard problems with energy efficiencies unattainable for von Neumann architectures. For image processing, silicon neuromorphic processors outperform graphic processing units in energy efficiency by a large margin, but deliver much lower chip-scale throughput. The performance-efficiency dilemma for silicon processors may not be overcome by Moore's law scaling of silicon transistors. Scalable and biomimetic active memristor neurons and passive memristor synapses form a self-sufficient basis for a transistorless neural network. However, previous demonstrations of memristor neurons only showed simple integrate-and-fire behaviors and did not reveal the rich dynamics and computational complexity of biological neurons. Here we report that neurons built with nanoscale vanadium dioxide active memristors possess all three classes of excitability and most of the known biological neuronal dynamics, and are intrinsically stochastic. With the favorable size and power scaling, there is a path toward an all-memristor neuromorphic cortical computer.

Cooling reverses pathological bifurcations to spontaneous firing caused by mild traumatic injury

Mild traumatic injury can modify the key sodium (Na⁺) current underlying the excitability of neurons. It causes the activation and inactivation properties of this current to become shifted to more negative trans-membrane voltages. This so-called coupled left shift (CLS) leads to a chronic influx of Na⁺ into the cell that eventually causes spontaneous or "ectopic" firing along the axon, even in the absence of stimuli. The bifurcations underlying this enhanced excitability have been worked out in full ionic models of this effect. Here, we present computational evidence that increased temperature T can exacerbate this pathological state. Conversely, and perhaps of clinical relevance, mild cooling is shown to move the naturally quiescent cell further away from the threshold of ectopic behavior. The origin of this stabilization-by-cooling effect is analyzed by knocking in and knocking out, one at a time, various processes thought to be T-dependent. The T-dependence of the Na⁺ current, quantified by its Q _10-Na factor, has the biggest impact on the threshold, followed by Q _10-pump of the sodium-potassium exchanger. Below the ectopic boundary, the steady state for the gating variables and the resting potential are not modified by temperature, since our model separately tallies the Na⁺ and K⁺ ions including their separate leaks through the pump. When only the gating kinetics are considered, cooling is detrimental, but in the full T-dependent model, it is beneficial because the other processes dominate. Cooling decreases the pump's activity, and since the pump hyperpolarizes, less hyperpolarization should lead to more excitability and ectopic behavior. But actually the opposite happens in the full model because decreased pump activity leads to smaller gradients of Na⁺ and K⁺, which in turn decreases the driving force of the Na⁺ current.

Activity patterns with silent states in a heterogeneous network of gap-junction coupled Huber-Braun model neurons

A mathematical model of a network of nearest neighbor gap-junction coupled neurons has been used to examine the impact of neuronal heterogeneity on the networks' activity during increasing coupling strength. Heterogeneity has been introduced by Huber-Braun model neurons with randomization of the temperature as a scaling factor. This leads to neurons of an enormous diversity of impulse pattern, including burst discharges, chaotic activity, and two different types of tonic firing-all of them experimentally observed in the peripheral as well as central nervous system. When the network is composed of all these types of neurons, randomly selected, a particular phenomenon can be observed. At a certain coupling strength, the network goes into a completely silent state. Examination of voltage traces and inter-spike intervals of individual neurons suggests that all neurons, irrespective of their original pattern, go through a well-known bifurcation scenario, resembling those of single neurons especially on external current injection. All the originally spontaneously firing neurons can achieve constant membrane potentials at which all intrinsic and gap-junction currents are balanced. With limited diversity, i.e., taking out neurons of specific patterns from the lower and upper temperature range, spontaneous firing can be reinstalled with further increasing coupling strength, especially when the tonic firing regimes are missing. Reinstalled firing develops from slowly increasing subthreshold oscillations leading to tonic firing activity with already fairly well synchronized action potentials, while the subthreshold potentials can still be significantly different. Full in phase synchronization is not achieved. Additional studies are needed elucidating the underlying mechanisms and the conditions under which such particular transitions can appear.

Effect of spike-timing-dependent plasticity on stochastic burst synchronization in a scale-free neuronal network

We consider an excitatory population of subthreshold Izhikevich neurons which cannot fire spontaneously without noise. As the coupling strength passes a threshold, individual neurons exhibit noise-induced burstings. This neuronal population has adaptive dynamic synaptic strengths governed by the spike-timing-dependent plasticity (STDP). However, STDP was not considered in previous works on stochastic burst synchronization (SBS) between noise-induced burstings of sub-threshold neurons. Here, we study the effect of additive STDP on SBS by varying the noise intensity D in the Barabási-Albert scale-free network (SFN). One of our main findings is a Matthew effect in synaptic plasticity which occurs due to a positive feedback process. Good burst synchronization (with higher bursting measure) gets better via long-term potentiation (LTP) of synaptic strengths, while bad burst synchronization (with lower bursting measure) gets worse via long-term depression (LTD). Consequently, a step-like rapid transition to SBS occurs by changing D, in contrast to a relatively smooth transition in the absence of STDP. We also investigate the effects of network architecture on SBS by varying the symmetric attachment degree [Formula: see text] and the asymmetry parameter [Formula: see text] in the SFN, and Matthew effects are also found to occur by varying [Formula: see text] and [Formula: see text]. Furthermore, emergences of LTP and LTD of synaptic strengths are investigated in details via our own microscopic methods based on both the distributions of time delays between the burst onset times of the pre- and the post-synaptic neurons and the pair-correlations between the pre- and the post-synaptic instantaneous individual burst rates (IIBRs). Finally, a multiplicative STDP case (depending on states) with soft bounds is also investigated in comparison with the additive STDP case (independent of states) with hard bounds. Due to the soft bounds, a Matthew effect with some quantitative differences is also found to occur for the case of multiplicative STDP.

Synchronous spikes are necessary but not sufficient for a synchrony code in populations of spiking neurons

Synchronous activity in populations of neurons potentially encodes special stimulus features. Selective readout of either synchronous or asynchronous activity allows formation of two streams of information processing. Theoretical work predicts that such a synchrony code is a fundamental feature of populations of spiking neurons if they operate in specific noise and stimulus regimes. Here we experimentally test the theoretical predictions by quantifying and comparing neuronal response properties in tuberous and ampullary electroreceptor afferents of the weakly electric fish Apteronotus leptorhynchus These related systems show similar levels of synchronous activity, but only in the more irregularly firing tuberous afferents a synchrony code is established, whereas in the more regularly firing ampullary afferents it is not. The mere existence of synchronous activity is thus not sufficient for a synchrony code. Single-cell features such as the irregularity of spiking and the frequency dependence of the neuron's transfer function determine whether synchronous spikes possess a distinct meaning for the encoding of time-dependent signals.

The shaping of intrinsic membrane potential oscillations: positive/negative feedback, ionic resonance/amplification, nonlinearities and time scales

The generation of intrinsic subthreshold (membrane potential) oscillations (STOs) in neuronal models requires the interaction between two processes: a relatively fast positive feedback that favors changes in voltage and a slower negative feedback that opposes these changes. These are provided by the so-called resonant and amplifying gating variables associated to the participating ionic currents. We investigate both the biophysical and dynamic mechanisms of generation of STOs and how their attributes (frequency and amplitude) depend on the model parameters for biophysical (conductance-based) models having qualitatively different types of resonant currents (activating and inactivating) and an amplifying current. Combinations of the same types of ionic currents (same models) in different parameter regimes give rise to different types of nonlinearities in the voltage equation: quasi-linear, parabolic-like and cubic-like. On the other hand, combinations of different types of ionic currents (different models) may give rise to the same type of nonlinearities. We examine how the attributes of the resulting STOs depend on the combined effect of these resonant and amplifying ionic processes, operating at different effective time scales, and the various types of nonlinearities. We find that, while some STO properties and attribute dependencies on the model parameters are determined by the specific combinations of ionic currents (biophysical properties), and are different for models with different such combinations, others are determined by the type of nonlinearities and are common for models with different types of ionic currents. Our results highlight the richness of STO behavior in single cells as the result of the various ways in which resonant and amplifying currents interact and affect the generation and termination of STOs as control parameters change. We make predictions that can be tested experimentally and are expected to contribute to the understanding of how rhythmic activity in neuronal networks emerge from the interplay of the intrinsic properties of the participating neurons and the network connectivity.

A Coupled Phase-Temperature Model for Dynamics of Transient Neuronal Signal in Mammals Cold Receptor

We propose a theoretical model consisting of coupled differential equation of membrane potential phase and temperature for describing the neuronal signal in mammals cold receptor. Based on the results from previous work by Roper et al., we modified a nonstochastic phase model for cold receptor neuronal signaling dynamics in mammals. We introduce a new set of temperature adjusted functional parameters which allow saturation characteristic at high and low steady temperatures. The modified model also accommodates the transient neuronal signaling process from high to low temperature by introducing a nonlinear differential equation for the “effective temperature” changes which is coupled to the phase differential equation. This simple model can be considered as a candidate for describing qualitatively the physical mechanism of the corresponding transient process.

Fluctuation-Driven Neural Dynamics Reproduce Drosophila Locomotor Patterns

The neural mechanisms determining the timing of even simple actions, such as when to walk or rest, are largely mysterious. One intriguing, but untested, hypothesis posits a role for ongoing activity fluctuations in neurons of central action selection circuits that drive animal behavior from moment to moment. To examine how fluctuating activity can contribute to action timing, we paired high-resolution measurements of freely walking Drosophila melanogaster with data-driven neural network modeling and dynamical systems analysis. We generated fluctuation-driven network models whose outputs-locomotor bouts-matched those measured from sensory-deprived Drosophila. From these models, we identified those that could also reproduce a second, unrelated dataset: the complex time-course of odor-evoked walking for genetically diverse Drosophila strains. Dynamical models that best reproduced both Drosophila basal and odor-evoked locomotor patterns exhibited specific characteristics. First, ongoing fluctuations were required. In a stochastic resonance-like manner, these fluctuations allowed neural activity to escape stable equilibria and to exceed a threshold for locomotion. Second, odor-induced shifts of equilibria in these models caused a depression in locomotor frequency following olfactory stimulation. Our models predict that activity fluctuations in action selection circuits cause behavioral output to more closely match sensory drive and may therefore enhance navigation in complex sensory environments. Together these data reveal how simple neural dynamics, when coupled with activity fluctuations, can give rise to complex patterns of animal behavior.

TRPM8-Dependent Dynamic Response in a Mathematical Model of Cold Thermoreceptor

Cold-sensitive nerve terminals (CSNTs) encode steady temperatures with regular, rhythmic temperature-dependent firing patterns that range from irregular tonic firing to regular bursting (static response). During abrupt temperature changes, CSNTs show a dynamic response, transiently increasing their firing frequency as temperature decreases and silencing when the temperature increases (dynamic response). To date, mathematical models that simulate the static response are based on two depolarizing/repolarizing pairs of membrane ionic conductance (slow and fast kinetics). However, these models fail to reproduce the dynamic response of CSNTs to rapid changes in temperature and notoriously they lack a specific cold-activated conductance such as the TRPM8 channel. We developed a model that includes TRPM8 as a temperature-dependent conductance with a calcium-dependent desensitization. We show by computer simulations that it appropriately reproduces the dynamic response of CSNTs from mouse cornea, while preserving their static response behavior. In this model, the TRPM8 conductance is essential to display a dynamic response. In agreement with experimental results, TRPM8 is also needed for the ongoing activity in the absence of stimulus (i.e. neutral skin temperature). Free parameters of the model were adjusted by an evolutionary optimization algorithm, allowing us to find different solutions. We present a family of possible parameters that reproduce the behavior of CSNTs under different temperature protocols. The detection of temperature gradients is associated to a homeostatic mechanism supported by the calcium-dependent desensitization.

Noise-induced burst and spike synchronizations in an inhibitory small-world network of subthreshold bursting neurons

We are interested in noise-induced firings of subthreshold neurons which may be used for encoding environmental stimuli. Noise-induced population synchronization was previously studied only for the case of global coupling, unlike the case of subthreshold spiking neurons. Hence, we investigate the effect of complex network architecture on noise-induced synchronization in an inhibitory population of subthreshold bursting Hindmarsh-Rose neurons. For modeling complex synaptic connectivity, we consider the Watts-Strogatz small-world network which interpolates between regular lattice and random network via rewiring, and investigate the effect of small-world connectivity on emergence of noise-induced population synchronization. Thus, noise-induced burst synchronization (synchrony on the slow bursting time scale) and spike synchronization (synchrony on the fast spike time scale) are found to appear in a synchronized region of the [Formula: see text]-[Formula: see text] plane ([Formula: see text]: synaptic inhibition strength and [Formula: see text]: noise intensity). As the rewiring probability [Formula: see text] is decreased from 1 (random network) to 0 (regular lattice), the region of spike synchronization shrinks rapidly in the [Formula: see text]-[Formula: see text] plane, while the region of the burst synchronization decreases slowly. We separate the slow bursting and the fast spiking time scales via frequency filtering, and characterize the noise-induced burst and spike synchronizations by employing realistic order parameters and statistical-mechanical measures introduced in our recent work. Thus, the bursting and spiking thresholds for the burst and spike synchronization transitions are determined in terms of the bursting and spiking order parameters, respectively. Furthermore, we also measure the degrees of burst and spike synchronizations in terms of the statistical-mechanical bursting and spiking measures, respectively.

Origin of intrinsic irregular firing in cortical interneurons

Cortical spike trains are highly irregular both during ongoing, spontaneous activity and when driven at high firing rates. There is uncertainty about the source of this irregularity, ranging from intrinsic noise sources in neurons to collective effects in large-scale cortical networks. Cortical interneurons display highly irregular spike times (coefficient of variation of the interspike intervals >1) in response to dc-current injection in vitro. This is in marked contrast to cortical pyramidal cells, which spike highly irregularly in vivo, but regularly in vitro. We show with in vitro recordings and computational models that this is due to the fast activation kinetics of interneuronal K(+) currents. This explanation holds over a wide parameter range and with Gaussian white, power-law, and Ornstein-Uhlenbeck noise. The intrinsically irregular spiking of interneurons could contribute to the irregularity of the cortical network.

Role of Ih in the firing pattern of mammalian cold thermoreceptor endings

Mammalian peripheral cold thermoreceptors respond to cooling of their sensory endings with an increase in firing rate and modification of their discharge pattern. We recently showed that cultured trigeminal cold-sensitive (CS) neurons express a prominent hyperpolarization-activated current ( Ih), mainly carried by HCN1 channels, supporting subthreshold resonance in the soma without participating in the response to acute cooling. However, peripheral pharmacological blockade of Ih, or characterization of HCN1−/− mice, reveals a deficit in acute cold detection. Here we investigated the role of Ih in CS nerve endings, where cold sensory transduction actually takes place. Corneal CS nerve endings in mice show a rhythmic spiking activity at neutral skin temperature that switches to bursting mode when the temperature is lowered. Ih blockers ZD7288 and ivabradine alter firing patterns of CS nerve endings, lengthening interspike intervals and inducing bursts at neutral skin temperature. We characterized the CS nerve endings from HCN1−/− mouse corneas and found that they behave similar to wild type, although with a lower slope in the firing frequency vs. temperature relationship, thus explaining the deficit in cold perception of HCN1−/− mice. The firing pattern of nerve endings from HCN1−/− mice was also affected by ZD7288, which we attribute to the presence of HCN2 channels in the place of HCN1. Mathematical modeling shows that the firing phenotype of CS nerve endings from HCN1−/− mice can be reproduced by replacing HCN1 channels with the slower HCN2 channels rather than by abolishing Ih. We propose that Ih carried by HCN1 channels helps tune the frequency of the oscillation and the length of bursts underlying regular spiking in cold thermoreceptors, having important implications for neural coding of cold sensation.

Spontaneous excitation patterns computed for axons with injury-like impairments of sodium channels and Na/K pumps

In injured neurons, “leaky” voltage-gated sodium channels (Nav) underlie dysfunctional excitability that ranges from spontaneous subthreshold oscillations (STO), to ectopic (sometimes paroxysmal) excitation, to depolarizing block. In recombinant systems, mechanical injury to Nav1.6-rich membranes causes cytoplasmic Na⁺-loading and “Nav-CLS”, i.e., coupled left-(hyperpolarizing)-shift of Nav activation and availability. Metabolic injury of hippocampal neurons (epileptic discharge) results in comparable impairment: left-shifted activation and availability and hence left-shifted I_Na-window. A recent computation study revealed that CLS-based I_Na-window left-shift dissipates ion gradients and impairs excitability. Here, via dynamical analyses, we focus on sustained excitability patterns in mildly damaged nodes, in particular with more realistic Gaussian-distributed Nav-CLS to mimic “smeared” injury intensity. Since our interest is axons that might survive injury, pumps (sine qua non for live axons) are included. In some simulations, pump efficacy and system volumes are varied. Impacts of current noise inputs are also characterized. The diverse modes of spontaneous rhythmic activity evident in these scenarios are studied using bifurcation analysis. For “mild CLS injury”, a prominent feature is slow pump/leak-mediated E_Ion oscillations. These slow oscillations yield dynamic firing thresholds that underlie complex voltage STO and bursting behaviors. Thus, Nav-CLS, a biophysically justified mode of injury, in parallel with functioning pumps, robustly engenders an emergent slow process that triggers a plethora of pathological excitability patterns. This minimalist “device” could have physiological analogs. At first nodes of Ranvier and at nociceptors, e.g., localized lipid-tuning that modulated Nav midpoints could produce Nav-CLS, as could co-expression of appropriately differing Nav isoforms.

Nerve cells damaged by trauma, stroke, epilepsy, inflammatory conditions etc, have chronically leaky sodium channels that eventually kill. The usual job of sodium channels is to make brief voltage signals –action potentials– for long distance propagation. After sodium channels open to generate action potentials, sodium pumps work harder to re-establish the intracellular/extracellular sodium imbalance that is, literally, the neuron's battery for firing action potentials. Wherever tissue damage renders membranes overly fluid, we hypothesize, sodium channels become chronically leaky. Our experimental findings justify this. In fluidized membranes, sodium channel voltage sensors respond too easily, letting channels spend too much time open. Channels leak, pumps respond. By mathematical modeling, we show that in damaged channel-rich membranes the continual pump/leak counterplay would trigger the kinds of bizarre intermittent action potential bursts typical of injured neurons. Arising ectopically from injury regions, such neuropathic firing is unrelated to events in the external world. Drugs that can silence these deleterious electrical barrages without blocking healthy action potentials are needed. If fluidized membranes house the problematic leaky sodium channels, then drug side effects could be diminished by using drugs that accumulate most avidly into fluidized membranes, and that bind their targets with highest affinity there.

A cool channel in cold transduction

Transient receptor potential melastatin 8 (TRPM8), a calcium-permeable cation channel activated by cold, cooling compounds and voltage, is the main molecular entity responsible for detection of cold temperatures in the somatosensory system. Here, we review the biophysical properties, physiological role, and near-membrane trafficking of this exciting polymodal ion channel.

Characterizing mixed mode oscillations shaped by noise and bifurcation structure

Many neuronal systems and models display a certain class of mixed mode oscillations (MMOs) consisting of periods of small amplitude oscillations interspersed with spikes. Various models with different underlying mechanisms have been proposed to generate this type of behavior. Stochastic versions of these models can produce similarly looking time series, often with noise-driven mechanisms different from those of the deterministic models. We present a suite of measures which, when applied to the time series, serves to distinguish models and classify routes to producing MMOs, such as noise-induced oscillations or delay bifurcation. By focusing on the subthreshold oscillations, we analyze the interspike interval density, trends in the amplitude, and a coherence measure. We develop these measures on a biophysical model for stellate cells and a phenomenological FitzHugh-Nagumo-type model and apply them on related models. The analysis highlights the influence of model parameters and resets and return mechanisms in the context of a novel approach using noise level to distinguish model types and MMO mechanisms. Ultimately, we indicate how the suite of measures can be applied to experimental time series to reveal the underlying dynamical structure, while exploiting either the intrinsic noise of the system or tunable extrinsic noise.

Phase synchronization in noise-driven bursting neurons

The generation and synchronization of bursts are studied in intrinsically spiking neurons due to stimulation with random intracellular calcium fluctuations. It is demonstrated that sufficiently strong noise could induce qualitative change in the firing patterns of a single neuron from periodic spiking to bursting modes. The dynamical mechanism of noise-induced bursting is presented based on a global bifurcation analysis. Furthermore, it is found that a pair of uncoupled and nonidentical spiking neurons, subjected to a common noise, can exhibit synchronous firing in terms of noise-induced bursting. Furthermore, the synchronization is overall enhanced with the noise intensity increasing, and synchronization transitions are exhibited at intermediate noise levels.

Electrical coupling promotes fidelity of responses in the networks of model neurons

We consider an integrate-and-fire element subject to randomly perturbed synaptic input and an electrically coupled ensemble of such elements. The latter is interpreted as either a model of electrically coupled population of neurons or a multicompartment model of a dendrite. Random fluctuations blur the input signal and cause false responses in the system dynamics. For instance, under the influence of noise, the system may respond with an action potential to a subthreshold stimulus. We show that the responses of the elements within the network are more reliable than the responses of the same elements in isolation. Specifically, we show that the variances of the stochastic processes generated by the coupled model can be made arbitrarily small (i.e., the network responses can be made arbitrarily accurate) by increasing the number of elements in the network and the strength of electrical coupling. Our results suggest that the organization of cells in electrically coupled groups on the network level, or the dendritic morphology on the cellular level, may be involved in the filtering noise and therefore may play an important role in the information processing mechanisms operating on the network or cellular level respectively.

Noise-Induced Transition to Bursting in Responses of Paddlefish Electroreceptor Afferents

The response properties of ampullary electroreceptors of paddlefish, Polyodon spathula, were studied in vivo, as single-unit afferent responses to external electrical stimulation with varied intensities of several types of noise waveforms, all Gaussian and zero-mean. They included broadband white noise, Ornstein–Uhlenbeck noise, low- or high-frequency band-limited noise, or natural noise recorded from swarms of Daphnia zooplankton prey, or from individual prey. Normally the afferents fire spontaneously in a tonic manner, which is actually quasiperiodic due to embedded oscillators. 1) Weak noise stimuli increased the variability of afferent firing, but it remained tonic. 2) In contrast, stimulation with less-weak broadband noise led to a qualitative change of the firing patterns, to parabolic bursting, even though the mean firing rate was scarcely affected. 3) The transition to afferent bursting was marked by the development of two well-separated timescales: the fast frequency of spiking inside bursts at ≤250 spikes/s and the slow frequency of burst occurrences at about 9 (range 5–13) bursts/s. These two timescales were manifested as two regimes in afferent power spectra, bimodal interspike interval histograms, return maps, and autocorrelation functions of afferent spike trains. 4) The stochastic approximately 9-Hz bursts were not simply driven by similar-frequency components of noise stimuli because bursts could be dissociated from stimulus waveforms using high-pass filtered noise, or a 0.1-Hz sine-wave stimulus. 5) Arrhenius plots showed that the threshold noise intensity required to elicit bursting depended on the frequency content of a noise stimulus, being lowest, about 1.2 μV/cm, for stimuli matching the 1- to 20-Hz best response band of these cathodally excited ampullary electroreceptors. This is only slightly higher than previous behavioral estimates of the electrosensory threshold as 0.5 μV/cm. 6) Comparable threshold values for bursting came from an alternate analytical approach, based on correlation times of spike trains. 7) Simultaneous recordings from pairs of afferents showed that their bursting frequencies (bursts/s) always converged as the amplitude of a noise stimulus was raised. Thus the slow timescale of bursting is similar for different electroreceptors, even though their mean spiking rates can differ. In conclusion, the ampullary electroreceptors of paddlefish have two distinct modes of operation: their spontaneous tonic firing is modulated by the weakest stimuli, but they switch to bursting output for less-weak stimuli. We propose that afferent bursting may mediate close-range tracking of planktonic prey.

Conductance versus current noise in a neuronal model for noisy subthreshold oscillations and related spike generation

Biological systems are notoriously noisy. Noise, therefore, also plays an important role in many models of neural impulse generation. Noise is not only introduced for more realistic simulations but also to account for cooperative effects between noisy and nonlinear dynamics. Often, this is achieved by a simple noise term in the membrane equation (current noise). However, there are ongoing discussions whether such current noise is justified or whether rather conductance noise should be introduced because it is closer to the natural origin of noise. Therefore, we have compared the effects of current and conductance noise in a neuronal model for subthreshold oscillations and action potential generation. We did not see any significant differences in the model behavior with respect to voltage traces, tuning curves of interspike intervals, interval distributions or frequency responses when the noise strength is adjusted. These findings indicate that simple current noise can give reasonable results in neuronal simulations with regard to physiological relevant noise effects.

Stimulus-response curves of a neuronal model for noisy subthreshold oscillations and related spike generation

We investigate the stimulus-dependent tuning properties of a noisy ionic conductance model for intrinsic subthreshold oscillations in membrane potential and associated spike generation. Upon depolarization by an applied current, the model exhibits subthreshold oscillatory activity with an occasional spike generation when oscillations reach the spike threshold. We consider how the amount of applied current, the noise intensity, variation of maximum conductance values, and scaling to different temperature ranges alter the responses of the model with respect to voltage traces, interspike intervals and their statistics, and the mean spike frequency curves. We demonstrate that subthreshold oscillatory neurons in the presence of noise can sensitively and also selectively be tuned by the stimulus-dependent variation of model parameters.

Information processing in noisy burster models of sensory neurons

Processing of external stimuli by sensory neurons often involves bursting, when epochs of fast firing alternate with intervals of quiescence. In particular, sensory neurons of electroreceptors in paddlefish (Polyodon spathula) undergo bursting when stimulated externally with broad-band noise, but otherwise fire spontaneously in a quasiperiodic tonic manner. We use a simple phenomenological model for noise-induced bursting to quantify analytically, by means of the Kullback entropy and Fisher information, the gain in information transfer and electroreceptor sensitivity for external noisy stimuli. A good agreement between theoretical predictions, numerical simulations and experimental data is shown.

Membrane resonance and stochastic resonance modulate firing patterns of thalamocortical neurons

We examined the interactions of subthreshold membrane resonance and stochastic resonance using whole-cell patch clamp recordings in thalamocortical neurons of rat brain slices, as well as with a Hodgkin-Huxley-type mathematical model of thalamocortical neurons. The neurons exhibited the subthreshold resonance when stimulated with small amplitude sine wave currents of varying frequency, and stochastic resonance when noise was added to sine wave inputs. Stochastic resonance was manifest as a maximum in signal-to-noise ratio of output response to subthreshold periodic input combined with noise. Stochastic resonance in conjunction with subthreshold resonance resulted in action potential patterns that showed frequency selectivity for periodic inputs. Stochastic resonance was maximal near subthreshold resonance frequency and a high noise level was required for detection of high frequency signals. We speculate that combined membrane and stochastic resonances have physiological utility in coupling synaptic activity to preferred firing frequency and in network synchronization under noise.

Oscillations, resonances and noise: basis of flexible neuronal pattern generation

Modulation of neuronal impulse pattern is examined by means of a simplified Hodgkin-Huxley type computer model which refers to experimental recordings of cold receptor discharges. This model essentially consists of two potentially oscillating subsystems: a spike generator and a subthreshold oscillator. With addition of noise the model successfully mimics the major types of experimentally recorded impulse patterns and thereby elucidate different resonance behaviors. (1) There is a range of rhythmic spiking or bursting where the spike generator is strongly coupled to the subthreshold oscillator. (2) There is a pacemaker activity of more complex interactions where the spike generator has overtaken part of the control. (3) There is a situation where the two subsystems are decoupled and only resonate with the help of noise.

On episode sensitization in recurrent affective disorders: the role of noise

Episode sensitization is postulated as a key mechanism underlying the long-term course of recurrent affective disorders. Functionally, episode sensitization represents positive feedback between a disease process and its disease episodes resulting in a transition from externally triggered to autonomous episode generation. Recently, we introduced computational approaches to elucidate the functional properties of sensitization. Specifically, we considered the dynamics of episode sensitization with a simple computational model. The present study extends this work by investigating how naturally occurring, internal or external, random influences ("noise") affect episode sensitization. Our simulations demonstrate that actions of noise differ qualitatively in dependence on both the model's activity state as well as the noise intensity. Thereby induction as well as suppression of sensitization can be observed. Most interestingly, externally triggered sensitization development can be minimized by tuning the noise to intermediate intensities. Our findings contribute to the conceptual understanding of the clinical kindling model for affective disorders and also indicate interesting roles for random fluctuations in kindling and sensitization at the neuronal level.

Synchronization of noise-induced bursts in noncoupled sensory neurons

We report experimental observation of phase synchronization in an array of nonidentical noncoupled noisy neuronal oscillators, due to stimulation with external noise. The synchronization derives from a noise-induced qualitative change in the firing pattern of single neurons, which changes from a quasiperiodic to a bursting mode. We show that at a certain noise intensity the onsets of bursts in different neurons become synchronized, even though the number of spikes inside the bursts may vary for different neurons. We demonstrate this effect both experimentally for the electroreceptor afferents of paddlefish, and numerically for a canonical phase model, and characterize it in terms of stochastic synchronization.

Noise-induced impulse pattern modifications at different dynamical period-one situations in a computer model of temperature encoding

We used a minimal Hodgkin-Huxley type model of cold receptor discharges to examine how noise interferes with the non-linear dynamics of the ionic mechanisms of neuronal stimulus encoding. The model is based on the assumption that spike-generation depends on subthreshold oscillations. With physiologically plausible temperature scaling, it passes through different impulse patterns which, with addition of noise, are in excellent agreement with real experimental data. The interval distributions of purely deterministic simulations, however, exhibit considerable differences compared to the noisy simulations especially at the bifurcations of deterministically period-one discharges. We, therefore, analyzed the effects of noise in different situations of deterministically regular period-one discharges: (1) at high-temperatures near the transition to subthreshold oscillations and to burst discharges, and (2) at low-temperatures close to and more far away from the bifurcations to chaotic dynamics. The data suggest that addition of noise can considerably extend the dynamical behavior of the system with coexistence of different dynamical situations at deterministically fixed parameter constellations. Apart from well-described coexistence of spike-generating and subthreshold oscillations also mixtures of tonic and bursting patterns can be seen and even transitions to unstable period-one orbits seem to appear. The data indicate that cooperative effects between low- and high-dimensional dynamics have to be considered as qualitatively important factors in neuronal encoding.

Stochastic resonance in neuron models: endogenous stimulation revisited

The paradigm of stochastic resonance (SR)-the idea that signal detection and transmission may benefit from noise-has met with great interest in both physics and the neurosciences. We investigate here the consequences of reducing the dynamics of a periodically driven neuron to a renewal process (stimulation with reset or endogenous stimulation). This greatly simplifies the mathematical analysis, but we show that stochastic resonance as reported earlier occurs in this model only as a consequence of the reduced dynamics.

Schizophrenia: reduced signal-to-noise ratio and impaired phase-locking during information processing

OBJECTIVE

This study was performed in order to clarify the mechanisms which underlie the reduced signal-to-noise of event-related potentials in schizophrenic patients. Specifically, we wanted to find out, whether it is reduced activation and/or synchronization (phase-locking) in specific frequency bands of the ongoing EEG which is related to the decreased signal amplitude and signal-to-noise ratio in schizophrenics.

METHODS

We investigated 41 unmedicated schizophrenics (10 of them drug-naïve) and compared them with healthy control subjects (n = 233) as well as unmedicated subjects with schizotypal personality (n = 21), who were considered to be high-risk subjects for schizophrenia, and unmedicated depressive patients (n = 71). We measured event-related activity during an acoustical choice reaction paradigm and calculated the signal-to-noise ratio, signal power and noise for a time interval of 50-200 ms after stimulus presentation. Signal-to-noise ratio was calculated from the power of the averaged trials (signal power) divided by the mean power of the single trials minus the power of the average (noise power). Also, we performed a frequency analysis of the pre- and poststimulus EEG based on a factor analytical approach. Group comparisons were performed with ANCOVA.

RESULTS

As expected, a decreased signal-to-noise ratio of evoked activity was found in the schizophrenic and a non-significant trend in the schizotypal subjects and the depressive patients. We were able to show that the observed decrease is due to a reduced signal power and an increase of absolute noise power. Frequency analysis of the evoked activity revealed that normals, schizophrenics schizotypal subjects and depressive patients increased theta/delta activity between pre- and poststimulus interval to a similar extend. However, this theta/delta-augmentation does not correlate with signal power in schizophrenics. Also, normals and depressive subjects augment coherence between both temporal lobes during information processing, which is not found in schizophrenics and schizotypal subjects. In contrast, these two groups augment frontal lobe coherence, which goes along with an increase of noise.

CONCLUSIONS

Reduced stimulus-induced phase-locking and bitemporal coherence of cortically evoked activity but not a failure to activate the cortex may be responsible for the observed low signal-to-noise ratio during information processing in schizophrenics. Accordingly, schizophrenics increase noise after stimulus presentation instead of building up a signal. This is discussed in the framework of the theory of stochastic resonance.

A phase model of temperature-dependent mammalian cold receptors

We present a tractable stochastic phase model of the temperature sensitivity of a mammalian cold receptor. Using simple linear dependencies of the amplitude, frequency, and bias on temperature, the model reproduces the experimentally observed transitions between bursting, beating, and stochastically phase-locked firing patterns. We analyze the model in the deterministic limit and predict, using a Strutt map, the number of spikes per burst for a given temperature. The inclusion of noise produces a variable number of spikes per burst and also extends the dynamic range of the neuron, both of which are analyzed in terms of the Strutt map. Our analysis can be readily applied to other receptors that display various bursting patterns following temperature changes.

Homoclinic bifurcation in a Hodgkin-Huxley model of thermally sensitive neurons

We study global bifurcations of the chaotic attractor in a modified Hodgkin-Huxley model of thermally sensitive neurons. The control parameter for this model is the temperature. The chaotic behavior is realized over a wide range of temperatures and is visualized using interspike intervals. We observe an abrupt increase of the interspike intervals in a certain temperature region. We identify this as a homoclinic bifurcation of a saddle-focus fixed point which is embedded in the chaotic attractors. The transition is accompanied by intermittency, which obeys a universal scaling law for the average length of trajectory segments exhibiting only short interspike intervals with the distance from the onset of intermittency. We also present experimental results of interspike interval measurements taken from the crayfish caudal photoreceptor, which qualitatively demonstrate the same bifurcation structure. (c) 2000 American Institute of Physics.

Consequences of deterministic and random dynamics for the course of affective disorders

BACKGROUND

Uni- and bipolar affective disorders tend to be recurrent and progressive. Illness patterns can evolve from isolated episodes to more rapid, rhythmic, and "chaotic" mood patterns. Nonlinear deterministic dynamics are currently proposed to explain this progression. However, most natural systems are nonlinear and noisy, and cooperative behavior of possible clinical relevance can result.

METHODS

The latter issue has been studied with a mathematical model for progression of disease patterns in affective disorders.

RESULTS

Deterministic dynamics can reproduce a progression from stable, to periodic, to chaotic patterns. Noise increases the spectrum of dynamic behaviors, enhances the responsiveness to weak activations, and facilitates the occurrence of aperiodic patterns.

CONCLUSIONS

Noise might amplify subclinical vulnerabilities into disease onset and could induce transitions to rapid-changing dysrhythmic mood patterns. We suggest that noise-mediated cooperative behavior, including stochastic resonance, should be considered in appropriate models for affective illness.

Low-dimensional dynamics in sensory biology 2: facial cold receptors of the rat

We report the results of a search for evidence of unstable periodic orbits in the sensory afferents of the facial cold receptors of the rat. Cold receptors are unique in that they exhibit a diversity of action potential firing patterns as well as pronounced transients in firing rate following rapid temperature changes. These characteristics are the result of an internal oscillator operating at the level of the membrane potential. If such oscillators have three or more degree of freedom, and at least one of which also exhibits a nonlinearity, they are potentially capable of complex activity. By detecting the existence of unstable periodic orbits, we demonstrate low-dimensional dynamical behavior whose characteristics depend on the temperature range, impulse pattern, and temperature transients.

Cortical activation, signal-to-noise ratio and stochastic resonance during information processing in man

OBJECTIVES

The goal of this study was to determine the relation between EEG, event-related potentials and information processing as measured by an acoustical choice reaction time task. In particular, we wanted to find out to what extent reaction-time performance is related to the pre-stimulus EEG activity (frequency domain) and the magnitude of signal power as well as noise power (stimulus-uncorrelated activity) after the tones (time domain).

MATERIALS AND METHODS

For parametrization, EEG-activity was factorized across pre-defined frequency bands and 19 electrode positions, applying spectral power and coherence analysis. Signal power was estimated by calculating the mean power of the evoked single sweeps. Noise power was computed by subtracting the latter minus the power of the average evoked potential. We investigated 254 healthy subjects who had to perform an acoustical choice reaction task during running EEG.

RESULTS

In the frequency domain, it was found that high frontally pronounced delta-power in the pre-stimulus EEG correlates with fast reaction-time performance, which was regarded as the expression of a readiness potential in the frequency domain, reflecting increased cortical activation. In the time domain, fast reaction times were found to be correlated with the amplitude of the event-related potential N100 as well as with the signal power and signal-to-noise ratio of the evoked activity. This result pointed to the frequently described relation between evoked signals and information processing. In accordance with the theory of stochastic resonance, we also found a positive correlation between the magnitude of noise power after the stimulus and reaction-time performance. Besides, noise power was found to be positively correlated with pre-stimulus cortical activation (mainly in the delta and alphal frequency band), whereas no relation was found between pre-stimulus EEG and the signal power of the event-related activity, except for a weak relation to the alpha2 power.

CONCLUSION

Our findings support the notion that information processing is not only dependent on signal strength but also on a certain amount of basic noise, reflecting the overall energy state of the brain.

Periodically-modulated inhibition of living pacemaker neurons--III. The heterogeneity of the postsynaptic spike trains, and how control parameters affect it

Codings involving spike trains at synapses with inhibitory postsynaptic potentials on pacemakers were examined in crayfish stretch receptor organs by modulating presynaptic instantaneous rates periodically (triangles or sines; frequencies, slopes and depths under, respectively, 5.0 Hz, 40.0/s/s and 25.0/s). Timings were described by interspike and cross-intervals ("phases"); patterns (dispersions, sequences) and forms (timing classes) were identified using pooled graphs (instant along the cycle when a spike occurs vs preceding interval) and return maps (plots of successive intervals). A remarkable heterogeneity of postsynaptic intervals and phases characterizes each modulation. All cycles separate into the same portions: each contains a particular form and switches abruptly to the next. Forms differ in irregularity and predictability: they are (see text) "p:q alternations", "intermittent", "phase walk-throughs", "messy erratic" and "messy stammering". Postsynaptic cycles are asymmetric (hysteresis). This contrasts with the presynaptic homogeneity, smoothness and symmetry. All control parameters are, individually and jointly, strongly influential. Presynaptic slopes, say, act through a postsynaptic sensitivity to their magnitude and sign; when increasing, hysteresis augments and forms change or disappear. Appropriate noise attenuates between-train contrasts, providing modulations are under 0.5 Hz. Postsynaptic natural intervals impose critical time bases, separating presynaptic intervals (around, above or below them) with dissimilar consequences. Coding rules are numerous and have restricted domains; generalizations are misleading. Modulation-driven forms are trendy pacemaker-driven forms. However, dissimilarities, slight when patterns are almost pacemaker, increase as inhibition departs from pacemaker and incorporate unpredictable features. Physiological significance-(1) Pacemaker-driven forms, simple and ubiquitous, appear to be elementary building blocks of synaptic codings, present always but in each case distorted typically. (2) Synapses are prototype: similar behaviours should be widespread, and networks simulations benefit by nonlinear units generating all forms. (3) Relevant to periodic functions are that few variables need be involved in form selection, that distortions are susceptible to noise levels and, if periods are heterogeneous, that simple input cycles impose heterogeneous outputs. (4) Slow Na inactivations are necessary for obtaining complex forms and hysteresis. Formal significance--(1) Pacemaker-driven forms and presumably their modulation-driven counterparts, pertain to universal periodic, intermittent, quasiperiodic and chaotic categories whose formal properties carry physiological connotations. (2) Only relatively elaborate, nonlinear geometric models show all forms; simpler ones, show only alternations and walk-throughs. (3) Bifurcations resemble those of simple maps that can provide useful guidelines. (4) Heterogeneity poses the unanswered question of whether or not the entire cycle and all portions have the same behaviours: therefore, whether trajectories are continuous or have discontinuities and/or singular points.

Ion channel stochasticity may be critical in determining the reliability and precision of spike timing

The firing reliability and precision of an isopotential membrane patch consisting of a realistically large number of ion channels is investigated using a stochastic Hodgkin-Huxley (HH) model. In sharp contrast to the deterministic HH model, the biophysically inspired stochastic model reproduces qualitatively the different reliability and precision characteristics of spike firing in response to DC and fluctuating current input in neocortical neurons, as reported by Mainen & Sejnowski (1995). For DC inputs, spike timing is highly unreliable; the reliability and precision are significantly increased for fluctuating current input. This behavior is critically determined by the relatively small number of excitable channels that are opened near threshold for spike firing rather than by the total number of channels that exist in the membrane patch. Channel fluctuations, together with the inherent bistability in the HH equations, give rise to three additional experimentally observed phenomena: subthreshold oscillations in the membrane voltage for DC input, "spontaneous" spikes for subthreshold inputs, and "missing" spikes for suprathreshold inputs. We suggest that the noise inherent in the operation of ion channels enables neurons to act as "smart" encoders. Slowly varying, uncorrelated inputs are coded with low reliability and accuracy and, hence, the information about such inputs is encoded almost exclusively by the spike rate. On the other hand, correlated presynaptic activity produces sharp fluctuations in the input to the postsynaptic cell, which are then encoded with high reliability and accuracy. In this case, information about the input exists in the exact timing of the spikes. We conclude that channel stochasticity should be considered in realistic models of neurons.

Stimulus sensitivity and neuromodulatory properties of noisy intrinsic neuronal oscillators

Intrinsic subthreshold oscillations in the membrane potential are a common property of many neurons in the peripheral and central nervous system. When such oscillations are combined with noise, interesting signal encoding and neuromodulatory properties are obtained which allow, for example, sensitivity adjustment or differential encoding of stimuli. Here we demonstrate that a noisy Hodgkin/Huxley-model for subthreshold oscillations, when tuned to maximum sensitivity, can be significantly modulated by even minor physiological changes in the oscillation parameters amplitude or frequency. Given the ubiquity of subthreshold oscillating neurons, it can be assumed that these findings reflect principle encoding properties which are relevant for an understanding of sensitivity and neuromodulation in peripheral and central neurons.

Low-dimensional dynamics in sensory biology. 1: Thermally sensitive electroreceptors of the catfish

We report the results of a search for evidence of periodic unstable orbits in the electroreceptors of the catfish. The function of these receptor organs is to sense weak external electric fields. In addition, they respond to the ambient temperature and to the ionic composition of the water. These quantities are encoded by receptors that make use of an internal oscillator operating at the level of the membrane potential. If such oscillators have three or more degrees of freedom, and at least one of which also exhibits a nonlinearity, they are potentially capable of chaotic dynamics. By detecting the existence of stable and unstable periodic orbits, we demonstrate bifurcations between noisy stable and chaotic behavior using the ambient temperature as a parameter. We suggest that the technique developed herein be regarded as an additional tool for the analysis of data in sensory biology and thus can be potentially useful in studies of functional responses to external stimuli. We speculate that the appearance of unstable orbits may be indicative of a state of heightened sensory awareness by the animal.