Integrate-and-fire models with nonlinear leakage

Can we express biophysical neuronal models as integrate-and-fire (IF) models with leakage coefficients which are no longer constant, as in the conventional leaky IF model, but functions of membrane potential and other biophysical variables? We illustrate the answer to this question using the FitzHugh-Nagumo (FHN) model as an example. A novel IF type model, the IF-FHN model, which approximates to the FHN model, is obtained. The leakage coefficient derived in the IF-FHN model has nonmonotonic relationship with membrane potential, revealing at least in part the intrinsic mechanisms underlying the FHN models. The IF-FHN model correspondingly exhibits more complex behaviour than the standard IF model. For example, in some parameter regions, the IF-FHN model has a coefficient of variation of the output interspike interval which is independent of the number of inhibitory inputs, being close to unity over the whole range, comparable to the FHN model as we noted previously (Brown et al., 1999).     

Population approach to a neural discrimination task

This article gives insights into the possible neuronal processes involved in visual discrimination. We study the performance of a spiking network of Integrate-and-Fire (IF) neurons when performing a benchmark discrimination task. The task we adopted consists of determining the direction of moving dots in a noisy context using similar stimuli to those in the experiments of Newsome and colleagues. We present a neural model that performs the discrimination involved in this task. By varying the synaptic parameters of the IF neurons, we illustrate the counter-intuitive importance of the second-order statistics (input noise) in improving the discrimination accuracy of the model. We show that measuring the Firing Rate (FR) over a population enables the model to discriminate in realistic times, and even surprisingly significantly increases its discrimination accuracy over the single neuron case, despite the faster processing. We also show that increasing the input noise increases the discrimination accuracy but only at the expense of the speed at which we can read out the FR.     

A single mutation in the IF3 N-terminal domain perturbs the fidelity of translation initiation at three levels

Bacterial translation initiation factor 3 (IF3) is involved in the fidelity of translation initiation at several levels, including start-codon discrimination, mRNA translation, and initiator-tRNA selection. The IF3 C-terminal domain (CTD) is required for binding to the 30S ribosomal subunit. N-terminal domain (NTD) function is less certain, but likely contributes to initiation fidelity. Point mutations in either domain can decrease initiation fidelity, but C-terminal domain mutations may be indirect. Here, the Y75N substitution mutation in the NTD is examined in vitro and in vivo. IF3_Y75N protein binds 30S subunits normally, but is defective in start-codon discrimination, inhibition of initiation on leaderless mRNA, and initiator-tRNA selection, thereby establishing a direct role for the IF3 NTD in these initiation processes. A model illustrating how IF3 modulates an inherent function of the 30S subunit is discussed.     

Inhibitory synchrony as a mechanism for attentional gain modulation

Recordings from area V4 of monkeys have revealed that when the focus of attention is on a visual stimulus within the receptive field of a cortical neuron, two distinct changes can occur: The firing rate of the neuron can change and there can be an increase in the coherence between spikes and the local field potential (LFP) in the gamma-frequency range (30-50 Hz). The hypothesis explored here is that these observed effects of attention could be a consequence of changes in the synchrony of local interneuron networks. We performed computer simulations of a Hodgkin-Huxley type neuron driven by a constant depolarizing current, I, representing visual stimulation and a modulatory inhibitory input representing the effects of attention via local interneuron networks. We observed that the neuron's firing rate and the coherence of its output spike train with the synaptic inputs was modulated by the degree of synchrony of the inhibitory inputs. When inhibitory synchrony increased, the coherence of spiking model neurons with the synaptic input increased, but the firing rate either increased or remained the same. The mean number of synchronous inhibitory inputs was a key determinant of the shape of the firing rate versus current (f-I) curves. For a large number of inhibitory inputs (approximately 50), the f-I curve saturated for large I and an increase in input synchrony resulted in a shift of sensitivity-the model neuron responded to weaker inputs I. For a small number (approximately 10), the f-I curves were non-saturating and an increase in input synchrony led to an increase in the gain of the response-the firing rate in response to the same input was multiplied by an approximately constant factor. The firing rate modulation with inhibitory synchrony was highest when the input network oscillated in the gamma frequency range. Thus, the observed changes in firing rate and coherence of neurons in the visual cortex could be controlled by top-down inputs that regulated the coherence in the activity of a local inhibitory network discharging at gamma frequencies.     

Effect of central CO(2) drive on lung inflation responses of expiratory bulbospinal neurons in dogs

The purpose of these studies is to better understand the nature of the reflex interactions that control the discharge patterns of caudal medullary, expiratory (E) bulbospinal neurons. We examined the effect of central chemodrive inputs measured as arterial CO(2) tension (Pa(CO(2))) during hyperoxia on the excitatory and inhibitory components of the lung inflation responses of these neurons in thiopental sodium-anesthetized, paralyzed dogs. Data from slow ramp inflation and deflation test patterns, which were separated by several control inflation cycles, were used to produce plots of neuronal discharge frequency (F(n)) versus transpulmonary pressure (P(t)). P(t) was used as an index of the activity arising from the slowly adapting pulmonary stretch receptors (PSRs). Changes in inspired CO(2) concentrations were used to produce Pa(CO(2)) levels that ranged from 20 to 80 mmHg. The data obtained from 41 E neurons were used to derive an empirical model that quantifies the average relationship for F(n) versus both P(t) and Pa(CO(2)). This model can be used to predict the time course and magnitude of E neuronal responses to these inputs. These data suggest that the interaction between Pa(CO(2)) and PSR-mediated excitation and inhibition of F(n) is mainly additive, but synergism between Pa(CO(2)) and excitatory inputs is also present. The implications of these findings are discussed.     

Pupillary dilation response as an indicator of auditory discrimination in the barn owl

The pupil of an awake, untrained, head-restrained barn owl was found to dilate in response to sounds with a latency of about 25 ms. The magnitude of the dilation scaled with signal-to-noise ratio. The dilation response habituated when a sound was repeated, but recovered when stimulus frequency or location was changed. The magnitude of the recovered response was related to the degree to which habituating and novel stimuli differed and was therefore exploited to measure frequency and spatial discrimination. Frequency discrimination was examined by habituating the response to a reference tone at 3 kHz or 6 kHz and determining the minimum change in frequency required to induce recovery. We observed frequency discrimination of 125 Hz at 3 kHz and 250 Hz at 6 kHz – values comparable to those reported by others using an operant task. Spatial discrimination was assessed by habituating the response to a stimulus from one location and determining the minimum horizontal speaker separation required for recovery. This yielded the first measure of the minimum audible angle in the barn owl: 3° for broadband noise and 4.5° for narrowband noise. The acoustically evoked pupillary dilation is thus a promising indicator of auditory discrimination requiring neither training nor aversive stimuli. Accepted: 28 February 2000     

Dissociable Processes for Orientation Discrimination Learning and Contextual Illusion Magnitude

Previous research suggests an inverse relationship between human orientation discrimination sensitivity and tilt illusion magnitude. To test whether these perceptual functions are inherently linked, we measured both orientation discrimination sensitivity and the magnitude of the tilt illusion before and after participants had been trained for three days on an orientation discrimination task. Discrimination sensitivity improved with training and this improvement remained one month after the initial learning. However, tilt illusion magnitude remained unchanged before and after orientation training, at either trained or untrained orientations. Our results suggest that orientation discrimination sensitivity and illusion magnitude are not inherently linked. They also provide further evidence that, at least for the training periods we employed, perceptual learning of orientation discrimination may involve high-level processes.     

The structure of bovine IF(1), the regulatory subunit of mitochondrial F-ATPase.

In mitochondria, the hydrolytic activity of ATP synthase is regulated by an inhibitor protein, IF(1). Its binding to ATP synthase depends on pH, and below neutrality, IF(1) is dimeric and forms a stable complex with the enzyme. At higher pH values, IF(1) forms tetramers and is inactive. In the 2.2 A structure of the bovine IF(1) described here, the four monomers in the asymmetric unit are arranged as a dimer of dimers. Monomers form dimers via an antiparallel alpha-helical coiled coil in the C-terminal region. Dimers are associated into oligomers and form long fibres in the crystal lattice, via coiled-coil interactions in the N-terminal and inhibitory regions (residues 14-47). Therefore, tetramer formation masks the inhibitory region, preventing IF(1) binding to ATP synthase.     

Is Attention Based on Spatial Contextual Memory Preferentially Guided by Low Spatial Frequency Signals?

A popular model of visual perception states that coarse information (carried by low spatial frequencies) along the dorsal stream is rapidly transmitted to prefrontal and medial temporal areas, activating contextual information from memory, which can in turn constrain detailed input carried by high spatial frequencies arriving at a slower rate along the ventral visual stream, thus facilitating the processing of ambiguous visual stimuli. We were interested in testing whether this model contributes to memory-guided orienting of attention. In particular, we asked whether global, low-spatial frequency (LSF) inputs play a dominant role in triggering contextual memories in order to facilitate the processing of the upcoming target stimulus. We explored this question over four experiments. The first experiment replicated the LSF advantage reported in perceptual discrimination tasks by showing that participants were faster and more accurate at matching a low spatial frequency version of a scene, compared to a high spatial frequency version, to its original counterpart in a forced-choice task. The subsequent three experiments tested the relative contributions of low versus high spatial frequencies during memory-guided covert spatial attention orienting tasks. Replicating the effects of memory-guided attention, pre-exposure to scenes associated with specific spatial memories for target locations (memory cues) led to higher perceptual discrimination and faster response times to identify targets embedded in the scenes. However, either high or low spatial frequency cues were equally effective; LSF signals did not selectively or preferentially contribute to the memory-driven attention benefits to performance. Our results challenge a generalized model that LSFs activate contextual memories, which in turn bias attention and facilitate perception.     

History-dependent excitability as a single-cell substrate of transient memory for information discrimination

Neurons react differently to incoming stimuli depending upon their previous history of stimulation. This property can be considered as a single-cell substrate for transient memory, or context-dependent information processing: depending upon the current context that the neuron "sees" through the subset of the network impinging on it in the immediate past, the same synaptic event can evoke a postsynaptic spike or just a subthreshold depolarization. We propose a formal definition of History-Dependent Excitability (HDE) as a measure of the propensity to firing in any moment in time, linking the subthreshold history-dependent dynamics with spike generation. This definition allows the quantitative assessment of the intrinsic memory for different single-neuron dynamics and input statistics. We illustrate the concept of HDE by considering two general dynamical mechanisms: the passive behavior of an Integrate and Fire (IF) neuron, and the inductive behavior of a Generalized Integrate and Fire (GIF) neuron with subthreshold damped oscillations. This framework allows us to characterize the sensitivity of different model neurons to the detailed temporal structure of incoming stimuli. While a neuron with intrinsic oscillations discriminates equally well between input trains with the same or different frequency, a passive neuron discriminates better between inputs with different frequencies. This suggests that passive neurons are better suited to rate-based computation, while neurons with subthreshold oscillations are advantageous in a temporal coding scheme. We also address the influence of intrinsic properties in single-cell processing as a function of input statistics, and show that intrinsic oscillations enhance discrimination sensitivity at high input rates. Finally, we discuss how the recognition of these cell-specific discrimination properties might further our understanding of neuronal network computations and their relationships to the distribution and functional connectivity of different neuronal types.     

Right-left discrimination in a biologically oriented model of the cockroach escape system

We present a biologically oriented model that accounts for left-right discrimination in the cockroach's escape behavior. The model includes the main groups of neurons found to be involved in the escape response. Each one of the included neurons is described by the actual processes taking place in an individual neuron (formation of an action potential, transmitter release, conductance changes, etc.). Furthermore, realistic chemical synapses (excitatory or inhibitory and able to undergo different types of modulation) connect the various neurons. With this model, we were able to achieve, for a wide range of inputs representing different wind directions, behavior which resembles that found experimentally. The model indicates that several synaptic properties, in particular postsynaptic inhibition and presynaptic facilitation, play a key role in the discrimination of wind direction. Received: 22 January 1999 / Accepted in revised form: 1 March 1999     

Possible dual effect of synapses that are putatively purely excitatory or purely inhibitory: bases in stability theory and implications for neural network behavior

Depolarization of an excitable membrane has a dual effect; excitatory in that it causes rapid opening of calcium and/or sodium channels but inhibitory in that it also causes those channels to inactivate. We considered whether apparently paradoxical or dual behavior might be exhibited by excitatory and inhibitory synaptic inputs. We used the classic Hodgkin-Huxley model for voltage-gated channels plus leakage channels of appropriate selectivity for ligand-gated postsynaptic channels. We summarize a model cell's behavior by calculating elicited firing frequency as a function of reversal potential and conductance of summed synaptic inputs, using stability theory and direct simulations. Dual behavior is elicited in the model with reasonable densities of ligand-gated channels. Thus a particular synaptic input to a neuron may be either excitatory or inhibitory depending on simultaneous activity of other synaptic inputs to the cell. This input-output map may give rise to biologically realistic and rich behaviors as an element of computed neural networks, and still be computationally tractable.     

Effects of correlated and synchronized stochastic inputs to leaky integrator neuronal model

We present an analysis of neuronal model behaviour with correlated synaptic inputs including the cases that correlated inputs are equivalent to exactly synchronized inputs and correlated inputs are not equivalent to exactly synchronized inputs. For the former case, it is found that the fully (synaptically) correlated inputs assumption (see Section 1 for definition), which is used in most, if not all, theoretical and experimental work in the past few years, results in a waste of resources and might be an unrealistic assumption; with an exactly balanced excitatory and inhibitory, and synaptically correlated input, the integrate-and-fire model simply behaves as a synchrony detector in certain parameter regions; the well-known diffusion model, upon which most theoretical work is based, fails to approximate the model with synaptically correlated Poisson inputs. A novel way to approximate synaptically correlated Poisson inputs is then presented;an optimization principle on neuronal models with partially (synaptically) correlated inputs is proposed, which enables us to predict microscopic structures in neuronal systems. For the latter case,with tightly synchronized inputs (see Section 1 for definition), the model behaviour depends on its integration time of input signals and could exhibit bursting discharge.for loosely synchronized inputs, we found that correlated inputs are equivalent to the post-spike voltage reset mechanism proposed in the literature.     

Auditory Discrimination Learning: Role of Working Memory

Perceptual training is generally assumed to improve perception by modifying the encoding or decoding of sensory information. However, this assumption is incompatible with recent demonstrations that transfer of learning can be enhanced by across-trial variation of training stimuli or task. Here we present three lines of evidence from healthy adults in support of the idea that the enhanced transfer of auditory discrimination learning is mediated by working memory (WM). First, the ability to discriminate small differences in tone frequency or duration was correlated with WM measured with a tone n-back task. Second, training frequency discrimination around a variable frequency transferred to and from WM learning, but training around a fixed frequency did not. The transfer of learning in both directions was correlated with a reduction of the influence of stimulus variation in the discrimination task, linking WM and its improvement to across-trial stimulus interaction in auditory discrimination. Third, while WM training transferred broadly to other WM and auditory discrimination tasks, variable-frequency training on duration discrimination did not improve WM, indicating that stimulus variation challenges and trains WM only if the task demands stimulus updating in the varied dimension. The results provide empirical evidence as well as a theoretic framework for interactions between cognitive and sensory plasticity during perceptual experience.     

A hinge of the endogeneous ATP synthase inhibitor protein: the link between inhibitory and anchoring domains

The ATP synthase of bovine heart mitochondria possesses a regulatory subunit called the endogenous inhibitory protein (IF(1)). This subunit regulates the catalytic activity of the F(1) sector in the mitochondrial inner membrane. When DeltamuH(+) falls, IF(1) binds to the enzyme and inhibits ATP hydrolysis. On the other hand, the establishment of a DeltamuH(+) induces the release of the inhibitory action of IF(1), allowing ATP synthesis to proceed. IF(1) is also involved in the dimerization of soluble F(1). Dynamic domain analysis and normal mode analysis of the reported crystallographic structure of IF(1) revealed that it has an effective hinge formed by residues 46-52. Molecular dynamics data of a 27 residue fragment confirmed the existence of the hinge. The hinge may act as a regulatory region that links the inhibitory and anchoring domains of IF(1). The residues assigned to the hinge are conserved between mammals, but not in other species, such as yeasts. Likewise, unlike the heart inhibitor, the yeast protein does not have the residues that allow it to form stable dimers through coiled-coil interactions. Collectively, the data suggest that the hinge and the dimerization domain of the inhibitor protein from bovine heart are related to its ability to form stable dimers and to interact with other subunits of the ATP synthase.     

Network Models of Frequency Modulated Sweep Detection

Frequency modulated (FM) sweeps are common in species-specific vocalizations, including human speech. Auditory neurons selective for the direction and rate of frequency change in FM sweeps are present across species, but the synaptic mechanisms underlying such selectivity are only beginning to be understood. Even less is known about mechanisms of experience-dependent changes in FM sweep selectivity. We present three network models of synaptic mechanisms of FM sweep direction and rate selectivity that explains experimental data: (1) The ‘facilitation’ model contains frequency selective cells operating as coincidence detectors, summing up multiple excitatory inputs with different time delays. (2) The ‘duration tuned’ model depends on interactions between delayed excitation and early inhibition. The strength of delayed excitation determines the preferred duration. Inhibitory rebound can reinforce the delayed excitation. (3) The ‘inhibitory sideband’ model uses frequency selective inputs to a network of excitatory and inhibitory cells. The strength and asymmetry of these connections results in neurons responsive to sweeps in a single direction of sufficient sweep rate. Variations of these properties, can explain the diversity of rate-dependent direction selectivity seen across species. We show that the inhibitory sideband model can be trained using spike timing dependent plasticity (STDP) to develop direction selectivity from a non-selective network. These models provide a means to compare the proposed synaptic and spectrotemporal mechanisms of FM sweep processing and can be utilized to explore cellular mechanisms underlying experience- or training-dependent changes in spectrotemporal processing across animal models. Given the analogy between FM sweeps and visual motion, these models can serve a broader function in studying stimulus movement across sensory epithelia.     

Learning a grating discrimination task broadens human spatial frequency tuning

 The effect of spatial frequency discrimination learning on spatial frequency detection tuning curves, obtained by a summation to threshold paradigm, has been investigated. Three human observers were exposed to a grating discrimination task for longer than two weeks, and their detection thresholds for compound Gabor gratings were measured before and after this time interval. Discrimination thresholds decreased continuously and substantially during the course of learning, while the spatial frequency detection tuning curves show significant broadening in the posttest. Calculating the discrimination resolution of an ensemble of sensory coding units shows that larger bandwidths lead to better spatial frequency discrimination performance if pattern discrimination rests on multidimensional comparison or one-dimensional scaling of the spatial frequency parameter. Further, it is shown that a multiple-mechanism nonlinear pooling model is capable of explaining the results if plasticity of coding unit bandwidth or adaptive weights of the coding unit responses at the stage of response integration is assumed. The alternative sources of plasticity and the consequences of the findings for psychophysical modeling are discussed. Received: 8 September 1999 / Accepted in revised form: 16 October 2000     

Mechanism of opioid and substance P-mediated modulation of cortical signal transduction through the striatum

A mechanism of opioid and substance P-mediated modulation of a cortical signal transduction through the striatum is suggested. According to this mechanism, an activation of postsynaptic receptors, bound to Gi/0 proteins, should increase the magnitude of NMDA-dependent (NMDA-independent) LTD (LTP) of excitatory inputs and LTP (LTD) of inhibitory inputs to all types of striatal cells. An activation of postsynaptic receptors, bound to Gs or Gq/11 proteins, should oppositely modulate LTD and LTD in the same inputs. It follows from the model that the negative feedback loops can held the activity of a striatal output cells at the stable level due to recurrent activation by endogenous opioids of delta receptors on striatopallidal cells, mu and kappa receptors on striatonigral cells of striosomes and matrix, respectively, and subsequent suppression of the efficacy of corticostriatal inputs. Cholinergic interneurons, affected by enkephalin and substance P, are also involved in these feedback loops. We hypothesized that an activation of mu and delta receptors and/or inactivation of kappa receptors on striatal spiny cells might alleviate parkinsonian symptoms and recover locomotor activity.     

Spatiotemporal asymmetry of associative synaptic plasticity in fear conditioning pathways

Input-specific long-term potentiation (LTP) in afferent inputs to the amygdala serves an essential function in the acquisition of fear memory. Factors underlying input specificity of synaptic modifications implicated in information transfer in fear conditioning pathways remain unclear. Here we show that the strength of naive synapses in two auditory inputs converging on a single neuron in the lateral nucleus of the amygdala (LA) is only modified when a postsynaptic action potential closely follows a synaptic response. The stronger inhibitory drive in thalamic pathway, as compared with cortical input, hampers the induction of LTP at thalamo-amygdala synapses, contributing to the spatial specificity of LTP in convergent inputs. These results indicate that spike timing-dependent synaptic plasticity in afferent projections to the LA is both temporarily and spatially asymmetric, thus providing a mechanism for the conditioned stimulus discrimination during fear behavior.