Analysis and simulation of double-layer neural networks with mutually inhibiting interconnections

Double-layer neural networks with mutually inhibiting interconnections are analyzed using a continuous-variable model of the neuron. The first layer consists of excitatory neurons while the second layer consists of inhibitory neurons. Both feedforward and feedback interconnections exist between the two layers. An autonomous system of nonlinear differential equations is introduced to describe the network dynamics, and the stability conditions for some classes of equilibria are investigated in detail. Several simulation results are also presented. It is shown that even those networks which are formed with rather powerless synapses are capable of carrying out input pattern sharpening, temporary information storage, and periodic signal generation.     

蛙下丘听觉神经元对双耳强度差检测功能的建模和仿真

建立了蛙下丘听觉神经元对双耳刺激强度差检测功能的一个数学模型。按此模型所作的计算机仿真和相应实验结果比较的一致性支持了下列假设 :下丘中的EO神经元对同侧刺激不产生反应可能是由于接受了来自同侧的强烈抑制性输入 ,从而掩盖了它同时接受到的来自同侧耳的兴奋性输入。而来自同侧的抑制性输入 ,与来自对侧的兴奋性输入可能通过突触前抑制的相互作用 ,则导致了EE神经元的双耳抑制现象。     

Modelling Feedback Excitation,Pacemaker Properties and Sensory Switching of Electrically Coupled Brainstem Neurons Controlling Rhythmic Activity

What cellular and network properties allow reliable neuronal rhythm generation or firing that can be started and stopped by brief synaptic inputs? We investigate rhythmic activity in an electrically-coupled population of brainstem neurons driving swimming locomotion in young frog tadpoles, and how activity is switched on and off by brief sensory stimulation. We build a computational model of 30 electrically-coupled conditional pacemaker neurons on one side of the tadpole hindbrain and spinal cord. Based on experimental estimates for neuron properties, population sizes, synapse strengths and connections, we show that: long-lasting, mutual, glutamatergic excitation between the neurons allows the network to sustain rhythmic pacemaker firing at swimming frequencies following brief synaptic excitation; activity persists but rhythm breaks down without electrical coupling; NMDA voltage-dependency doubles the range of synaptic feedback strengths generating sustained rhythm. The network can be switched on and off at short latency by brief synaptic excitation and inhibition. We demonstrate that a population of generic Hodgkin-Huxley type neurons coupled by glutamatergic excitatory feedback can generate sustained asynchronous firing switched on and off synaptically. We conclude that networks of neurons with NMDAR mediated feedback excitation can generate self-sustained activity following brief synaptic excitation. The frequency of activity is limited by the kinetics of the neuron membrane channels and can be stopped by brief inhibitory input. Network activity can be rhythmic at lower frequencies if the neurons are electrically coupled. Our key finding is that excitatory synaptic feedback within a population of neurons can produce switchable, stable, sustained firing without synaptic inhibition.     

Lateral sharpening of cortical frequency tuning by approximately balanced inhibition

Cortical inhibition plays an important role in shaping neuronal processing. The underlying synaptic mechanisms remain controversial. Here, in vivo whole-cell recordings from neurons in the rat primary auditory cortex revealed that the frequency tuning curve of inhibitory input was broader than that of excitatory input. This results in relatively stronger inhibition in frequency domains flanking the preferred frequencies of the cell and a significant sharpening of the frequency tuning of membrane responses. The less selective inhibition can be attributed to a broader bandwidth and lower threshold of spike tonal receptive field of fast-spike inhibitory neurons than nearby excitatory neurons, although both types of neurons receive similar ranges of excitatory input and are organized into the same tonotopic map. Thus, the balance between excitation and inhibition is only approximate, and intracortical inhibition with high sensitivity and low selectivity can laterally sharpen the frequency tuning of neurons, ensuring their highly selective representation.     

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     

Recurrent networks of submucous neurons controlling intestinal secretion: a modeling study

Secretomotor neurons, immunoreactive for vasoactive intestinal peptide (VIP), are important in controlling chloride secretion in the small intestine. These neurons form functional synapses with other submucosal VIP neurons and transmit via slow excitatory postsynaptic potentials (EPSPs). Thus they form a recurrent network with positive feedback. Intrinsic sensory neurons within the submucosa are also likely to form recurrent networks with positive feedback, provide substantial output to VIP neurons, and receive input from VIP neurons. If positive feedback within recurrent networks is sufficiently large, then neurons in the network respond to even small stimuli by firing at their maximum possible rate, even after the stimulus is removed. However, it is not clear whether such a mechanism operates within the recurrent networks of submucous neurons. We investigated this question by performing computer simulations of realistic models of VIP and intrinsic sensory neuron networks. In the expected range of electrophysiological properties, we found that activity in the VIP neuron network decayed slowly after cessation of a stimulus, indicating that positive feedback is not strong enough to support the uncontrolled firing state. The addition of intrinsic sensory neurons produced a low stable firing rate consistent with the common finding that basal secretory activity is, in part, neurogenic. Changing electrophysiological properties enables these recurrent networks to support the uncontrolled firing state, which may have implications with hypersecretion in the presence of enterotoxins such as cholera-toxin.     

Emergent Oscillations in a Realistic Network: The Role of Inhibition and the Effect of the Spatiotemporal Distribution of the Input

We have simulated a network of 10,000 two-compartment cells, spatially distributed on a two-dimensional sheet; 15% of the cells were inhibitory. The input to the network was spatially delimited. Global oscillations frequently were achieved with a simple set of connectivity rules. The inhibitory neurons paced the network, whereas the excitatory neurons amplified the input, permitting oscillations at low-input intensities. Inhibitory neurons were active over a greater area than excitatory ones, forming a ring of inhibition. The oscillation frequency was modulated to some extent by the input intensity, as has been shown experimentally in the striate cortex, but predominantly by the properties of the inhibitory neurons and their connections: the membrane and synaptic time constants and the distribution of delays.In networks that showed oscillations and in those that did not, widely distributed inputs could lead to the specific recruitment of the inhibitory neurons and to near zero activity of the excitatory cells. Hence the spatial distribution of excitatory inputs could provide a means of selectively exciting or inhibiting a target network. Finally, neither the presence of oscillations nor the global spike activity provided any reliable indication of the level of excitatory output from the network.     

Emergent oscillations in a realistic network: the role of inhibition and the effect of the spatiotemporal distribution of the input.

We have simulated a network of 10,000 two-compartment cells, spatially distributed on a two-dimensional sheet; 15% of the cells were inhibitory. The input to the network was spatially delimited. Global oscillations frequently were achieved with a simple set of connectivity rules. The inhibitory neurons paced the network, whereas the excitatory neurons amplified the input, permitting oscillations at low-input intensities. Inhibitory neurons were active over a greater area than excitatory ones, forming a ring of inhibition. The oscillation frequency was modulated to some extent by the input intensity, as has been shown experimentally in the striate cortex, but predominantly by the properties of the inhibitory neurons and their connections: the membrane and synaptic time constants and the distribution of delays. In networks that showed oscillations and in those that did not, widely distributed inputs could lead to the specific recruitment of the inhibitory neurons and to near zero activity of the excitatory cells. Hence the spatial distribution of excitatory inputs could provide a means of selectively exciting or inhibiting a target network. Finally, neither the presence of oscillations nor the global spike activity provided any reliable indication of the level of excitatory output from the network.     

Redundancy reducing processes in single neurons

Interaction mechanisms between excitatory and inhibitory impulse sequences operating on neurons play an important role for the processing of information by the nervous system. For instance, the convergence of excitatory and inhibitory influences on retinal ganglion cells to form their receptive fields has been taken as an example for the process of neuronal sharpening by lateral inhibition. In order to analyze quantitatively the functional behavior of such a system, Shannon's entropy method for multiple access channels has been applied to biological two-inputs-one-output systems using the theoretical model developed by Tsukada et al. (1979). Here we give an extension of this procedure from the point of view to reduce redundancy of information in the input signal space of single neurons and attempt to obtain a new interpretation for the information processing of the system. The concept for the redundancy reducing mechanism in single neurons is examined and discussed for the following two processes. The first process is concerned with a signal space formed by superposing two random sequences on the input of a neuron. In this process, we introduce a coding technique to encode the inhibitory sequence by using the timing of the excitatory sequence, which is closely related to an encoding technique of multiple access channels with a correlated source (Marko, 1966, 1970, 1973; Slepian and Wolf, 1973) and which is an invariant transformation in the input signal space without changing the information contents of the input. The second process is concerned with a procedure of reducing redundant signals in the signal space mentioned before. In this connection, it is an important point to see how single neurons reduce the dimensionality of the signal space via transformation with a minimum loss of effective information. For this purpose we introduce the criterion that average transmission of information from signal space to the output does not change when redundant signals are added. This assumption is based on the fact that two signals are equivalent if and only if they have identical input-output behavior. The mechanism is examined and estimated by using a computer-simulated model. As the result of such a simulation we can estimate the minimal segmentation in the signal space which is necessary and sufficient for temporal pattern sensitivity in neurons.     

Performance of a model for a local neuron population

A model of a local neuron population is considered that contains three subsets of neurons, one main excitatory subset, an auxiliary excitatory subset and an inhibitory subset. They are connected in one positive and one negative feedback loop, each containing linear dynamic and nonlinear static elements. The network also allows for a positive linear feedback loop. The behaviour of this network is studied for sinusoidal and white noise inputs. First steady state conditions are investigated and with this as starting point the linearized network is defined and conditions for stability is discovered. With white noise as input the stable network produces rhythmic activity whose spectral properties are investigated for various input levels. With a mean input of a certain level the network becomes unstable and the characteristics of these limit cycles are investigated in terms of occurence and amplitude. An electronic model has been built to study more closely the waveforms under both stable and unstable conditions. It is shown to produce signals that resemble EEG background activity and certain types of paroxysmal activity, in particular spikes.     

锐化蝙蝠听皮层神经元频率调谐的柱特征

用双声刺激和多管电极方法在 6只大棕蝠 (bigbrownbat,Eptesicusfuscus)的 98个神经元上研究了锐化 (sharpening)蝙蝠听皮层 (primaryauditorycortex ,AC)神经元频率调谐的柱特征。结果发现 ,电极直插在 1个电极通道内连续记录到多个神经元时 ,它们锐化频率调谐的抑制性调谐曲线或抑制区基本相似。电极与AC表面呈 45°斜向推入使其跨越多个功能柱时 ,可观察到锐化频率调谐的抑制区构成也随电极进入不同的功能柱而发生相应的改变。两种不同的电极插入方式均证明锐化AC神经元频率调谐的神经抑制呈柱状组构。这些神经元组合起来排列在同一听觉功能柱内 ,构成AC频率分析的基本功能组构单位“微频率处理器”。实验中还观察到多峰频率调谐曲线神经元 ,它们在声通讯和声定位中不同波谱区域的时间匹配中起作用。此外 ,也有理由认为多峰调谐神经元亦被用于作为复杂波谱信息的“高级调谐预处理器” ,从而极大地提高了神经元对频率分析的能力。为研究锐化频率调谐的神经抑制机制 ,用多管电极电泳γ -氨基丁酸 (γ aminobutyricacid ,GA BA)能a受体拮抗剂荷包牡丹碱 (bicuculline ,Bic)至所记录的神经元 ,发现能大部分或几乎全部取消抑制区 ,从而表明在正常情况下GABA能抑制参与构成锐化AC神经元频率调谐的抑制区 ,     

Recurrent circuitry dynamically shapes the activation of piriform cortex

In the piriform cortex, individual odorants activate a unique ensemble of neurons that are distributed without discernable spatial order. Piriform neurons receive convergent excitatory inputs from random collections of olfactory bulb glomeruli. Pyramidal cells also make extensive recurrent connections with other excitatory and inhibitory neurons. We introduced channelrhodopsin into the piriform cortex to characterize these intrinsic circuits and to examine their contribution to activity driven by afferent bulbar inputs. We demonstrated that individual pyramidal cells are sparsely interconnected by thousands of excitatory synaptic connections that extend, largely undiminished, across the piriform cortex, forming a large excitatory network that can dominate the bulbar input. Pyramidal cells also activate inhibitory interneurons that mediate strong, local feedback inhibition that scales with excitation. This recurrent network can enhance or suppress bulbar input, depending on whether the input arrives before or after the cortex is activated. This circuitry may shape the ensembles of piriform cells that encode odorant identity.     

The responses of auditory ventral-cord neurons ofLocusta migratoria to vibration stimuli

Summary Most of the auditory neurons in the ventral nerve cord ofLocusta migratoria carry information not only from the tympanal organs but also from the subgenual organs (vibration sensors). Six of the eight neuron types studied electrophysiologically respond to at least these two modalities. Artificial sounds (white noise and pure tones varying in frequency and intensity) and sinusoidal vibration (200 Hz with an acceleration of 15.8 cm/s₂ or 2000 Hz and 87 cm/s₂) were used as stimuli.Complex excitatory and/or inhibitory interactions of the signals from both tympanal organs form the discharge patterns of auditory ventral-cord neurons in response to stimulation with air-borne sound. Normally the input of the ipsilateral sense organ dominates. The response patterns of these same neurons elicited by vibration stimuli are formed differently, as follows: (1) the sensory inputs of all subgenual organs are integrated in the responses of the ventral-cord neurons; in a single neuron they have either excitatory or inhibitory effects, but not both. (2) The more legs vibrated, the larger is the response. (3) The subgenual organs in the middle legs are most effective, those in the hind legs least so. (4) Ipsilateral vibration has more effect than contralateral.The six auditory neurons react to vibration combined with air-borne sound in different ways. The B neuron is the only one inhibited by vibration stimuli. The G neuron has been studied more intensively; because its anatomical arrangement and the location of the endings of the subgenual receptor fibers are known, it could be inferred from effects of transection of the connectives that interneurons are interposed between receptor cells and the G neuron.Part of the program Sonderforschungsbereich 114 (Bionach) Bochum, under the auspices of the Deutsche Forschungsgemeinschaft, with the support of the Slovenic Research Society (RSS)     

A Neural Network Model of Chemotaxis Predicts Functions of Synaptic Connections in the Nematode Caenorhabditis elegans

The anatomical connectivity of the nervous system of the nematode Caenorhabditis elegans has been almost completely described, but determination of the neurophysiological basis of behavior in this system is just beginning. Here we used an optimization algorithm to search for patterns of connectivity sufficient to compute the sensorimotor transformation underlying C. elegans chemotaxis, a simple form of spatial orientation behavior in which turning probability is modulated by the rate of change of chemical concentration. Optimization produced differentiator networks capable of simulating chemotaxis. A surprising feature of these networks was inhibitory feedback connections on all neurons. Further analysis showed that feedback regulates the latency between sensory input and behavior. Common patterns of connectivity between the model and biological networks suggest new functions for previously identified connections in the C. elegans nervous system.     

The locust olfactory system as a case study for modeling dynamics of neurobiological networks: from discrete time neurons to continuous time neurons

Both chaotic and periodic activities are observed in networks of the central nervous systems. We choose the locust olfactory system as a good case study to analyze the relationships between networks' structure and the types of dynamics involved in coding mechanisms. In our modeling approach, we first build a fully connected recurrent network of synchronously updated McCulloch and Pitts neurons (MC-P type). In order to measure the use of the temporal dimension in the complex spatio-temporal patterns produced by the networks, we have defined an index the Normalized Euclidian Distance NED. We find that for appropriate parameters of input and connectivity, when adding some strong connections to the initial random synaptic matrices, it was easy to get the emergence of both robust oscillations and distributed synchrony in the spatiotemporal patterns. Then, in order to validate the MC-P model as a tool for analysis for network properties, we examine the dynamic behavior of networks of continuous time model neuron (Izhikevitch Integrate and Fire model -IFI-), implementing the same network characteristics. In both models, similarly to biological PN, the activity of excitatory neurons are phase-locked to different cycles of oscillations which remind the ones of the local field potential (LFP), and nevertheless exhibit dynamic behavior complex enough to be the basis of spatio-temporal codes.     

Membrane properties and the balance between excitation and inhibition control gamma-frequency oscillations arising from feedback inhibition

Computational studies as well as in vivo and in vitro results have shown that many cortical neurons fire in a highly irregular manner and at low average firing rates. These patterns seem to persist even when highly rhythmic signals are recorded by local field potential electrodes or other methods that quantify the summed behavior of a local population. Models of the 30-80 Hz gamma rhythm in which network oscillations arise through 'stochastic synchrony' capture the variability observed in the spike output of single cells while preserving network-level organization. We extend upon these results by constructing model networks constrained by experimental measurements and using them to probe the effect of biophysical parameters on network-level activity. We find in simulations that gamma-frequency oscillations are enabled by a high level of incoherent synaptic conductance input, similar to the barrage of noisy synaptic input that cortical neurons have been shown to receive in vivo. This incoherent synaptic input increases the emergent network frequency by shortening the time scale of the membrane in excitatory neurons and by reducing the temporal separation between excitation and inhibition due to decreased spike latency in inhibitory neurons. These mechanisms are demonstrated in simulations and in vitro current-clamp and dynamic-clamp experiments. Simulation results further indicate that the membrane potential noise amplitude has a large impact on network frequency and that the balance between excitatory and inhibitory currents controls network stability and sensitivity to external inputs.     

A neural network model for trace conditioning

We studied the dynamics of a neural network that has both recurrent excitatory and random inhibitory connections. Neurons started to become active when a relatively weak transient excitatory signal was presented and the activity was sustained due to the recurrent excitatory connections. The sustained activity stopped when a strong transient signal was presented or when neurons were disinhibited. The random inhibitory connections modulated the activity patterns of neurons so that the patterns evolved without recurrence with time. Hence, a time passage between the onsets of the two transient signals was represented by the sequence of activity patterns. We then applied this model to represent the trace eye blink conditioning, which is mediated by the hippocampus. We assumed this model as CA3 of the hippocampus and considered an output neuron corresponding to a neuron in CA1. The activity pattern of the output neuron was similar to that of CA1 neurons during trace eye blink conditioning, which was experimentally observed.     

Avalanches in a Stochastic Model of Spiking Neurons

Neuronal avalanches are a form of spontaneous activity widely observed in cortical slices and other types of nervous tissue, both in vivo and in vitro. They are characterized by irregular, isolated population bursts when many neurons fire together, where the number of spikes per burst obeys a power law distribution. We simulate, using the Gillespie algorithm, a model of neuronal avalanches based on stochastic single neurons. The network consists of excitatory and inhibitory neurons, first with all-to-all connectivity and later with random sparse connectivity. Analyzing our model using the system size expansion, we show that the model obeys the standard Wilson-Cowan equations for large network sizes ( neurons). When excitation and inhibition are closely balanced, networks of thousands of neurons exhibit irregular synchronous activity, including the characteristic power law distribution of avalanche size. We show that these avalanches are due to the balanced network having weakly stable functionally feedforward dynamics, which amplifies some small fluctuations into the large population bursts. Balanced networks are thought to underlie a variety of observed network behaviours and have useful computational properties, such as responding quickly to changes in input. Thus, the appearance of avalanches in such functionally feedforward networks indicates that avalanches may be a simple consequence of a widely present network structure, when neuron dynamics are noisy. An important implication is that a network need not be “critical” for the production of avalanches, so experimentally observed power laws in burst size may be a signature of noisy functionally feedforward structure rather than of, for example, self-organized criticality.     

Efficient Transmission of Subthreshold Signals in Complex Networks of Spiking Neurons

We investigate the efficient transmission and processing of weak, subthreshold signals in a realistic neural medium in the presence of different levels of the underlying noise. Assuming Hebbian weights for maximal synaptic conductances—that naturally balances the network with excitatory and inhibitory synapses—and considering short-term synaptic plasticity affecting such conductances, we found different dynamic phases in the system. This includes a memory phase where population of neurons remain synchronized, an oscillatory phase where transitions between different synchronized populations of neurons appears and an asynchronous or noisy phase. When a weak stimulus input is applied to each neuron, increasing the level of noise in the medium we found an efficient transmission of such stimuli around the transition and critical points separating different phases for well-defined different levels of stochasticity in the system. We proved that this intriguing phenomenon is quite robust, as it occurs in different situations including several types of synaptic plasticity, different type and number of stored patterns and diverse network topologies, namely, diluted networks and complex topologies such as scale-free and small-world networks. We conclude that the robustness of the phenomenon in different realistic scenarios, including spiking neurons, short-term synaptic plasticity and complex networks topologies, make very likely that it could also occur in actual neural systems as recent psycho-physical experiments suggest.