A kinetic lattice model of liquid-to-gel phase transition in lipid membrane: Experimental calibration and physiological implications

A kinetic lattice model of chain-melting phase transition has been developed. Its time scale has been calibrated with the acoustic relaxation spectroscopic data. The model permits analysis and predictions of kinetic features of those physiological processes in biological membranes the mechanism of which is based în a phase transition in the lipid component. It is shown that the phase-transition mechanism can sustain the high rate of synaptic exocytosis known for the fastest synapses in the central nervous system. It is also demonstrated that this mechanism can be an essential factor of synaptic plasticity.     

Shaping Neuronal Network Activity by Presynaptic Mechanisms

Neuronal microcircuits generate oscillatory activity, which has been linked to basic functions such as sleep, learning and sensorimotor gating. Although synaptic release processes are well known for their ability to shape the interaction between neurons in microcircuits, most computational models do not simulate the synaptic transmission process directly and hence cannot explain how changes in synaptic parameters alter neuronal network activity. In this paper, we present a novel neuronal network model that incorporates presynaptic release mechanisms, such as vesicle pool dynamics and calcium-dependent release probability, to model the spontaneous activity of neuronal networks. The model, which is based on modified leaky integrate-and-fire neurons, generates spontaneous network activity patterns, which are similar to experimental data and robust under changes in the model''s primary gain parameters such as excitatory postsynaptic potential and connectivity ratio. Furthermore, it reliably recreates experimental findings and provides mechanistic explanations for data obtained from microelectrode array recordings, such as network burst termination and the effects of pharmacological and genetic manipulations. The model demonstrates how elevated asynchronous release, but not spontaneous release, synchronizes neuronal network activity and reveals that asynchronous release enhances utilization of the recycling vesicle pool to induce the network effect. The model further predicts a positive correlation between vesicle priming at the single-neuron level and burst frequency at the network level; this prediction is supported by experimental findings. Thus, the model is utilized to reveal how synaptic release processes at the neuronal level govern activity patterns and synchronization at the network level.     

A kinetic lattice model of the chain-melting phase transition in lipid membrane: its experimental calibration and physiological implications

A kinetic lattice model of chain-melting phase transition has been developed. Its time scale has been calibrated with the acoustic relaxation spectroscopic data. The model presents a tool for the analysis and predictions of kinetic features of those physiological processes in biological membranes whose mechanism is based on the phase transition in the lipid component. It has been shown that the phase-transitional mechanism can provide a high rate of synaptic exocytosis known for the fastest synapses in the central nervous system. It was also demonstrated that this mechanism can serve as an essential factor of synaptic plasticity.     

Voltage transients in neuronal dendritic trees.

An analytical method is outlined for calculating the passive voltage transient at each point in an extensively branched neuron model for arbitrary current injection at a single branch. The method is based on a convolution formula that employs the transient response function, the voltage response to an instantaneous pulse of current. For branching that satisfies Rall's equivalent cylinder constraint, the response function is determined explicitly. Voltage transients, for a brief current injected at a branch terminal, are evaluated at several locations to illustrate the attenuation and delay characteristics of passive spread. A comparison with the same transient input terminal input, the fraction of input charge dissipated by various branches in the neuron model is illustrated. These fractions are independent of the input time course. For transient synaptic conductance change at a single branch terminal, a numerical example demonstrates the nonlinear effect of reduced synaptic driving potential. The branch terminal synaptic input is compared with the same synaptic conductance input applied to the soma on the basis of excitatory postsynaptic potential amplitude at the soma and charge delivered to the soma.     

A clustered plasticity model of long-term memory engrams

Long-term memory and its putative synaptic correlates the late phases of both long-term potentiation and long-term depression require enhanced protein synthesis. On the basis of recent data on translation-dependent synaptic plasticity and on the supralinear effect of activation of nearby synapses on action potential generation, we propose a model for the formation of long-term memory engrams at the single neuron level. In this model, which we call clustered plasticity, local translational enhancement, along with synaptic tagging and capture, facilitates the formation of long-term memory engrams through bidirectional synaptic weight changes among synapses within a dendritic branch.     

Non-weak inhibition and phase resetting at negative values of phase in cells with fast-slow dynamics at hyperpolarized potentials

Phase response is a powerful concept in the analysis of both weakly and non-weakly perturbed oscillators such as regularly spiking neurons, and is applicable if the oscillator returns to its limit cycle trajectory between successive perturbations. When the latter condition is violated, a formal application of the phase return map may yield phase values outside of its definition domain; in particular, strong synaptic inhibition may result in negative values of phase. The effect of a second perturbation arriving close to the first one is undetermined in this case. However, here we show that for a Morris–Lecar model of a spiking cell with strong time scale separation, extending the phase response function definition domain to an additional negative value branch allows to retain the accuracy of the phase response approach in the face of such strong inhibitory coupling. We use the resulting extended phase response function to accurately describe the response of a Morris–Lecar oscillator to consecutive non-weak synaptic inputs. This method is particularly useful when analyzing the dynamics of three or more non-weakly coupled cells, whereby more than one synaptic perturbation arrives per oscillation cycle into each cell. The method of perturbation prediction based on the negative-phase extension of the phase response function may be applicable to other excitable cell models characterized by slow voltage dynamics at hyperpolarized potentials.     

Synaptic modifications depend on synapse location and activity: a biophysical model of STDP

In spike-timing-dependent plasticity (STDP) the synapses are potentiated or depressed depending on the temporal order and temporal difference of the pre- and post-synaptic signals. We present a biophysical model of STDP which assumes that not only the timing, but also the shapes of these signals influence the synaptic modifications. The model is based on a Hebbian learning rule which correlates the NMDA synaptic conductance with the post-synaptic signal at synaptic location as the pre- and post-synaptic quantities. As compared to a previous paper [Saudargiene, A., Porr, B., Worgotter, F., 2004. How the shape of pre- and post-synaptic signals can influence stdp: a biophysical model. Neural Comp.], here we show that this rule reproduces the generic STDP weight change curve by using real neuronal input signals and combinations of more than two (pre- and post-synaptic) spikes. We demonstrate that the shape of the STDP curve strongly depends on the shape of the depolarising membrane potentials, which induces learning. As these potentials vary at different locations of the dendritic tree, model predicts that synaptic changes are location dependent. The model is extended to account for the patterns of more than two spikes of the pre- and post-synaptic cells. The results show that STDP weight change curve is also activity dependent.     

Receptor actions of synaptically released glutamate: the role of transporters on the scale from nanometers to microns

Actions of the excitatory neurotransmitter glutamate inside and outside the synaptic cleft determine the activity of neural circuits in the brain. However, to what degree local glutamate transporters affect these actions on a submicron scale remains poorly understood. Here we focus on hippocampal area CA1, a common subject of synaptic physiology studies. First, we use a two-photon excitation technique to obtain an estimate of the apparent (macroscopic) extracellular diffusion coefficient for glutamate, ∼0.32 μm²/ms. Second, we incorporate this measurement into a Monte Carlo model of the typical excitatory synapse and examine the influence of distributed glutamate transporter molecules on signal transmission. Combined with the results of whole-cell recordings, such simulations argue that, although glutamate transporters have little effect on the activation of synaptic α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptors, this does not rule out the occurrence of up to several dozens of transporters inside the cleft. We further evaluate how the expression pattern of transporter molecules (on the 10-100 nm scale) affects the activation of N-methyl-D-aspartic acid or metabotropic glutamate receptors in the synaptic vicinity. Finally, we extend our simulations to the macroscopic scale, estimating that synaptic activity sufficient to excite principal neurons could intermittently raise extracellular glutamate to ∼1 μM only at sparse (microns apart) hotspots. Greater rises of glutamate occur only when <5% of transporters are available (for instance, when an astrocyte fails). The results provide a quantitative framework for a better understanding of the relationship between glutamate transporters and glutamate receptor signaling.     

Acquiring new information in a neuronal network: from Hebb's concept to homeostatic plasticity

Synaptic plasticity is the cellular mechanism underlying the phenomena of learning and memory. Much of the research on synaptic plasticity is based on the postulate of Hebb (1949) who proposed that, when a neuron repeatedly takes part in the activation of another neuron, the efficacy of the connections between these neurons is increased. Plasticity has been extensively studied, and often demonstrated through the processes of LTP (Long Term Potentiation) and LTD (Long Term Depression), which represent an increase and a decrease of the efficacy of long-term synaptic transmission. This review summarizes current knowledge concerning the cellular mechanisms of LTP and LTD, whether at the level of excitatory synapses, which have been the most studied, or at the level of inhibitory synapses. However, if we consider neuronal networks rather than the individual synapses, the consequences of synaptic plasticity need to be considered on a large scale to determine if the activity of networks are changed or not. Homeostatic plasticity takes into account the mechanisms which control the efficacy of synaptic transmission for all the synaptic inputs of a neuron. Consequently, this new concept deals with the coordinated activity of excitatory and inhibitory networks afferent to a neuron which maintain a controlled level of excitability during the acquisition of new information related to the potentiation or to the depression of synaptic efficacy. We propose that the protocols of stimulation used to induce plasticity at the synaptic level set up a "homeostatic potentiation" or a "homeostatic depression" of excitation and inhibition at the level of the neuronal networks. The coordination between excitatory and inhibitory circuits allows the neuronal networks to preserve a level of stable activity, thus avoiding episodes of hyper- or hypo-activity during the learning and memory phases.     

Noise Suppression and Surplus Synchrony by Coincidence Detection

The functional significance of correlations between action potentials of neurons is still a matter of vivid debate. In particular, it is presently unclear how much synchrony is caused by afferent synchronized events and how much is intrinsic due to the connectivity structure of cortex. The available analytical approaches based on the diffusion approximation do not allow to model spike synchrony, preventing a thorough analysis. Here we theoretically investigate to what extent common synaptic afferents and synchronized inputs each contribute to correlated spiking on a fine temporal scale between pairs of neurons. We employ direct simulation and extend earlier analytical methods based on the diffusion approximation to pulse-coupling, allowing us to introduce precisely timed correlations in the spiking activity of the synaptic afferents. We investigate the transmission of correlated synaptic input currents by pairs of integrate-and-fire model neurons, so that the same input covariance can be realized by common inputs or by spiking synchrony. We identify two distinct regimes: In the limit of low correlation linear perturbation theory accurately determines the correlation transmission coefficient, which is typically smaller than unity, but increases sensitively even for weakly synchronous inputs. In the limit of high input correlation, in the presence of synchrony, a qualitatively new picture arises. As the non-linear neuronal response becomes dominant, the output correlation becomes higher than the total correlation in the input. This transmission coefficient larger unity is a direct consequence of non-linear neural processing in the presence of noise, elucidating how synchrony-coded signals benefit from these generic properties present in cortical networks.     

Memory Maintenance in Synapses with Calcium-Based Plasticity in the Presence of Background Activity

Most models of learning and memory assume that memories are maintained in neuronal circuits by persistent synaptic modifications induced by specific patterns of pre- and postsynaptic activity. For this scenario to be viable, synaptic modifications must survive the ubiquitous ongoing activity present in neural circuits in vivo. In this paper, we investigate the time scales of memory maintenance in a calcium-based synaptic plasticity model that has been shown recently to be able to fit different experimental data-sets from hippocampal and neocortical preparations. We find that in the presence of background activity on the order of 1 Hz parameters that fit pyramidal layer 5 neocortical data lead to a very fast decay of synaptic efficacy, with time scales of minutes. We then identify two ways in which this memory time scale can be extended: (i) the extracellular calcium concentration in the experiments used to fit the model are larger than estimated concentrations in vivo. Lowering extracellular calcium concentration to in vivo levels leads to an increase in memory time scales of several orders of magnitude; (ii) adding a bistability mechanism so that each synapse has two stable states at sufficiently low background activity leads to a further boost in memory time scale, since memory decay is no longer described by an exponential decay from an initial state, but by an escape from a potential well. We argue that both features are expected to be present in synapses in vivo. These results are obtained first in a single synapse connecting two independent Poisson neurons, and then in simulations of a large network of excitatory and inhibitory integrate-and-fire neurons. Our results emphasise the need for studying plasticity at physiological extracellular calcium concentration, and highlight the role of synaptic bi- or multistability in the stability of learned synaptic structures.     

Synchronization without oscillatory neurons

Experimental results suggest that neurons in the cortex synchronize their action potentials on the millisecond time scale. More importantly this binding expresses functional relationships between the neurons. A model of neuronal interactions is proposed in which simultaneous discharges of neurons develop through specialized synaptic circuits. As an important prerequisite for this synchronization it is demonstrated that SynFire chains, generating different levels of excitation, propagate their activity waves at distinct velocities. Two chains were coupled by excitatory synapses and their activity was initiated at different times. Due to synaptic interactions, activity in the earlier-initiated chain accelerates propagation in the other chain until the two activity waves are synchronized. Compared with several neural network models with oscillatory units, physiologically more plausible neurons are simulated. It is still under debate whether neurons in the cortex show oscillatory dischargesper se. In particular, a high rate of noise relative to very weak synaptic gains cannot impair our results in the neural network simulations.     

Spine calcium transients induced by synaptically-evoked action potentials can predict synapse location and establish synaptic democracy

CA1 pyramidal neurons receive hundreds of synaptic inputs at different distances from the soma. Distance-dependent synaptic scaling enables distal and proximal synapses to influence the somatic membrane equally, a phenomenon called "synaptic democracy". How this is established is unclear. The backpropagating action potential (BAP) is hypothesised to provide distance-dependent information to synapses, allowing synaptic strengths to scale accordingly. Experimental measurements show that a BAP evoked by current injection at the soma causes calcium currents in the apical shaft whose amplitudes decay with distance from the soma. However, in vivo action potentials are not induced by somatic current injection but by synaptic inputs along the dendrites, which creates a different excitable state of the dendrites. Due to technical limitations, it is not possible to study experimentally whether distance information can also be provided by synaptically-evoked BAPs. Therefore we adapted a realistic morphological and electrophysiological model to measure BAP-induced voltage and calcium signals in spines after Schaffer collateral synapse stimulation. We show that peak calcium concentration is highly correlated with soma-synapse distance under a number of physiologically-realistic suprathreshold stimulation regimes and for a range of dendritic morphologies. Peak calcium levels also predicted the attenuation of the EPSP across the dendritic tree. Furthermore, we show that peak calcium can be used to set up a synaptic democracy in a homeostatic manner, whereby synapses regulate their synaptic strength on the basis of the difference between peak calcium and a uniform target value. We conclude that information derived from synaptically-generated BAPs can indicate synapse location and can subsequently be utilised to implement a synaptic democracy.     

Memory retention in pyramidal neurons: a unified model of energy-based homo and heterosynaptic plasticity with homeostasis

The brain can learn new tasks without forgetting old ones. This memory retention is closely associated with the long-term stability of synaptic strength. To understand the capacity of pyramidal neurons to preserve memory under different tasks, we established a plasticity model based on the postsynaptic membrane energy state, in which the change in synaptic strength depends on the difference between the energy state after stimulation and the resting energy state. If the post-stimulation energy state is higher than the resting energy state, then synaptic depression occurs. On the contrary, the synapse is strengthened. Our model unifies homo- and heterosynaptic plasticity and can reproduce synaptic plasticity observed in multiple experiments, such as spike-timing-dependent plasticity, and cooperative plasticity with few and common parameters. Based on the proposed plasticity model, we conducted a simulation study on how the activation patterns of dendritic branches by different tasks affect the synaptic connection strength of pyramidal neurons. We further investigate the formation mechanism by which different tasks activate different dendritic branches. Simulation results show that compare to the classic plasticity model, the plasticity model we proposed can achieve a better spatial separation of different branches activated by different tasks in pyramidal neurons, which deepens our insight into the memory retention mechanism of brains.     

Signal integration on the dendrites of a pyramidal neuron model

This paper studied the synaptic and dendritic integration with different spatial distributions of synapses on the dendrites of a biophysically-detailed layer 5 pyramidal neuron model. It has been observed that temporally synchronous and spatially clustered synaptic inputs make dendrites perform a highly nonlinear integration. The effect of clustering degree of synaptic distribution on neuronal responsiveness is investigated by changing the number of top apical dendrites where active synapses are allocated. The neuron shows maximum responsiveness to synaptic inputs which have an intermediate clustering degree of spatial distribution, indicating complex interactions among dendrites with the existence of nonlinear synaptic and dendritic integrations.     

Spike-Timing Dependence of Structural Plasticity Explains Cooperative Synapse Formation in the Neocortex

Structural plasticity governs the long-term development of synaptic connections in the neocortex. While the underlying processes at the synapses are not fully understood, there is strong evidence that a process of random, independent formation and pruning of excitatory synapses can be ruled out. Instead, there must be some cooperation between the synaptic contacts connecting a single pre- and postsynaptic neuron pair. So far, the mechanism of cooperation is not known. Here we demonstrate that local correlation detection at the postsynaptic dendritic spine suffices to explain the synaptic cooperation effect, without assuming any hypothetical direct interaction pathway between the synaptic contacts. Candidate biomolecular mechanisms for dendritic correlation detection have been identified previously, as well as for structural plasticity based thereon. By analyzing and fitting of a simple model, we show that spike-timing correlation dependent structural plasticity, without additional mechanisms of cross-synapse interaction, can reproduce the experimentally observed distributions of numbers of synaptic contacts between pairs of neurons in the neocortex. Furthermore, the model yields a first explanation for the existence of both transient and persistent dendritic spines and allows to make predictions for future experiments.     

Anti-allodynic and promotive effect on inhibitory synaptic transmission of riluzole in rat spinal dorsal horn

Riluzole (2-amino-6-(trifluoromethoxy)benzothiazole) is a drug known for its inhibitory effect on glutamatergic transmission and its anti-nociceptive and anti-allodynic effects in neuropathic pain rat models. Riluzole also has an enhancing effect on GABAergic synaptic transmission. However, the effect on the spinal dorsal horn, which plays an important role in modulating nociceptive transmission, remains unknown. We investigated the ameliorating effect of riluzole on mechanical allodynia using the von Frey test in a rat model of neuropathic pain and analyzed the synaptic action of riluzole on inhibitory synaptic transmission in substantia gelatinosa (SG) neurons using whole-cell patch clamp recordings. We found that single-dose intraperitoneal riluzole (4 mg/kg) administration effectively attenuated mechanical allodynia in the short term in a rat model of neuropathic pain. Moreover, 300 μM riluzole induced an outward current in rat SG neurons. The outward current induced by riluzole was not suppressed in the presence of tetrodotoxin. Furthermore, we found that the outward current was suppressed by simultaneous bicuculline and strychnine application, but not by strychnine alone. Altogether, these results suggest that riluzole enhances inhibitory synaptic transmission monosynaptically by potentiating GABAergic synaptic transmission in the rat spinal dorsal horn.     

Synapse fits neuron: joint reduction by model inversion

In this paper, we introduce a novel simplification method for dealing with physical systems that can be thought to consist of two subsystems connected in series, such as a neuron and a synapse. The aim of our method is to help find a simple, yet convincing model of the full cascade-connected system, assuming that a satisfactory model of one of the subsystems, e.g., the neuron, is already given. Our method allows us to validate a candidate model of the full cascade against data at a finer scale. In our main example, we apply our method to part of the squid’s giant fiber system. We first postulate a simple, hypothetical model of cell-to-cell signaling based on the squid’s escape response. Then, given a FitzHugh-type neuron model, we derive the verifiable model of the squid giant synapse that this hypothesis implies. We show that the derived synapse model accurately reproduces synaptic recordings, hence lending support to the postulated, simple model of cell-to-cell signaling, which thus, in turn, can be used as a basic building block for network models.     

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.     

Competitive anatomical and physiological plasticity: a neurotrophic bridge

Understanding the mechanisms of competitive synaptic plasticity, both anatomical and physiological, is of central importance to developmental neuroscience. Neurotrophic factors (NTFs) are implicated at almost every level of synaptic plasticity, from rapid physiological effects to slower anatomical effects, in addition to being implicated in competitive plasticity. Previously, we have built and analysed a mathematical model of anatomical synaptic plasticity based on competition for neurotrophic support. Here, we extend our work to build a combined, anatomical and physiological model. We find that, in order to understand the mechanisms of competitive physiological plasticity, we must postulate a central role for the change in expression of NTF receptors (NTFRs) on afferent synaptic terminals. Only by supposing that the expression of NTFRs is governed by NTF uptake do we find that physiological plasticity is competitive in character. We perform a fixed point analysis that establishes when afferent segregation is possible as a function of the parameters in the model, and simulate the model numerically to shed further light on its properties. A very clear prediction emerges from our model: that, as the efficacy of a terminal that is destined to be retracted due to competitive interactions reduces to zero, the NTFRs on that terminal should be down-regulated. Furthermore, our model requires that this reduction in synaptic efficacy never occurs significantly before the down-regulation in NTFRs. Such a prediction should be testable, and renders our model capable of being invalidated, in contrast to many other models of synaptic competition, which merely impose rather than seek to illuminate the quintessential feature of developmental synaptic plasticity. Received: 14 May 1999 / Accepted in revised form: 29 November 1999