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.     

Activity-dependent matching of excitatory and inhibitory inputs during refinement of visual receptive fields

The receptive field (RF) of single visual neurons undergoes progressive refinement during development. It remains largely unknown how the excitatory and inhibitory inputs on single developing neurons are refined in a coordinated manner to allow the formation of functionally correct circuits. Using whole-cell voltage-clamp recording from Xenopus tectal neurons, we found that RFs determined by excitatory and inhibitory inputs in more mature tectal neurons are spatially matched, with each spot stimulus evoking balanced synaptic excitation and inhibition. This emerges during development through a gradual reduction in the RF size and a transition from disparate to matched topography of excitatory and inhibitory inputs to the tectal neurons. Altering normal spiking activity of tectal neurons by either blocking or elevating GABA(A) receptor activity significantly impeded the developmental reduction and topographic matching of RFs. Thus, appropriate inhibitory activity is essential for the coordinated refinement of excitatory and inhibitory connections.     

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     

Phenomenological Incorporation of Nonlinear Dendritic Integration Using Integrate-and-Fire Neuronal Frameworks

It has been discovered recently in experiments that the dendritic integration of excitatory glutamatergic inputs and inhibitory GABAergic inputs in hippocampus CA1 pyramidal neurons obeys a simple arithmetic rule as , where , and are the respective voltage values of the summed somatic potential, the excitatory postsynaptic potential (EPSP) and the inhibitory postsynaptic potential measured at the time when the EPSP reaches its peak value. Moreover, the shunting coefficient in this rule only depends on the spatial location but not the amplitude of the excitatory or inhibitory input on the dendrite. In this work, we address the theoretical issue of how much the above dendritic integration rule can be accounted for using subthreshold membrane potential dynamics in the soma as characterized by the conductance-based integrate-and-fire (I&F) model. Then, we propose a simple I&F neuron model that incorporates the spatial dependence of the shunting coefficient by a phenomenological parametrization. Our analytical and numerical results show that this dendritic-integration-rule-based I&F (DIF) model is able to capture many experimental observations and it also yields predictions that can be used to verify the validity of the DIF model experimentally. In addition, the DIF model incorporates the dendritic integration effects dynamically and is applicable to more general situations than those in experiments in which excitatory and inhibitory inputs occur simultaneously in time. Finally, we generalize the DIF neuronal model to incorporate multiple inputs and obtain a similar dendritic integration rule that is consistent with the results obtained by using a realistic neuronal model with multiple compartments. This generalized DIF model can potentially be used to study network dynamics that may involve effects arising from dendritic integrations.     

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.     

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.     

Top-Down Modulation on Perceptual Decision with Balanced Inhibition through Feedforward and Feedback Inhibitory Neurons

Recent physiological studies have shown that neurons in various regions of the central nervous systems continuously receive noisy excitatory and inhibitory synaptic inputs in a balanced and covaried fashion. While this balanced synaptic input (BSI) is typically described in terms of maintaining the stability of neural circuits, a number of experimental and theoretical studies have suggested that BSI plays a proactive role in brain functions such as top-down modulation for executive control. Two issues have remained unclear in this picture. First, given the noisy nature of neuronal activities in neural circuits, how do the modulatory effects change if the top-down control implements BSI with different ratios between inhibition and excitation? Second, how is a top-down BSI realized via only excitatory long-range projections in the neocortex? To address the first issue, we systematically tested how the inhibition/excitation ratio affects the accuracy and reaction times of a spiking neural circuit model of perceptual decision. We defined an energy function to characterize the network dynamics, and found that different ratios modulate the energy function of the circuit differently and form two distinct functional modes. To address the second issue, we tested BSI with long-distance projection to inhibitory neurons that are either feedforward or feedback, depending on whether these inhibitory neurons do or do not receive inputs from local excitatory cells, respectively. We found that BSI occurs in both cases. Furthermore, when relying on feedback inhibitory neurons, through the recurrent interactions inside the circuit, BSI dynamically and automatically speeds up the decision by gradually reducing its inhibitory component in the course of a trial when a decision process takes too long.     

Excitatory actions of GABA in the cortex

Little is known about how GABAergic inputs interact with excitatory inputs under conditions that maintain physiological concentrations of intracellular anions. Using extracellular and gramicidin perforated-patch recording, we show that somatic and dendritic GABA responses in mature cortical pyramidal neurons are depolarizing from rest and can facilitate action potential generation when combined with proximal excitatory input. Dendritic GABA responses were excitatory regardless of timing, whereas somatic GABA responses were inhibitory when coincident with excitatory input but excitatory at earlier times. These excitatory actions of GABA occur even though the GABA reversal potential is below action potential threshold and largely uniform across the somato-dendritic axis, and arise when GABAergic inputs are temporally or spatially isolated from concurrent excitation. Our findings demonstrate that under certain circumstances GABA will have an excitatory role in synaptic integration in the cortex.     

Balanced neurons: analysis of leaky integrate-and-fire neurons with reversal potentials

 A new technique is presented for analyzing leaky integrate-and-fire neurons that incorporates reversal potentials, which impose a biologically realistic lower bound to the membrane potential. The time distribution of the synaptic inputs is modeled as a Poisson process. The analysis is carried out in the Gaussian approximation, which comparison with numerical simulations confirms is most accurate in the limit of a large number of inputs. The hypothesis that the observed variability in the spike times of cortical neurons is caused by a balance of excitatory and inhibitory synaptic inputs is supported by the results for the coefficient of variation of the interspike intervals. Its value decreases with both increasing numbers and amplitude of inputs, and is consistently lower than 1.0 over a wide range of realistic parameter values. The dependence of the output spike rate upon the rate, number, and amplitude of the synaptic inputs, as well as upon the value of the inhibitory reversal potential, is given. Received: 15 February 2001 / Accepted in revised form: 27 March 2001     

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.     

Cerebellar Cortex Granular Layer Interneurons in the Macaque Monkey Are Functionally Driven by Mossy Fiber Pathways through Net Excitation or Inhibition

The granular layer is the input layer of the cerebellar cortex. It receives information through mossy fibers, which contact local granular layer interneurons (GLIs) and granular layer output neurons (granule cells). GLIs provide one of the first signal processing stages in the cerebellar cortex by exciting or inhibiting granule cells. Despite the importance of this early processing stage for later cerebellar computations, the responses of GLIs and the functional connections of mossy fibers with GLIs in awake animals are poorly understood. Here, we recorded GLIs and mossy fibers in the macaque ventral-paraflocculus (VPFL) during oculomotor tasks, providing the first full inventory of GLI responses in the VPFL of awake primates. We found that while mossy fiber responses are characterized by a linear monotonic relationship between firing rate and eye position, GLIs show complex response profiles characterized by “eye position fields” and single or double directional tunings. For the majority of GLIs, prominent features of their responses can be explained by assuming that a single GLI receives inputs from mossy fibers with similar or opposite directional preferences, and that these mossy fiber inputs influence GLI discharge through net excitatory or inhibitory pathways. Importantly, GLIs receiving mossy fiber inputs through these putative excitatory and inhibitory pathways show different firing properties, suggesting that they indeed correspond to two distinct classes of interneurons. We propose a new interpretation of the information flow through the cerebellar cortex granular layer, in which mossy fiber input patterns drive the responses of GLIs not only through excitatory but also through net inhibitory pathways, and that excited and inhibited GLIs can be identified based on their responses and their intrinsic properties.     

Local circuit input to the medullary reticular formation from the rostral nucleus of the solitary tract

The intermediate reticular formation (IRt) subjacent to the rostral (gustatory) nucleus of the solitary tract (rNST) receives projections from the rNST and appears essential to the expression of taste-elicited ingestion and rejection responses. We used whole cell patch-clamp recording and calcium imaging to characterize responses from an identified population of prehypoglossal neurons in the IRt to electrical stimulation of the rNST in a neonatal rat pup slice preparation. The calcium imaging studies indicated that IRt neurons could be activated by rNST stimulation and that many neurons were under tonic inhibition. Whole cell patch-clamp recording revealed mono- and polysynaptic projections from the rNST to identified prehypoglossal neurons. The projection was primarily excitatory and glutamatergic; however, there were some inhibitory GABAergic projections, and many neurons received excitatory and inhibitory inputs. There was also evidence of disinhibition. Overall, bath application of GABA(A) antagonists increased the amplitude of excitatory currents, and, in several neurons, stimulation of the rNST systematically decreased inhibitory currents. We have hypothesized that the transition from licks to gapes by natural stimuli, such as quinine monohydrochloride, could occur via such disinhibition. We present an updated dynamic model that summarizes the complex synaptic interface between the rNST and the IRt and demonstrates how inhibition could contribute to the transition from ingestion to rejection.     

A kainate receptor increases the efficacy of GABAergic synapses

Brain functions are based on the dynamic interaction of excitatory and inhibitory inputs. Spillover of glutamate from excitatory synapses may diffuse to and modulate nearby inhibitory synapses. By recording unitary inhibitory postsynaptic currents (uIPSCs) from cell pairs in CA1 of the hippocampus, we demonstrated that low concentrations of Kainate receptor (KAR) agonists increased the success rate (P(s)) of uIPSCs, whereas high concentrations of KAR agonists depressed GABAergic synapses. Ambient glutamate released by basal activities or stimulation of the stratum radiatum increases the efficacy of GABAergic synapses by activating presynaptic KARs, which facilitate Ca(2+)-dependent GABA release. The results suggest that glutamate released from excitatory synapses may also function as an intermediary between excitatory and inhibitory synapses to protect overexcitation of local circuits.     

Coexistence of lateral and co-tuned inhibitory configurations in cortical networks

The responses of neurons in sensory cortex depend on the summation of excitatory and inhibitory synaptic inputs. How the excitatory and inhibitory inputs scale with stimulus depends on the network architecture, which ranges from the lateral inhibitory configuration where excitatory inputs are more narrowly tuned than inhibitory inputs, to the co-tuned configuration where both are tuned equally. The underlying circuitry that gives rise to lateral inhibition and co-tuning is yet unclear. Using large-scale network simulations with experimentally determined connectivity patterns and simulations with rate models, we show that the spatial extent of the input determined the configuration: there was a smooth transition from lateral inhibition with narrow input to co-tuning with broad input. The transition from lateral inhibition to co-tuning was accompanied by shifts in overall gain (reduced), output firing pattern (from tonic to phasic) and rate-level functions (from non-monotonic to monotonically increasing). The results suggest that a single cortical network architecture could account for the extended range of experimentally observed response types between the extremes of lateral inhibitory versus co-tuned configurations.     

Balancing feed-forward excitation and inhibition via Hebbian inhibitory synaptic plasticity

It has been suggested that excitatory and inhibitory inputs to cortical cells are balanced, and that this balance is important for the highly irregular firing observed in the cortex. There are two hypotheses as to the origin of this balance. One assumes that it results from a stable solution of the recurrent neuronal dynamics. This model can account for a balance of steady state excitation and inhibition without fine tuning of parameters, but not for transient inputs. The second hypothesis suggests that the feed forward excitatory and inhibitory inputs to a postsynaptic cell are already balanced. This latter hypothesis thus does account for the balance of transient inputs. However, it remains unclear what mechanism underlies the fine tuning required for balancing feed forward excitatory and inhibitory inputs. Here we investigated whether inhibitory synaptic plasticity is responsible for the balance of transient feed forward excitation and inhibition. We address this issue in the framework of a model characterizing the stochastic dynamics of temporally anti-symmetric Hebbian spike timing dependent plasticity of feed forward excitatory and inhibitory synaptic inputs to a single post-synaptic cell. Our analysis shows that inhibitory Hebbian plasticity generates 'negative feedback' that balances excitation and inhibition, which contrasts with the 'positive feedback' of excitatory Hebbian synaptic plasticity. As a result, this balance may increase the sensitivity of the learning dynamics to the correlation structure of the excitatory inputs.     

Synaptic dendritic activity modulates the single synaptic event

Synaptic transmission is the key system for the information transfer and elaboration among neurons. Nevertheless, a synapse is not a standing alone structure but it is a part of a population of synapses inputting the information from several neurons on a specific area of the dendritic tree of a single neuron. This population consists of excitatory and inhibitory synapses the inputs of which drive the postsynaptic membrane potential in the depolarizing (excitatory synapses) or depolarizing (inhibitory synapses) direction modulating in such a way the postsynaptic membrane potential. The postsynaptic response of a single synapse depends on several biophysical factors the most important of which is the value of the membrane potential at which the response occurs. The concurrence in a specific time window of inputs by several synapses located in a specific area of the dendritic tree can, consequently, modulate the membrane potential such to severely influence the single postsynaptic response. The degree of modulation operated by the synaptic population depends on the number of synapses active, on the relative proportion between excitatory and inbibitory synapses belonging to the population and on their specific mean firing frequencies. In the present paper we show results obtained by the simulation of the activity of a single Glutamatergic excitatory synapse under the influence of two different populations composed of the same proportion of excitatory and inhibitory synapses but having two different sizes (total number of synapses). The most relevant conclusion of the present simulations is that the information transferred by the single synapse is not and independent simple transition between a pre- and a postsynaptic neuron but is the result of the cooperation of all the synapses which concurrently try to transfer the information to the postsynaptic neuron in a given time window. This cooperativeness is mainly operated by a simple mechanism of modulation of the postsynaptic membrane potential which influences the amplitude of the different components forming the postsynaptic excitatory response.     

Implementing Dynamic Clamp with Synaptic and Artificial Conductances in Mouse Retinal Ganglion Cells

Ganglion cells are the output neurons of the retina and their activity reflects the integration of multiple synaptic inputs arising from specific neural circuits. Patch clamp techniques, in voltage clamp and current clamp configurations, are commonly used to study the physiological properties of neurons and to characterize their synaptic inputs. Although the application of these techniques is highly informative, they pose various limitations. For example, it is difficult to quantify how the precise interactions of excitatory and inhibitory inputs determine response output. To address this issue, we used a modified current clamp technique, dynamic clamp, also called conductance clamp ^{1, 2, 3} and examined the impact of excitatory and inhibitory synaptic inputs on neuronal excitability. This technique requires the injection of current into the cell and is dependent on the real-time feedback of its membrane potential at that time. The injected current is calculated from predetermined excitatory and inhibitory synaptic conductances, their reversal potentials and the cell''s instantaneous membrane potential. Details on the experimental procedures, patch clamping cells to achieve a whole-cell configuration and employment of the dynamic clamp technique are illustrated in this video article. Here, we show the responses of mouse retinal ganglion cells to various conductance waveforms obtained from physiological experiments in control conditions or in the presence of drugs. Furthermore, we show the use of artificial excitatory and inhibitory conductances generated using alpha functions to investigate the responses of the cells.     

Synaptic interactions between nonspiking local interneurones in the terminal abdominal ganglion of the crayfish

Nonspiking local interneurones are the important premotor elements in arthropod motor control systems. We have analyzed the synaptic interactions between nonspiking interneurones in the crayfish terminal (6th) abdominal ganglion using simultaneous intracellular recordings. Only 15% of nonspiking interneurones formed bi-directional excitatory connections. In 77% of connections, however, the nonspiking interneurones showed a one-way inhibitory interaction. In these cases, the presynaptic nonspiking interneurones received excitatory synaptic inputs from the sensory afferents innervating hairs on the surface of the uropods and the postsynaptic nonspiking interneurones received inhibitory synaptic inputs that were partly mediated by the inputs to the presynaptic nonspiking interneurones. The membrane hyperpolarization of the postsynaptic nonspiking interneurones mediated by the presynaptic nonspiking interneurones was reduced in amplitude when the hyperpolarizing current was injected into the postsynaptic interneurones, or when the external bathing solution was replaced with one containing low calcium and high magnesium concentrations. The role of these interactions in the circuits controlling the movements of the terminal appendages is discussed.Abbreviations AL antero-lateral - epsp excitatory postsynaptic potential - ipsp inhibitory postsynaptic potential - PL postero-lateral     

Electrophysiology of the Fetal Spinal Cord : II. Interaction among peripheral inputs and recurrent inhibition

Interactions of peripheral inputs to the motoneuron of the kitten fetus as young as 3 weeks prenatal were studied by reflex discharge from the ventral root as well as by recording from single motoneurons. Facilitation was found between two synergists in fetuses 1 to 2 weeks before birth. Intracellular recording showed that the facilitation could be explained by summation of excitatory postsynaptic potentials. Inhibition was found between antagonists in the fetuses 2 to 3 weeks before birth and was accompanied by inhibitory postsynaptic potentials. Recurrent inhibition was very powerful in the fetal spinal cord as shown by large motoneuron hyperpolarization by antidromic stimulation. Cells presumed to be "Renshaw cells" and which responded to both ortho- and antidromic stimulation with repetitive firing were shown in the 2 weeks prenatal fetus. These results lead to the conclusion that there is considerable effective synaptic connection of afferent collaterals already established by the later stage of intrauterine life and that this may be achieved independently of external stimuli.     

A possible mechanism of the influence of neuromodulators and modifiable inhibition on long-term potentiation and long-term depression of excitatory inputs to main hippocampal neurons

A hypothetic mechanism explaining the influence of various neuromodulators and modifiable disynaptic inhibition on the long-term potentiation and depression (LTP and LTD) of excitatory inputs to granule and pyramidal hippocampal cells is proposed. According to this mechanism, facilitation of the LTD/LTP of excitatory inputs to an inhibitory interneuron caused by the action of a neuromodulator on a receptor bound with Gi/0/(Gs or Gq/11) protein can reduce/augment the GABA release, weaken/intensify the target cell inhibition, and promote the induction of the LTP/LTD of excitatory inputs to this cell. In the absence of the inhibition, the same neuromodulator would promote the LTD/LTP induction in the target cell by activating the same receptor types. The resulting effect of a neuromodulator on a target cell depends on the ratio between the "strengths" of its excitatory and inhibitory inputs, on the presence of receptors of the same or different types at the interneuron and the target cell, and on the neuromodulator concentration due to its different affinity for receptors, interaction with which provide its influence on postsynaptic processes in opposite directions. The consequences of suggested mechanism are in agreement with the known experimental data.