Effect of different glucose supply conditions on neuronal energy metabolism

The glucose-excited neurons in brain can sense blood glucose levels and reflect different firing states, which are mainly associated with regulation of blood glucose and energy demand in the brain. In this paper, a new model of glucose-excited neuron in hypothalamus is proposed. The firing properties and energy consumption of this type of neuron under conditions of different glucose levels are simulated and analyzed. The results show that the firing rate and firing duration of the neuron both increase with increasing extracellular glucose levels, but the maximum energy power for an AP is reduced. Further study suggests that the neuron firstly absorbs energy substrates (e.g. glucose) from the blood to prepare for the high energy demand of high-frequency spikes.     

Multisynaptic activity in a pyramidal neuron model and neural code

The highly irregular firing of mammalian cortical pyramidal neurons is one of the most striking observation of the brain activity. This result affects greatly the discussion on the neural code, i.e. how the brain codes information transmitted along the different cortical stages. In fact it seems to be in favor of one of the two main hypotheses about this issue, named the rate code. But the supporters of the contrasting hypothesis, the temporal code, consider this evidence inconclusive. We discuss here a leaky integrate-and-fire model of a hippocampal pyramidal neuron intended to be biologically sound to investigate the genesis of the irregular pyramidal firing and to give useful information about the coding problem. To this aim, the complete set of excitatory and inhibitory synapses impinging on such a neuron has been taken into account. The firing activity of the neuron model has been studied by computer simulation both in basic conditions and allowing brief periods of over-stimulation in specific regions of its synaptic constellation. Our results show neuronal firing conditions similar to those observed in experimental investigations on pyramidal cortical neurons. In particular, the variation coefficient (CV) computed from the inter-spike intervals (ISIs) in our simulations for basic conditions is close to the unity as that computed from experimental data. Our simulation shows also different behaviors in firing sequences for different frequencies of stimulation.     

Ensembles of Spiking Neurons with Noise Support Optimal Probabilistic Inference in a Dynamically Changing Environment

It has recently been shown that networks of spiking neurons with noise can emulate simple forms of probabilistic inference through “neural sampling”, i.e., by treating spikes as samples from a probability distribution of network states that is encoded in the network. Deficiencies of the existing model are its reliance on single neurons for sampling from each random variable, and the resulting limitation in representing quickly varying probabilistic information. We show that both deficiencies can be overcome by moving to a biologically more realistic encoding of each salient random variable through the stochastic firing activity of an ensemble of neurons. The resulting model demonstrates that networks of spiking neurons with noise can easily track and carry out basic computational operations on rapidly varying probability distributions, such as the odds of getting rewarded for a specific behavior. We demonstrate the viability of this new approach towards neural coding and computation, which makes use of the inherent parallelism of generic neural circuits, by showing that this model can explain experimentally observed firing activity of cortical neurons for a variety of tasks that require rapid temporal integration of sensory information.     

Synchronization and sensitivity enhancement of the Hodgkin-Huxley neurons due to inhibitory inputs

Recent experimental results imply that inhibitory postsynaptic potentials can play a functional role in realizing synchronization of neuronal firing in the brain. In order to examine the relation between inhibition and synchronous firing of neurons theoretically, we analyze possible effects of synchronization and sensitivity enhancement caused by inhibitory inputs to neurons with a biologically realistic model of the Hodgkin-Huxley equations. The result shows that, after an inhibitory spike, the firing probability of a single postsynaptic neuron exposed to random excitatory background activity oscillates with time. The oscillation of the firing probability can be related to synchronous firing of neurons receiving an inhibitory spike simultaneously. Further, we show that when an inhibitory spike input precedes an excitatory spike input, the presence of such preceding inhibition raises the firing probability peak of the neuron after the excitatory input. The result indicates that an inhibitory spike input can enhance the sensitivity of the postsynaptic neuron to the following excitatory spike input. Two neural network models based on these effects on postsynaptic neurons caused by inhibitory inputs are proposed to demonstrate possible mechanisms of detecting particular spatiotemporal spike patterns. Received: 15 April 1999 /Accepted in revised form: 25 November 1999     

To Burst or Not to Burst?

It is well known that some neurons tend to fire packets of action potentials followed by periods of quiescence (bursts) while others within the same stage of sensory processing fire in a tonic manner. However, the respective computational advantages of bursting and tonic neurons for encoding time varying signals largely remain a mystery. Weakly electric fish use cutaneous electroreceptors to convey information about sensory stimuli and it has been shown that some electroreceptors exhibit bursting dynamics while others do not. In this study, we compare the neural coding capabilities of tonically firing and bursting electroreceptor model neurons using information theoretic measures. We find that both bursting and tonically firing model neurons efficiently transmit information about the stimulus. However, the decoding mechanisms that must be used for each differ greatly: a non-linear decoder would be required to extract all the available information transmitted by the bursting model neuron whereas a linear one might suffice for the tonically firing model neuron. Further investigations using stimulus reconstruction techniques reveal that, unlike the tonically firing model neuron, the bursting model neuron does not encode the detailed time course of the stimulus. A novel measure of feature detection reveals that the bursting neuron signals certain stimulus features. Finally, we show that feature extraction and stimulus estimation are mutually exclusive computations occurring in bursting and tonically firing model neurons, respectively. Our results therefore suggest that stimulus estimation and feature extraction might be parallel computations in certain sensory systems rather than being sequential as has been previously proposed.     

Information in the Neuronal Representation of Individual Stimuli in the Primate Temporal Visual Cortex

To analyze the information provided about individual visual stimuliin the responses of single neurons in the primate temporal lobevisual cortex, neuronal responses to a set of 65 visual stimuli wererecorded in macaques performing a visual fixation task and analyzedusing information theoretical measures. The population of neuronsanalyzed responded primarily to faces. The stimuli included 23 facesand 42 nonface images of real-world scenes, so that the function ofthis brain region could be analyzed when it was processing relativelynatural scenes.It was found that for the majority of the neurons significantamounts of information were reflected about which of several of the23 faces had been seen. Thus the representation was not local, forin a local representation almost all the information available canbe obtained when the single stimulus to which the neuron respondsbest is shown. It is shown that the information available about anyone stimulus depended on how different (for example, how manystandard deviations) the response to that stimulus was from theaverage response to all stimuli. This was the case for responsesbelow the average response as well as above.It is shown that the fraction of information carried by the lowfiring rates of a cell was large—much larger than that carried bythe high firing rates. Part of the reason for this is that theprobability distribution of different firing rates is biased towardlow values (though with fewer very low values than would bepredicted by an exponential distribution). Another factor is thatthe variability of the response is large at intermediate and highfiring rates.Another finding is that at short sampling intervals (such as 20 ms)the neurons code information efficiently, by effectively acting asbinary variables and behaving less noisily than would be expectedof a Poisson process.     

Subicular neurons represent multiple variables of a hippocampal-dependent task by using theta rhythm

The subiculum is positioned at a critical juncture at the interface of the hippocampus with the rest of the brain. However, the exact roles of the subiculum in most hippocampal-dependent memory tasks remain largely unknown. One obstacle to make comparisons of neural firing patterns between the subiculum and hippocampus is the broad firing fields of the subicular cells. Here, we used spiking phases in relation to theta rhythm to parse the broad firing field of a subicular neuron into multiple subfields to find the unique functional contribution of the subiculum while male rats performed a hippocampal-dependent visual scene memory task. Some of the broad firing fields of the subicular neurons were successfully divided into multiple subfields similar to those in the CA1 by using the theta phase precession cycle. The new paradigm significantly improved the detection of task-relevant information in subicular cells without affecting the information content represented by CA1 cells. Notably, we found that multiple fields of a single subicular neuron, unlike those in the CA1, carried heterogeneous task-related information such as visual context and choice response. Our findings suggest that the subicular cells integrate multiple task-related factors by using theta rhythm to associate environmental context with action.

The subiculum is positioned at the interface between the hippocampus and the rest of the brain, but what is its role in hippocampal-dependent memory tasks? This neurophysiological study provides novel insights into how the subiculum represents multiple cognitive variables by using both rate and temporal codes.     

Mechanisms of Gain Control by Voltage-Gated Channels in Intrinsically-Firing Neurons

Gain modulation is a key feature of neural information processing, but underlying mechanisms remain unclear. In single neurons, gain can be measured as the slope of the current-frequency (input-output) relationship over any given range of inputs. While much work has focused on the control of basal firing rates and spike rate adaptation, gain control has been relatively unstudied. Of the limited studies on gain control, some have examined the roles of synaptic noise and passive somatic currents, but the roles of voltage-gated channels present ubiquitously in neurons have been less explored. Here, we systematically examined the relationship between gain and voltage-gated ion channels in a conductance-based, tonically-active, model neuron. Changes in expression (conductance density) of voltage-gated channels increased (Ca²⁺ channel), reduced (K⁺ channels), or produced little effect (h-type channel) on gain. We found that the gain-controlling ability of channels increased exponentially with the steepness of their activation within the dynamic voltage window (voltage range associated with firing). For depolarization-activated channels, this produced a greater channel current per action potential at higher firing rates. This allowed these channels to modulate gain by contributing to firing preferentially at states of higher excitation. A finer analysis of the current-voltage relationship during tonic firing identified narrow voltage windows at which the gain-modulating channels exerted their effects. As a proof of concept, we show that h-type channels can be tuned to modulate gain by changing the steepness of their activation within the dynamic voltage window. These results show how the impact of an ion channel on gain can be predicted from the relationship between channel kinetics and the membrane potential during firing. This is potentially relevant to understanding input-output scaling in a wide class of neurons found throughout the brain and other nervous systems.     

Encoding of spatio-temporal input characteristics by a CA1 pyramidal neuron model

The in vivo activity of CA1 pyramidal neurons alternates between regular spiking and bursting, but how these changes affect information processing remains unclear. Using a detailed CA1 pyramidal neuron model, we investigate how timing and spatial arrangement variations in synaptic inputs to the distal and proximal dendritic layers influence the information content of model responses. We find that the temporal delay between activation of the two layers acts as a switch between excitability modes: short delays induce bursting while long delays decrease firing. For long delays, the average firing frequency of the model response discriminates spatially clustered from diffused inputs to the distal dendritic tree. For short delays, the onset latency and inter-spike-interval succession of model responses can accurately classify input signals as temporally close or distant and spatially clustered or diffused across different stimulation protocols. These findings suggest that a CA1 pyramidal neuron may be capable of encoding and transmitting presynaptic spatiotemporal information about the activity of the entorhinal cortex-hippocampal network to higher brain regions via the selective use of either a temporal or a rate code.     

Neuronal population activity and functional imaging.

Human functional brain imaging detects blood flow changes that are thought to reflect the activity of neuronal populations and, thus, the responses of neurons that carry behaviourally relevant information. Since this relationship is poorly understood, we explored the link between the activity of single neurons and their neuronal population. The functional imaging results were in good agreement with levels of population activation predicted from the known effects of sensory stimulation, learning and attention on single cortical neurons. However, the nature of the relationship between population activation and single neuron firing was very surprising. Population activation was strongly influenced by those neurons firing at low rates and so was very sensitive to the baseline or 'spontaneous' firing rate. When neural representations were sparse and neurons were tuned to several stimulus dimensions, population activation was hardly influenced by the few neurons whose firing was most strongly modulated by the task or stimulus. Measures of population activation could miss changes in information processing given simultaneous changes in neurons' baseline firing, response modulation or tuning width. Factors that can modulate baseline firing, such as attention, may have a particularly large influence on population activation. The results have implications for the interpretation of functional imaging signals and for cross-calibration between different methods for measuring neuronal activity.     

Catastrophe theory of dopaminergic transmission: a revised dopamine hypothesis of schizophrenia

Mathematical modeling of experimentally observed parameters of dopaminergic neuronal activity suggests the occurrence of multiple equilibrium states in neurons characterized by certain precisely defined properties of the tyrosine hydroxylating system. These equilibria may become unstable under certain conditions and transitions between multiple states are predicted. In addition, modeling of the spatial interactions of dopamine neurons within a neural net leads to domain wall soliton-like solutions of neuronal firing. In the discrete spatial case, these equations are isomorphic to those of the Ising model of phase transitions in lattice spins.The hypothesis is proposed that the occurrence of multiple stable equilibrium states rather than excessive dopaminergic transmission forms the pathophysiological basis of the schizophrenic thought disorder.The model is internally consistent with known clinical effects of drugs such as neuroleptics, reserpine and amphetamine. In agreement with postmortem and other studies, the theory predicts the lack of increased concentrations of dopamine or its major metabolite, homovanillic acid, in brain and cerebrospinal fluid of schizophrenics.The mathematical model is compatible with the theory that postulates an attention deficit as an underlying mechanism of schizophrenic psychosis and allows for a possible genetic heterogeneity of the disease.     

Coexistence of Reward and Unsupervised Learning During the Operant Conditioning of Neural Firing Rates

A fundamental goal of neuroscience is to understand how cognitive processes, such as operant conditioning, are performed by the brain. Typical and well studied examples of operant conditioning, in which the firing rates of individual cortical neurons in monkeys are increased using rewards, provide an opportunity for insight into this. Studies of reward-modulated spike-timing-dependent plasticity (RSTDP), and of other models such as R-max, have reproduced this learning behavior, but they have assumed that no unsupervised learning is present (i.e., no learning occurs without, or independent of, rewards). We show that these models cannot elicit firing rate reinforcement while exhibiting both reward learning and ongoing, stable unsupervised learning. To fix this issue, we propose a new RSTDP model of synaptic plasticity based upon the observed effects that dopamine has on long-term potentiation and depression (LTP and LTD). We show, both analytically and through simulations, that our new model can exhibit unsupervised learning and lead to firing rate reinforcement. This requires that the strengthening of LTP by the reward signal is greater than the strengthening of LTD and that the reinforced neuron exhibits irregular firing. We show the robustness of our findings to spike-timing correlations, to the synaptic weight dependence that is assumed, and to changes in the mean reward. We also consider our model in the differential reinforcement of two nearby neurons. Our model aligns more strongly with experimental studies than previous models and makes testable predictions for future experiments.     

A Markov model for interspike interval distributions of auditory cortical neurons that do not show periodic firings

Spontaneous firing properties of individual auditory cortical neurons are interpreted in terms of local and global order present in functioning brain networks, such as alternating “up” and “down” states. A four-state modulated Markov process is used to model neuronal firings. The system alternates between a bound and an unbound state, both with Poisson-distributed lifetimes. During the unbound state, active and closed states alternate with Poisson-distributed lifetimes. Inside the active state, spikes are generated as a realization of a Poisson process. This combination of processes constitutes a four-state modulated Markov process, determined by five independent parameters. Analytical expressions for the probability density functions (pdfs) that describe the interspike interval (ISI) distribution and autocorrelation function are derived. The pdf for the ISI distribution is shown to be a linear combination of three exponential functions and is expressed through the five system parameters. Through fitting experimental ISI histograms by the theoretical ones, numerical values of the system parameters are obtained for the individual neurons. Both Monte Carlo simulations and goodness-of-fit tests are used to validate the fitting procedure. The values of the estimated system parameters related to the active-closed and bound–unbound processes and their independence on the neurons’ mean firing rate suggest that the underlying quasi-periodic processes reflect properties of the network in which the neurons are embedded. The characteristic times of autocorrelations, determined by the bound–unbound and active-closed processes, are also independent of the neuron’s firing rate. The agreement between experimental and theoretical ISI histograms and autocorrelation functions allows interpretation of the system parameters of the individual neurons in terms of slow and delta waves, and high-frequency oscillations observed in cortical networks. This procedure can identify and track the influence of changing brain states on the single-unit firing patterns in experimental animals.     

Whole cell recordings from brain of adult Drosophila

In this video, we demonstrate the procedure for isolating whole brains from adult Drosophila in preparation for recording from single neurons. We begin by describing the dissecting solution and capture of the adult females used in our studies. The procedure for removing the whole brain intact, including both optic lobes, is illustrated. Dissection of the overlying trachea is also shown. The isolated brain is not only small but needs special care in handling at this stage to prevent damage to the neurons, many of which are close to the outer surface of the tissue. We show how a special holder we developed is used to stabilize the brain in the recording chamber. A standard electrophysiology set up is used for recording from single neurons or pairs of neurons. A fluorescent image, viewed through the recording microscope, from a GAL4 line driving GFP expression (GH146) illustrates how projection neurons (PNs) are identified in the live brain. A high power Nomarski image shows a view of a single neuron that is being targeted for whole cell recording. When the brain is successfully removed without damage, the majority of the neurons are spontaneously active, firing action potentials and/or exhibiting spontaneous synaptic input. This in situ preparation, in which whole cell recording of identified neurons in the whole brain can be combined with genetic and pharmacological manipulations, is a useful model for exploring cellular physiology and plasticity in the adult CNS.     

Neurons in the amygdala with response-selectivity for anxiety in two ethologically based tests

The amygdala is a key area in the brain for detecting potential threats or dangers, and further mediating anxiety. However, the neuronal mechanisms of anxiety in the amygdala have not been well characterized. Here we report that in freely-behaving mice, a group of neurons in the basolateral amygdala (BLA) fires tonically under anxiety conditions in both open-field and elevated plus-maze tests. The firing patterns of these neurons displayed a characteristic slow onset and progressively increased firing rates. Specifically, these firing patterns were correlated to a gradual development of anxiety-like behaviors in the open-field test. Moreover, these neurons could be activated by any impoverished environment similar to an open-field; and introduction of both comfortable and uncomfortable stimuli temporarily suppressed the activity of these BLA neurons. Importantly, the excitability of these BLA neurons correlated well with levels of anxiety. These results demonstrate that this type of BLA neuron is likely to represent anxiety and/or emotional values of anxiety elicited by anxiogenic environmental stressors.     

Interactive responses of a thalamic neuron to formalin induced lasting pain in behaving mice

Thalamocortical (TC) neurons are known to relay incoming sensory information to the cortex via firing in tonic or burst mode. However, it is still unclear how respective firing modes of a single thalamic relay neuron contribute to pain perception under consciousness. Some studies report that bursting could increase pain in hyperalgesic conditions while others suggest the contrary. However, since previous studies were done under either neuropathic pain conditions or often under anesthesia, the mechanism of thalamic pain modulation under awake conditions is not well understood. We therefore characterized the thalamic firing patterns of behaving mice in response to nociceptive pain induced by inflammation. Our results demonstrated that nociceptive pain responses were positively correlated with tonic firing and negatively correlated with burst firing of individual TC neurons. Furthermore, burst properties such as intra-burst-interval (IntraBI) also turned out to be reliably correlated with the changes of nociceptive pain responses. In addition, brain stimulation experiments revealed that only bursts with specific bursting patterns could significantly abolish behavioral nociceptive responses. The results indicate that specific patterns of bursting activity in thalamocortical relay neurons play a critical role in controlling long-lasting inflammatory pain in awake and behaving mice.     

Characterization,scaling, and partial representation of diffuse and discrete input junctions to CA3 hippocampus

This paper applies a general mathematical system for characterizing and scaling functional connectivity and information flow across the diffuse (EC) and discrete (DG) input junctions to the CA3 hippocampus. Both gross connectivity and coordinated multiunit informational firing patterns are quantitatively characterized in terms of 32 defining parameters interrelated by 17 equations, and then scaled down according to rules for uniformly proportional scaling and for partial representation. The diffuse EC-CA3 junction is shown to be uniformly scalable with realistic representation of both essential spatiotemporal cooperativity and coordinated firing patterns down to populations of a few hundred neurons. Scaling of the discrete DG-CA3 junction can be effected with a two-step process, which necessarily deviates from uniform proportionality but nonetheless produces a valuable and readily interpretable reduced model, also utilizing a few hundred neurons in the receiving population. Partial representation produces a reduced model of only a portion of the full network where each model neuron corresponds directly to a biological neuron. The mathematical analysis illustrated here shows that although omissions and distortions are inescapable in such an application, satisfactorily complete and accurate models the size of pattern modules are possible. Finally, the mathematical characterization of these junctions generates a theory which sees the DG as a definer of the fine structure of embedded traces in the hippocampus and entire coordinated patterns of sequences of 14-cell links in CA3 as triggered by the firing of sequences of individual neurons in DG.     

Phasic Firing in Vasopressin Cells: Understanding Its Functional Significance through Computational Models

Vasopressin neurons, responding to input generated by osmotic pressure, use an intrinsic mechanism to shift from slow irregular firing to a distinct phasic pattern, consisting of long bursts and silences lasting tens of seconds. With increased input, bursts lengthen, eventually shifting to continuous firing. The phasic activity remains asynchronous across the cells and is not reflected in the population output signal. Here we have used a computational vasopressin neuron model to investigate the functional significance of the phasic firing pattern. We generated a concise model of the synaptic input driven spike firing mechanism that gives a close quantitative match to vasopressin neuron spike activity recorded in vivo, tested against endogenous activity and experimental interventions. The integrate-and-fire based model provides a simple physiological explanation of the phasic firing mechanism involving an activity-dependent slow depolarising afterpotential (DAP) generated by a calcium-inactivated potassium leak current. This is modulated by the slower, opposing, action of activity-dependent dendritic dynorphin release, which inactivates the DAP, the opposing effects generating successive periods of bursting and silence. Model cells are not spontaneously active, but fire when perturbed by random perturbations mimicking synaptic input. We constructed one population of such phasic neurons, and another population of similar cells but which lacked the ability to fire phasically. We then studied how these two populations differed in the way that they encoded changes in afferent inputs. By comparison with the non-phasic population, the phasic population responds linearly to increases in tonic synaptic input. Non-phasic cells respond to transient elevations in synaptic input in a way that strongly depends on background activity levels, phasic cells in a way that is independent of background levels, and show a similar strong linearization of the response. These findings show large differences in information coding between the populations, and apparent functional advantages of asynchronous phasic firing.     

Cerebellar Nuclear Neurons Use Time and Rate Coding to Transmit Purkinje Neuron Pauses

Neurons of the cerebellar nuclei convey the final output of the cerebellum to their targets in various parts of the brain. Within the cerebellum their direct upstream connections originate from inhibitory Purkinje neurons. Purkinje neurons have a complex firing pattern of regular spikes interrupted by intermittent pauses of variable length. How can the cerebellar nucleus process this complex input pattern? In this modeling study, we investigate different forms of Purkinje neuron simple spike pause synchrony and its influence on candidate coding strategies in the cerebellar nuclei. That is, we investigate how different alignments of synchronous pauses in synthetic Purkinje neuron spike trains affect either time-locking or rate-changes in the downstream nuclei. We find that Purkinje neuron synchrony is mainly represented by changes in the firing rate of cerebellar nuclei neurons. Pause beginning synchronization produced a unique effect on nuclei neuron firing, while the effect of pause ending and pause overlapping synchronization could not be distinguished from each other. Pause beginning synchronization produced better time-locking of nuclear neurons for short length pauses. We also characterize the effect of pause length and spike jitter on the nuclear neuron firing. Additionally, we find that the rate of rebound responses in nuclear neurons after a synchronous pause is controlled by the firing rate of Purkinje neurons preceding it.     

Chaotic solutions in the quadratic integrate-and-fire neuron with adaptation

The quadratic integrate-and-fire (QIF) model with adaptation is commonly used as an elementary neuronal model that reproduces the main characteristics of real neurons. In this paper, we introduce a QIF neuron with a nonlinear adaptive current. This model reproduces the neuron-computational features of real neurons and is analytically tractable. It is shown that under a constant current input chaotic firing is possible. In contrast to previous study the neuron is not sinusoidally forced. We show that the spike-triggered adaptation is a key parameter to understand how chaos is generated.