Identifying and Tracking Simulated Synaptic Inputs from Neuronal Firing: Insights from In Vitro Experiments

Accurately describing synaptic interactions between neurons and how interactions change over time are key challenges for systems neuroscience. Although intracellular electrophysiology is a powerful tool for studying synaptic integration and plasticity, it is limited by the small number of neurons that can be recorded simultaneously in vitro and by the technical difficulty of intracellular recording in vivo. One way around these difficulties may be to use large-scale extracellular recording of spike trains and apply statistical methods to model and infer functional connections between neurons. These techniques have the potential to reveal large-scale connectivity structure based on the spike timing alone. However, the interpretation of functional connectivity is often approximate, since only a small fraction of presynaptic inputs are typically observed. Here we use in vitro current injection in layer 2/3 pyramidal neurons to validate methods for inferring functional connectivity in a setting where input to the neuron is controlled. In experiments with partially-defined input, we inject a single simulated input with known amplitude on a background of fluctuating noise. In a fully-defined input paradigm, we then control the synaptic weights and timing of many simulated presynaptic neurons. By analyzing the firing of neurons in response to these artificial inputs, we ask 1) How does functional connectivity inferred from spikes relate to simulated synaptic input? and 2) What are the limitations of connectivity inference? We find that individual current-based synaptic inputs are detectable over a broad range of amplitudes and conditions. Detectability depends on input amplitude and output firing rate, and excitatory inputs are detected more readily than inhibitory. Moreover, as we model increasing numbers of presynaptic inputs, we are able to estimate connection strengths more accurately and detect the presence of connections more quickly. These results illustrate the possibilities and outline the limits of inferring synaptic input from spikes.     

Calcium responses of circadian pacemaker neurons of the cockroach Rhyparobia maderae to acetylcholine and histamine

The accessory medulla (aMe) is the pacemaker that controls circadian activity rhythms in the cockroach Rhyparobia maderae. Not much is known about the classical neurotransmitters of input pathways to the cockroach circadian system. The circadian pacemaker center receives photic input from the compound eye, via unknown excitatory and GABAergic inhibitory entrainment pathways. In addition, neuropeptidergic inputs couple both pacemaker centers. A histamine-immunoreactive centrifugal neuron connects the ventral aMe with projection areas in the lateral protocerebrum and may provide non-photic inputs. To identify neurotransmitters of input pathways to the circadian clock with Fura-2-dependent Ca²⁺ imaging, primary cell cultures of the adult aMe were stimulated with acetylcholine (ACh), as the most prominent excitatory, and histamine, as common inhibitory neurotransmitter. In most of aMe neurons, ACh application caused dose-dependent increases in intracellular Ca²⁺ levels via ionotropic nicotinic ACh receptors. These ACh-dependent rises in Ca²⁺ were mediated by mibefradil-sensitive voltage-activated Ca²⁺ channels. In contrast, histamine application decreased intracellular Ca²⁺ levels in only a subpopulation of aMe cells via H2-type histamine receptor chloride channels. Thus, our data suggest that ACh is part of the light entrainment pathway while histamine is involved in a non-photic input pathway to the ventral circadian clock of the Madeira cockroach.     

Impact of correlated inputs to neurons: modeling observations from in vivo intracellular recordings

In vivo recordings in rat somatosensory cortex suggest that excitatory and inhibitory inputs are often correlated during spontaneous and sensory-evoked activity. Using a computational approach, we study how the interplay of input correlations and timing observed in experiments controls the spiking probability of single neurons. Several correlation-based mechanisms are identified, which can effectively switch a neuron on and off. In addition, we investigate the transfer of input correlation to output correlation in pairs of neurons, at the spike train and the membrane potential levels, by considering spike-driving and non-spike-driving inputs separately. In particular, we propose a plausible explanation for the in vivo finding that membrane potentials in neighboring neurons are correlated, but the spike-triggered averages of membrane potentials preceding a spike are not: Neighboring neurons possibly receive an ongoing bombardment of correlated subthreshold background inputs, and occasionally uncorrelated spike-driving inputs.     

Glutamate-Bound NMDARs Arising from In Vivo-like Network Activity Extend Spatio-temporal Integration in a L5 Cortical Pyramidal Cell Model

In vivo, cortical pyramidal cells are bombarded by asynchronous synaptic input arising from ongoing network activity. However, little is known about how such ‘background’ synaptic input interacts with nonlinear dendritic mechanisms. We have modified an existing model of a layer 5 (L5) pyramidal cell to explore how dendritic integration in the apical dendritic tuft could be altered by the levels of network activity observed in vivo. Here we show that asynchronous background excitatory input increases neuronal gain and extends both temporal and spatial integration of stimulus-evoked synaptic input onto the dendritic tuft. Addition of fast and slow inhibitory synaptic conductances, with properties similar to those from dendritic targeting interneurons, that provided a ‘balanced’ background configuration, partially counteracted these effects, suggesting that inhibition can tune spatio-temporal integration in the tuft. Excitatory background input lowered the threshold for NMDA receptor-mediated dendritic spikes, extended their duration and increased the probability of additional regenerative events occurring in neighbouring branches. These effects were also observed in a passive model where all the non-synaptic voltage-gated conductances were removed. Our results show that glutamate-bound NMDA receptors arising from ongoing network activity can provide a powerful spatially distributed nonlinear dendritic conductance. This may enable L5 pyramidal cells to change their integrative properties as a function of local network activity, potentially allowing both clustered and spatially distributed synaptic inputs to be integrated over extended timescales.     

Simultaneous Recording of Input and Output of Lateral Geniculate Neurones

TO understand the way in which the cat dorsal lateral geniculate nucleus (LGN) processes visual information it would be useful to know the number and type of retinal inputs to individual LGN neurones. Using electrical stimulation of the optic nerve Bishop et al.¹concluded that an impulse in a single optic nerve fibre is sufficient to excite a single LGN neurone. From the appearance of excitatory postsynaptic potentials (EPSPs) recorded essentially intracellularly, Creutzfeldt suggested that LGN neurones are driven by perhaps one² or a few³ retinal ganglion cells. Hubel and Wiesel⁴ proposed models of convergence of several retinal inputs on single LGN neurones based on analyses of receptive fields. Guillery⁵ produced anatomical evidence that some types of LGN neurones receive inputs from several different retinal fibres. Now we report direct observations which were made by recording simultaneously from single LGN neurones and from individual retinal ganglion cells which provided excitatory input to them. We shall not consider inhibitory influences, which are currently under study.     

On some properties of stochastic information processes in neurons and neuron populations

The information in the nervous spike trains and its processing by neural units are discussed. In these problems, our attention is focused on the stochastic properties of neurons and neuron populations. There are three subjects in this paper, which are the spontaneous type neuron, the forced type neuron and the reciprocal inhibitory pairs.

1. The spontaneous type neuron produces spikes without excitatory inputs. The mathematical model has the following assumptions. The neuron potential (NP) has the fluctuation and obeys the Ornstein-Uhlenbeck process, because the N P is not so perfectly random as that of the Wiener process but has an attraction to the rest value. The threshold varies exponentially and the NP has the constant lower limit. When the NP reaches the threshold, the neuron fires and the NP is reset to a certain position. After a firing, an absolute refractory period exists. In discussing the stochastic properties of neurons, the transition probability density function and the first passage time density function are the important quantities, which are governed by the Kolmogorov's equations. Although they can be set up easily, we can rarely obtain the analytical solutions in time domain. Moreover, they cover only simple properties. Hence the numerical analysis is performed and a good deal of fair results are obtained and discussed.
2. The forced type neuron has input pulse trains which are assumed to be based on the Poisson process. Other assumptions and methods are almost the same as above except the diffusion approximation of the stochastic process. In this case, we encounter the inhomogeneous process due to the pulse-frequency-modulation, whose first passage time density reveals the multimodal distribution. The numerical analysis is also tried, and the output spike interval density is further discussed in the case of the periodic modulation.
3. Two types of reciprocal inhibitory pairs are discussed. The first type has two excitatory driving inputs which are mutually independent. The second type has one common excitatory input but it advances in two ways, one of which has a time lag. The neuron dynamics is the same as that of the forced type neuron and each neuron has an identical structure. The inputs are assumed to be based on the Poisson process and the inhibition occurs when the companion neuron fires. In this case, the equations of the probability density functions are not obtained. Hence the computer simulation is tried and it is observed that the stochastic rhythm emerges in spite of the temporally homogeneous inputs. Furthermore, the case of inhomogeneous inputs is discussed.

     

The principal neurons of the medial nucleus of the trapezoid body and NG2+ glial cells receive coordinated excitatory synaptic input

Glial cell processes are part of the synaptic structure and sense spillover of transmitter, while some glial cells can even receive direct synaptic input. Here, we report that a defined type of glial cell in the medial nucleus of the trapezoid body (MNTB) receives excitatory glutamatergic synaptic input from the calyx of Held (CoH). This giant glutamatergic terminal forms an axosomatic synapse with a single principal neuron located in the MNTB. The NG2 glia, as postsynaptic principal neurons, establish synapse-like structures with the CoH terminal. In contrast to the principal neurons, which are known to receive excitatory as well as inhibitory inputs, the NG2 glia receive mostly, if not exclusively, α-amino-3-hydroxy-5-methyl-isoxazole-4-propionic acid receptor–mediated evoked and spontaneous synaptic input. Simultaneous recordings from neurons and NG2 glia indicate that they partially receive synchronized spontaneous input. This shows that an NG2⁺ glial cell and a postsynaptic neuron share presynaptic terminals.     

Burst control: Synaptic conditions for burst generation in cortical layer 5 pyramidal neurons

The output of neocortical layer 5 pyramidal cells (L5PCs) is expressed by a train of single spikes with intermittent bursts of multiple spikes at high frequencies. The bursts are the result of nonlinear dendritic properties, including Na⁺, Ca²⁺, and NMDA spikes, that interact with the ~10,000 synapses impinging on the neuron’s dendrites. Output spike bursts are thought to implement key dendritic computations, such as coincidence detection of bottom-up inputs (arriving mostly at the basal tree) and top-down inputs (arriving mostly at the apical tree). In this study we used a detailed nonlinear model of L5PC receiving excitatory and inhibitory synaptic inputs to explore the conditions for generating bursts and for modulating their properties. We established the excitatory input conditions on the basal versus the apical tree that favor burst and show that there are two distinct types of bursts. Bursts consisting of 3 or more spikes firing at < 200 Hz, which are generated by stronger excitatory input to the basal versus the apical tree, and bursts of ~2-spikes at ~250 Hz, generated by prominent apical tuft excitation. Localized and well-timed dendritic inhibition on the apical tree differentially modulates Na⁺, Ca²⁺, and NMDA spikes and, consequently, finely controls the burst output. Finally, we explored the implications of different burst classes and respective dendritic inhibition for regulating synaptic plasticity.     

Presynaptic cGMP sets synaptic strength in the striatum and is important for motor learning

The striatum is a subcortical brain region responsible for the initiation and termination of voluntary movements. Striatal spiny projection neurons receive major excitatory synaptic input from neocortex and thalamus, and cyclic nucleotides have long been known to play important roles in striatal function. Yet, the precise mechanism of action is unclear. Here, we combine optogenetic stimulation, 2‐photon imaging, and genetically encoded scavengers to dissect the regulation of striatal synapses in mice. Our data show that excitatory striatal inputs are tonically depressed by phosphodiesterases (PDEs), in particular PDE1. Blocking PDE activity boosts presynaptic calcium entry and glutamate release, leading to strongly increased synaptic transmission. Although PDE1 degrades both cAMP and cGMP, we uncover that the concentration of cGMP, not cAMP, controls the gain of striatal inputs. Disturbing this gain control mechanism in vivo impairs motor skill learning in mice. The tight dependence of striatal excitatory synapses on PDE1 and cGMP offers a new perspective on the molecular mechanisms regulating striatal activity.     

Inferring synaptic inputs given a noisy voltage trace via sequential Monte Carlo methods

We discuss methods for optimally inferring the synaptic inputs to an electrotonically compact neuron, given intracellular voltage-clamp or current-clamp recordings from the postsynaptic cell. These methods are based on sequential Monte Carlo techniques ("particle filtering"). We demonstrate, on model data, that these methods can recover the time course of excitatory and inhibitory synaptic inputs accurately on a single trial. Depending on the observation noise level, no averaging over multiple trials may be required. However, excitatory inputs are consistently inferred more accurately than inhibitory inputs at physiological resting potentials, due to the stronger driving force associated with excitatory conductances. Once these synaptic input time courses are recovered, it becomes possible to fit (via tractable convex optimization techniques) models describing the relationship between the sensory stimulus and the observed synaptic input. We develop both parametric and nonparametric expectation-maximization (EM) algorithms that consist of alternating iterations between these synaptic recovery and model estimation steps. We employ a fast, robust convex optimization-based method to effectively initialize the filter; these fast methods may be of independent interest. The proposed methods could be applied to better understand the balance between excitation and inhibition in sensory processing in vivo.     

Emergence and fragmentation of the alpha-band driven by neuronal network dynamics

Rhythmic neuronal network activity underlies brain oscillations. To investigate how connected neuronal networks contribute to the emergence of the α-band and to the regulation of Up and Down states, we study a model based on synaptic short-term depression-facilitation with afterhyperpolarization (AHP). We found that the α-band is generated by the network behavior near the attractor of the Up-state. Coupling inhibitory and excitatory networks by reciprocal connections leads to the emergence of a stable α-band during the Up states, as reflected in the spectrogram. To better characterize the emergence and stability of thalamocortical oscillations containing α and δ rhythms during anesthesia, we model the interaction of two excitatory networks with one inhibitory network, showing that this minimal topology underlies the generation of a persistent α-band in the neuronal voltage characterized by dominant Up over Down states. Finally, we show that the emergence of the α-band appears when external inputs are suppressed, while fragmentation occurs at small synaptic noise or with increasing inhibitory inputs. To conclude, α-oscillations could result from the synaptic dynamics of interacting excitatory neuronal networks with and without AHP, a principle that could apply to other rhythms.     

Balanced Excitatory and Inhibitory Synaptic Currents Promote Efficient Coding and Metabolic Efficiency

A balance between excitatory and inhibitory synaptic currents is thought to be important for several aspects of information processing in cortical neurons in vivo, including gain control, bandwidth and receptive field structure. These factors will affect the firing rate of cortical neurons and their reliability, with consequences for their information coding and energy consumption. Yet how balanced synaptic currents contribute to the coding efficiency and energy efficiency of cortical neurons remains unclear. We used single compartment computational models with stochastic voltage-gated ion channels to determine whether synaptic regimes that produce balanced excitatory and inhibitory currents have specific advantages over other input regimes. Specifically, we compared models with only excitatory synaptic inputs to those with equal excitatory and inhibitory conductances, and stronger inhibitory than excitatory conductances (i.e. approximately balanced synaptic currents). Using these models, we show that balanced synaptic currents evoke fewer spikes per second than excitatory inputs alone or equal excitatory and inhibitory conductances. However, spikes evoked by balanced synaptic inputs are more informative (bits/spike), so that spike trains evoked by all three regimes have similar information rates (bits/s). Consequently, because spikes dominate the energy consumption of our computational models, approximately balanced synaptic currents are also more energy efficient than other synaptic regimes. Thus, by producing fewer, more informative spikes approximately balanced synaptic currents in cortical neurons can promote both coding efficiency and energy efficiency.     

Combined Hebbian development of geniculocortical and lateral connectivity in a model of primary visual cortex

We present a network model of visual map development in layer 4 of primary visual cortex. Our model comprises excitatory and inhibitory spiking neurons. The input to the network consists of correlated spike trains to mimick the activity of neurons in the lateral geniculate nucleus (LGN). An activity-driven Hebbian learning mechanism governs the development of both the network's lateral connectivity and feedforward projections from LGN to cortex. Plasticity of inhibitory synapses has been included into the model so as to control overall cortical activity. Even without feedforward input, Hebbian modification of the excitatory lateral connections can lead to the development of an intracortical orientation map. We have found that such an intracortical map can guide the development of feedforward connections from LGN to cortical simple cells so that the structure of the final feedforward orientation map is predetermined by the intracortical map. In a scenario in which left- and right-eye geniculocortical inputs develop sequentially one after the other, the resulting maps are therefore very similar, provided the intracortical connectivity remains unaltered. This may explain the outcome of so-called reverse lid-suture experiments, where animals are reared so that both eyes never receive input at the same time, but the orientation maps measured separately for the two eyes are nevertheless nearly identical. Received: 20 December 1999 / Accepted in revised form: 9 June 2000     

Modelling the spatial and temporal constrains of the GABAergic influence on neuronal excitability

GABA (γ-amino butyric acid) is an inhibitory neurotransmitter in the adult brain that can mediate depolarizing responses during development or after neuropathological insults. Under which conditions GABAergic membrane depolarizations are sufficient to impose excitatory effects is hard to predict, as shunting inhibition and GABAergic effects on spatiotemporal filtering of excitatory inputs must be considered. To evaluate at which reversal potential a net excitatory effect was imposed by GABA (E_GABA^Thr), we performed a detailed in-silico study using simple neuronal topologies and distinct spatiotemporal relations between GABAergic and glutamatergic inputs.These simulations revealed for GABAergic synapses located at the soma an E_GABA^Thr close to action potential threshold (E_AP^Thr), while with increasing dendritic distance E_GABA^Thr shifted to positive values. The impact of GABA on AMPA-mediated inputs revealed a complex temporal and spatial dependency. E_GABA^Thr depends on the temporal relation between GABA and AMPA inputs, with a striking negative shift in E_GABA^Thr for AMPA inputs appearing after the GABA input. The spatial dependency between GABA and AMPA inputs revealed a complex profile, with E_GABA^Thr being shifted to values negative to E_AP^Thr for AMPA synapses located proximally to the GABA input, while for distally located AMPA synapses the dendritic distance had only a minor effect on E_GABA^Thr. For tonic GABAergic conductances E_GABA^Thr was negative to E_AP^Thr over a wide range of g_GABA^tonic values. In summary, these results demonstrate that for several physiologically relevant situations E_GABA^Thr is negative to E_AP^Thr, suggesting that depolarizing GABAergic responses can mediate excitatory effects even if E_GABA did not reach E_AP^Thr.     

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。     

Bilinearity in Spatiotemporal Integration of Synaptic Inputs

Neurons process information via integration of synaptic inputs from dendrites. Many experimental results demonstrate dendritic integration could be highly nonlinear, yet few theoretical analyses have been performed to obtain a precise quantitative characterization analytically. Based on asymptotic analysis of a two-compartment passive cable model, given a pair of time-dependent synaptic conductance inputs, we derive a bilinear spatiotemporal dendritic integration rule. The summed somatic potential can be well approximated by the linear summation of the two postsynaptic potentials elicited separately, plus a third additional bilinear term proportional to their product with a proportionality coefficient . The rule is valid for a pair of synaptic inputs of all types, including excitation-inhibition, excitation-excitation, and inhibition-inhibition. In addition, the rule is valid during the whole dendritic integration process for a pair of synaptic inputs with arbitrary input time differences and input locations. The coefficient is demonstrated to be nearly independent of the input strengths but is dependent on input times and input locations. This rule is then verified through simulation of a realistic pyramidal neuron model and in electrophysiological experiments of rat hippocampal CA1 neurons. The rule is further generalized to describe the spatiotemporal dendritic integration of multiple excitatory and inhibitory synaptic inputs. The integration of multiple inputs can be decomposed into the sum of all possible pairwise integration, where each paired integration obeys the bilinear rule. This decomposition leads to a graph representation of dendritic integration, which can be viewed as functionally sparse.     

Harmonic analysis of Boolean networks: determinative power and perturbations

Consider a large Boolean network with a feed forward structure. Given a probability distribution on the inputs, can one find, possibly small, collections of input nodes that determine the states of most other nodes in the network? To answer this question, a notion that quantifies the determinative power of an input over the states of the nodes in the network is needed. We argue that the mutual information (MI) between a given subset of the inputs X={X₁,...,X_n} of some node i and its associated function f_i(X) quantifies the determinative power of this set of inputs over node i. We compare the determinative power of a set of inputs to the sensitivity to perturbations to these inputs, and find that, maybe surprisingly, an input that has large sensitivity to perturbations does not necessarily have large determinative power. However, for unate functions, which play an important role in genetic regulatory networks, we find a direct relation between MI and sensitivity to perturbations. As an application of our results, we analyze the large-scale regulatory network of Escherichia coli. We identify the most determinative nodes and show that a small subset of those reduces the overall uncertainty of the network state significantly. Furthermore, the network is found to be tolerant to perturbations of its inputs.     

Synaptic depression increases the selectivity of a neuron to its preferred pattern and binarizes the neural code

The preferred pattern of a neuron is defined here by the set of features detected by its excitatory inputs. It is shown that the Leaky integrate-and-fire (LIF) model of a neuron has a poor selectivity to its preferred pattern. Its response is determined by the total current injected by input spike trains. Thus, a few inputs with a high activity (an incomplete pattern) can elicit the same response as many inputs (a complete pattern) with a weak activity. A theoretical model of depressing synapse with linear recovery is proposed which eliminates this problem. Using this model, the time-averaged current injected in the soma by a spike train becomes independent on its frequency. The neural code thus becomes binary, and the response strength of the target neuron depends only on the number of active inputs. Simulations show that a biological model of strong synaptic depression has effects similar to those of the ideal linear model. The best selectivity is obtained with long somatic decay time constants (>50 ms) and with depression recovery time constants larger or equal to the somatic decay time constant. Thus, by eliminating information carried in the input firing rate, a neuron can improve its pattern recognition performance.     

Feedback from soil inorganic nitrogen on soil organic matter mineralisation and growth in a boreal forest ecosystem

Current nitrogen (N) deposition rates are considerably higher than during pre-industrial times and the growing interest in forest fertilisation requires better understanding of how the N and carbon (C) cycles interact. This study is based on experimental data showing how Scots pine (Pinus sylvestris L.) forests respond to single or consecutive pulse doses of N. The data were used to support the implementation of a dynamic feedback mechanism in the Q model, allowing for changes in soil N availability to regulate the rate of decomposer efficiency. Simulations of the long-term effects of slowly increasing N deposition with and without dynamic decomposer efficiency were then compared. Both versions of the model accurately predicted the response of tree growth to N fertilisation. Slowly increasing inputs of N over a century in the modified version acted on the inputs and outputs of soil C in opposing ways: (a) rate of litter input slowed down because more N was retained in the soil and thus not available for tree growth; (b) rate of C output, through soil heterotrophic respiration, was also gradually reduced due to increasing decomposer efficiency, although not enough to sufficiently balance the reduced litter input. Accurate prediction of the amount of added N retained in the ecosystem seems to be one of the key issues for estimating enhanced C sequestration.     

Presynaptic GABA(B) receptors modulate synaptic facilitation and depression at distinct synapses in fusiform cells of mouse dorsal cochlear nucleus

The mammalian dorsal cochlear nucleus (DCN) is considered to contribute to the localization of the sound sources. Fusiform cells (FCs), principal projection neurons in the DCN, integrate two excitatory inputs from auditory nerve fibers (ANFs) and parallel fibers (PFs). Although an immunohistochemical study suggested presence of GABA_B receptors at excitatory presynaptic terminals in the DCN, it has not been elucidated how GABA_B receptors modulate the synaptic transmission to FCs. Here, we examined effects of baclofen on the transmission in vitro. Baclofen reduced both PF-EPSC and ANF-EPSC by reducing transmitter releases, and it enhanced the facilitation in PF-FC synapses and prevented the depression in ANF-FC synapses. The enhancement and prevention were prominent during high-frequency (50 Hz) synaptic input, suggesting the activation of presynaptic GABA_B receptors may optimize both PF-FC and ANF-FC synapses for high-frequency transmission. Postsynaptic GABA_B receptors activated GIRK current and would further modulate the activity of FCs.