Simultaneous Bayesian Estimation of Excitatory and Inhibitory Synaptic Conductances by Exploiting Multiple Recorded Trials

Interaction of the excitatory and inhibitory synaptic inputs constructs the shape of the receptive fields and can elucidate the synaptic mechanism underlying the functional activities of neurons. Estimating trial-to-trial excitatory and inhibitory synaptic conductance from noisy observation of membrane potential or input current can reveal drivers of neurons and play an important role in our understanding of information processing in neuronal circuits. Although recent studies introduced statistical methods that estimate trial-to-trial variation of synaptic conductance [1,2], most previous works use the well-known least square (LS) method to estimate the excitatory and inhibitory synaptic conductance from the trial-mean of recorded traces of membrane potential or input current [3-5]. We first analytically show that the LS method is not only incompetent to capture trial-to-trial variation of synaptic conductance but also provide biased estimation of synaptic conductance and excitatory/inhibitory covariance if fluctuation of synaptic conductance and membrane potential is correlated. Next, we propose a novel method based on Gaussian mixture Kalman filtering (GMKF) that not only overcomes the aforementioned limitations of the LS method but also gives the opportunity of trial-to-trial estimation of the excitatory and inhibitory synaptic conductance. We show that our proposal requires fewer assumptions than the recent proposals [1,2] that also provide trial-to-trial estimation of synaptic conductance. In particular, the proposed technique outperforms [1] by providing the ability of estimating an unknown synaptic distribution using Gaussian mixture model (GMM). We believe that our findings have a significant influence on our understanding of the balance of excitatory and inhibitory synaptic input and the underlying cortical circuitry. Figure 1 Estimating excitatory and inhibitory synaptic conductance using LS Voltage-clamp (left) and GMKF (right). LS method cannot estimate trial-to-trial synaptic conductances (10 trials each lasted 1 sec is used to provide data for both methods). True values ...

It has been shown previously that background synaptic noise modulates the response gain of neocortical neurons. However, the role of the statistical properties of the noise in modulating firing rate is not known. Here, the dependence of firing rate on the statistical properties of the excitatory to inhibitory balance (EI) in cortical pyramidal neurons was studied. Excitatory glutamatergic and inhibitory GABAergic synaptic conductances were simulated as two stochastic processes and injected into individual neurons in vitro through use of the dynamic-clamp system. Response gain was significantly modulated as a function of the statistical interactions between excitatory and inhibitory synaptic conductances. Firing rates were compared for noisy synaptic conductance steps by varying either the EI correlation or the relative delay between correlated E and I. When inhibitory synaptic conductances exhibited a short temporal delay (5 ms) relative to correlated excitatory synaptic conductances, the response gain was increased compared with noise with no temporal delay but with an equivalent degree of correlation. The dependence of neuronal firing rate on the EI delay of the noisy background synaptic conductance suggests that individual excitatory pyramidal neurons are sensitive to the EI balance of the synaptic conductance. Therefore the statistical EI interactions encoded within the synaptic subthreshold membrane fluctuations are able to modulate neuronal firing properties.

Estimation of excitatory and inhibitory synaptic conductance variations in motoneurons during locomotor-like rhythmic activity

Voltage Clamp Errors During Estimation of Concurrent Excitatory and Inhibitory Synaptic Input to Neurons with Dendrites

Background: Dendritic integration is crucial in neuronal function, where excitatory and inhibitory signals are non-linearly summed to determine the generation of an action potential. Besides synaptic interactions, external electric fields also modulate neuronal activity. This study presents an extended differential equation that includes eigenmodes, providing detailed modeling of dendritic integration. Objectives: Develop and test a differential equation that predicts the generation or inhibition of action potentials in the axon, considering non-linearity and the effects of electric fields and eigenmodes under different stimulus conditions. Methods: The differential equation used is: CmdVmdt=−[gNa(Vm−ENa)+gK(Vm−EK)+gCa(Vm−ECa)]+∑igsyn,i(Vm−Esyn,i)+ϵextVm+α(Iion⋅Isyn)+βIext1+e−VmC_m frac{dV_m}{dt} = -left[ g_{Na}(V_m - E_{Na}) + g_{K}(V_m - E_{K}) + g_{Ca}(V_m - E_{Ca}) ight] + sum_{i} g_{syn,i}(V_m - E_{syn,i}) + epsilon_{ext} V_m + alpha (I_{ion} cdot I_{syn}) + eta frac{I_{ext}}{1 + e^{-V_m}}CmdtdVm=−[gNa(Vm−ENa)+gK(Vm−EK)+gCa(Vm−ECa)]+∑igsyn,i(Vm−Esyn,i)+ϵextVm+α(Iion⋅Isyn)+β1+e−VmIext The equation was numerically solved using the Euler method. Three conditions were simulated: increased excitatory synaptic conductance, increased inhibitory synaptic conductance, and increased influence of external electric fields. Results: Simulations under three distinct conditions showed the following findings: 1. Excitatory Synaptic Conductance: A moderate increase resulted in a rapid and pronounced depolarization, bringing the membrane potential closer to the firing threshold but still sub-threshold. 2. Inhibitory Synaptic Conductance: Increased inhibition caused continuous hyperpolarization, moving the membrane potential away from the firing threshold and stabilizing the cell. 3. External Electric Fields: Enhanced influence of electric fields provided moderate depolarization, indicating that while electric fields have significant influence, it is still controlled and insufficient to trigger an action potential. Conclusion: The results demonstrate that membrane potential depolarization is strongly influenced by changes in stimulus parameters. The inclusion of eigenmodes in the differential equation provides detailed and precise modeling of dendritic integration. Simulations showed how different stimulus conditions affect membrane potential depolarization. These results help better understand neuronal excitability modulation and open avenues for practical applications in theoretical neuroscience, including memory studies, synaptopathies, and other areas.

Neurons often receive massive concurrent bombardment of synaptic inhibition and excitation during functional network activity. This increases membrane conductance and causes fluctuations in membrane potential (Vm) and spike timing. The conductance increase is commonly attributed to synaptic conductance, but also includes the intrinsic conductances recruited during network activity. These two sources of conductance have contrasting dynamic properties at sub-threshold membrane potentials. Synaptic transmitter gated conductance changes abruptly and briefly with each presynaptic action potential. If the spikes arrive at random times the changes in synaptic conductance are therefore stochastic and rapid during intense network activity. In comparison, sub-threshold intrinsic conductances vary smoothly in time. In the present study this discrepancy is investigated using two conductance-based models: a (1) compartment model and a (2) compartment with realistic slow intrinsic conductances. We examine the effects of varying the relative contributions of non-fluctuating intrinsic conductance with fluctuating concurrent inhibitory and excitatory synaptic conductance. For given levels of correlation in the synaptic input we find that the magnitude of the membrane fluctuations uniquely determines the relative contribution of synaptic and intrinsic conductance. We also quantify how Vm-fluctuations vary with synaptic correlations for fixed ratios of synaptic and intrinsic conductance. Interestingly, the levels of Vm -fluctuations and conductance observed experimentally during functional network activity leave little room for intrinsic conductance to contribute. Even without intrinsic conductances the variance in Vm -fluctuations can only be explained by a high degree of correlated firing among presynaptic neurons.

Inferring network activity from synaptic noise

Unraveling synaptic interactions between excitatory and inhibitory interneurons within rhythmic neural circuits, such as central pattern generation (CPG) circuits for rhythmic motor behaviors, is critical for deciphering circuit interactions and functional architecture, which is a major problem for understanding how neural circuits operate. Here, we present a general method for extracting and separating patterns of inhibitory and excitatory synaptic conductances at high temporal resolution from single neuronal intracellular recordings in rhythmically active networks. These post-synaptic conductances reflect the combined synaptic inputs from the key interacting neuronal populations and can reveal the functional connectome of the active circuits. To illustrate the applicability of our analytic technique, we employ our method to infer the synaptic conductance profiles in identified rhythmically active interneurons within key microcircuits of the mammalian (mature rat) brainstem respiratory CPG and provide a perspective on how our approach can resolve the functional interactions and circuit organization of these interneuron populations. We demonstrate the versatility of our approach, which can be applied to any other rhythmic circuits where conditions allow for neuronal intracellular recordings.

The primary motor cortex (M1) plays a prominent role in the initiation and control of voluntary movements [1], but the cellular mechanisms regulating motor output are not well understood. Due to its direct link with behavior, M1 is an ideal platform to study how brain state and behavior are related to single neuron dynamics. Here we combined in vivo patch-clamp recordings and computational modeling to characterize the effects of behavioral state on the membrane potential dynamics and integrative properties of layer 5B pyramidal cells in the awake motor cortex. Furthermore, we injected a range of somatic EPSC-like current pulses during quiet wakefulness and movement to investigate how behavioral state affects input-output transformations in layer 5B excitatory neurons. We found that during quiet wakefulness L5B cells (n = 24) display moderate firing rates (5.6+-3.5 Hz) and depolarized membrane potential (-52.9+-4.4 mV). In superficial and deep cortical layers of M1, we show that the membrane potential during quiet wakefulness is characterized by slow fluctuations in the delta-band range (2-4 Hz), resulting in a large Vm standard deviation (3.5+-1.0 mV) that was similar in magnitude to that observed in L2/3 of the barrel cortex of awake mice [2]. By modeling the neuron as a single compartment leaky integrate and fire unit, we estimated that the sum of the average excitatory and inhibitory synaptic conductances were similar in magnitude to the leak conductance ( = 2.2 nS, 3.0 nS, Gl = 5.5 nS) and consistent with values measured in primary visual cortex of awake mice [3]. We classified L5B cells (the main output neurons in M1) into two functional different sub-populations, which either suppressed (3.4+-3.5 Hz, L5Bsupp, n = 10) or enhanced (12.7 +- 5.6 Hz, L5Benh, n = 14) their firing rates during movement. During movement, we observed a global suppression of slow Vm fluctuations resulting in a decrease of the Vm standard deviation in L5Bsupp cells (2.4 +-0.3 mV, p = 0.002). By injecting small somatic EPSC waveforms, we demonstrated that the decrease in Vm variance reduced the input sensitivity of L5Bsupp cells during movement. In contrast, L5Benh cells displayed a net depolarization (to -49.1+-4.2 mV, n = 14, p = 0.0006) due to a moderate increase in average excitatory conductance (ΔGe = +0.7 nS) and enhanced Vm fluctuations in the high frequency band (12-50 Hz, Figure 1B). Based on integrate-and-fire simulations, we estimate that during movement excitatory inputs to L5Benh cells increased by +30%, with enhanced fine time-scale correlations (pairwise correlation coefficient of the inputs is ~1% larger). These changes increased the input sensitivity of L5Benh neurons. Thus we find that behavioural state differentially regulates the membrane potential dynamics and integrative properties of discrete subpopulations of output neurons in M1. Our findings suggest that sensorimotor information is preferentially routed through distinct subpopulations of excitatory neurons during motor behavior. During movement motor output from M1 is controlled by the interplay between a global suppression of slow Vm fluctuations and selective increase in the rate and synchrony of excitatory synaptic inputs.

Cortical computations critically involve local neuronal circuits. The computations are often invariant across a cortical area yet are carried out by networks that can vary widely within an area according to its functional architecture. Here we demonstrate a mechanism by which orientation selectivity is computed invariantly in cat primary visual cortex across an orientation preference map that provides a wide diversity of local circuits. Visually evoked excitatory and inhibitory synaptic conductances are balanced exquisitely in cortical neurons and thus keep the spike response sharply tuned at all map locations. This functional balance derives from spatially isotropic local connectivity of both excitatory and inhibitory cells. Modeling results demonstrate that such covariation is a signature of recurrent rather than purely feed-forward processing and that the observed isotropic local circuit is sufficient to generate invariant spike tuning.

Bats and other mammals use interaural level differences (ILD) to estimate the direction of high-frequency sounds. To compute the ILD of a sound, independent of overall loudness, excitatory and inhibitory synaptic conductances (encoding the left and right amplitudes) are hypothesized to compete in the neurons of the lateral superior olive. Interestingly, this neural model can also accept power-law compressed amplitudes that can allow a much larger range of input signal levels, a common limitation in neural coding. This work demonstrates the use of square-root and cube-root compression with a neuromorphic VLSI neuron to expand the range of distances over which ILD can be used to estimate echo direction in a sonar system based on echolocating bats.

The long-delayed responses of neocortical neurons are thought to arise from cortical feedback activity that is related to sensory perception and cognition. The mechanism of neocortical late responses was investigated using multiple electrophysiological techniques and the findings indicate that it actually arises from the thalamus. In addition, during the late response, excitation and inhibition are balanced, but inhibition is dominant in patterning action potentials.

Gain Modulation from Background Synaptic Input

Neurons in the brain form thousands of connections, or synapses, with one another, allowing signals to pass from one cell to the next. To activate a neuron, a high enough activating signal or ‘action potential’ must be reached. However, the accepted view of signal transmission assumes that the great majority of synapses are too weak to activate neurons. This means that often simultaneous inputs from many neurons are required to trigger a single neuron’s activation. However, such coordination is likely unreliable as neurons can react differently to the same stimulus depending on the circumstances. An alternative way of transmitting signals has been reported in turtle brains, where impulses from a single neuron can trigger activity across a network of connections. Furthermore, these responses are reliably repeatable, activating the same neurons in the same order. Riquelme et al. set out to understand the mechanism that underlies this type of neuron activation using a mathematical model based on data from the turtle brain. These data showed that the neural network in the turtle’s brain had many weak synapses but also a few, rare, strong synapses. Simulating this neural network showed that those rare, strong synapses promote the signal’s reliability by providing a consistent route for the signal to travel through the network. The numerous weak synapses, on the other hand, have a regulatory role in providing flexibility to how the activation spreads. This combination of strong and weak connections produces a system that can reliably promote or stop the signal flow depending on the context. Riquelme et al.’s work describes a potential mechanism for how signals might travel reliably through neural networks in the brain, based on data from turtles. Experimental work will need to address whether strong connections play a similar role in other animal species, including humans. In the future, these results may be used as the basis to design new systems for artificial intelligence, building on the success of neural networks.

In this work, an expectation maximization (EM) algorithm is derived for maximum likelihood estimation of the autocorrelation function of a linear distortion channel as well as the level of additive noise, under the assumption that the source signal comes from a mixture of Gaussian sources. To facilitate parameter initialization in the EM algorithm, a correlation-matching based estimation algorithm is developed for the channel autocorrelation function. The proposed EM algorithm was evaluated on speech-derived simulated data of multiple autoregressive Gaussian sources and real speech of isolated digits under signal-to-noise ratios (SNRs) of 20 dB down to 0 dB. The algorithm is shown to produce convergent estimation results as well as estimates of signal statistics that lead to significantly improved classification accuracy under additive and convolutive noise conditions.