The processing speed of the brain depends on the ability of neurons to rapidly relay input changes. Prior theoretical and experimental studies of the time scale of population firing rate responses arrived at controversial conclusions, some advocating an ultra-fast response scale while others arguing for an inherent disadvantage of mean encoded signals for rapid detection of the stimulus onset. Here we assessed the time scale of population firing rate responses of neocortical neurons in experiments performed in the time domain and the frequency domain in vitro and in vivo. We show that populations of neocortical neurons can alter their firing rate within 1 millisecond in response to somatically delivered weak current signals presented on a fluctuating background. Signals with amplitudes of miniature postsynaptic currents can be robustly and rapidly detected in the population firing. We further show that population firing rate of neocortical neurons in vitro and in vivo can reliably encode weak signals varying at frequencies up to ~200–300 Hz, or ~50 times faster than the firing rate of individual neurons. These results provide coherent evidence for the ultra-fast, millisecond time-scale of cortical population responses. Notably, fast responses to weak stimuli are limited to the mean encoding. Rapid detection of current variance changes requires extraordinarily large signal amplitudes. Our study presents conclusive evidence showing that cortical neurons are capable of rapidly relaying subtle mean current signals. This provides a vital mechanism for the propagation of rate-coded information within and across brain areas.
Understanding of how neurons transform fluctuations of membrane potential, reflecting input activity, into spike responses, which communicate the ultimate results of single-neuron computation, is one of the central challenges for cellular and computational neuroscience. To study this transformation under controlled conditions, previous work has used a signal immersed in noise paradigm where neurons are injected with a current consisting of fluctuating noise that mimics on-going synaptic activity and a systematic signal whose transmission is studied. One limitation of this established paradigm is that it is designed to examine the encoding of only one signal under a specific, repeated condition. As a result, characterizing how encoding depends on neuronal properties, signal parameters, and the interaction of multiple inputs is cumbersome. Here we introduce a novel fully-defined signal mixture paradigm, which allows us to overcome these problems. In this paradigm, current for injection is synthetized as a sum of artificial postsynaptic currents (PSCs) resulting from the activity of a large population of model presynaptic neurons. PSCs from any presynaptic neuron(s) can be now considered as “signal”, while the sum of all other inputs is considered as “noise”. This allows us to study the encoding of a large number of different signals in a single experiment, thus dramatically increasing the throughput of data acquisition. Using this novel paradigm, we characterize the detection of excitatory and inhibitory PSCs from neuronal spike responses over a wide range of amplitudes and firing-rates. We show, that for moderately-sized neuronal populations the detectability of individual inputs is higher for excitatory than for inhibitory inputs during the 2–5 ms following PSC onset, but becomes comparable after 7–8 ms. This transient imbalance of sensitivity in favor of excitation may enhance propagation of balanced signals through neuronal networks. Finally, we discuss several open questions that this novel high-throughput paradigm may address.
The speed of computations in neocortical networks critically depends on the ability of populations of spiking neurons to rapidly detect subtle changes of the input and translate them into firing rate changes. However, high sensitivity to perturbations may lead to explosion of noise and increased energy consumption. Can neuronal networks reconcile the requirements for high sensitivity, operation in low-noise regime and constrained energy consumption? Using intracellular recordings in slices from rat visual cortex we show that layer 2/3 pyramidal neurons are highly sensitive to minor input perturbations. They can change their population firing rate in response to small artificial excitatory postsynaptic currents (EPSCs) immersed in fluctuating noise very quickly, within 2–2.5 ms. These quick responses were mediated by generation of new, additional action potentials, but also by shifting spikes into the response peak. In that latter case, the spike count increase during the peak and the decrease after the peak cancelled each other, thus producing quick responses without increases of total spike count and associated energy costs. The contribution of spikes from one or the other source depended on the EPSC timing relative to the waves of depolarization produced by on-going activity. Neurons responded by shifting spikes to EPSCs arriving at the beginning of a depolarization wave, but generated additional spikes in response to EPSCs arriving towards the end of a wave. We conclude that neuronal networks can combine high sensitivity to perturbations and operation in low-noise regime. Moreover, certain patterns of on-going activity favor this combination and energy-efficient computations.
rat neocortex; slices; population coding; response speed; signal detection time
Spike timing-dependent plasticity (STDP) and other conventional Hebbian-type plasticity rules are prone to produce runaway dynamics of synaptic weights. Once potentiated, a synapse would have higher probability to lead to spikes and thus to be further potentiated, but once depressed, a synapse would tend to be further depressed. The runaway synaptic dynamics can be prevented by precisely balancing STDP rules for potentiation and depression; however, experimental evidence shows a great variety of potentiation and depression windows and magnitudes. Here we show that modifications of synapses to layer 2/3 pyramidal neurons from rat visual and auditory cortices in slices can be induced by intracellular tetanization: bursts of postsynaptic spikes without presynaptic stimulation. Induction of these heterosynaptic changes depended on the rise of intracellular calcium, and their direction and magnitude correlated with initial state of release mechanisms. We suggest that this type of plasticity serves as a mechanism that stabilizes the distribution of synaptic weights and prevents their runaway dynamics. To test this hypothesis, we develop a cortical neuron model implementing both homosynaptic (STDP) and heterosynaptic plasticity with properties matching the experimental data. We find that heterosynaptic plasticity effectively prevented runaway dynamics for the tested range of STDP and input parameters. Synaptic weights, although shifted from the original, remained normally distributed and nonsaturated. Our study presents a biophysically constrained model of how the interaction of different forms of plasticity—Hebbian and heterosynaptic—may prevent runaway synaptic dynamics and keep synaptic weights unsaturated and thus capable of further plastic changes and formation of new memories.
The abilities of neuronal populations to encode rapidly varying stimuli and respond quickly to abrupt input changes are crucial for basic neuronal computations, such as coincidence detection, grouping by synchrony, and spike-timing-dependent plasticity, as well as for the processing speed of neuronal networks. Theoretical analyses have linked these abilities to the fast-onset dynamics of action potentials (APs). Using a combination of whole-cell recordings from rat neocortical neurons and computer simulations, we provide the first experimental evidence for this conjecture and prove its validity for the case of distal AP initiation in the axon initial segment (AIS), typical for cortical neurons. Neocortical neurons with fast-onset APs in the soma can phase-lock their population firing to signal frequencies up to ~300 – 400 Hz and respond within 1–2 ms to subtle changes of input current. The ability to encode high frequencies and response speed were dramatically reduced when AP onset was slowed by experimental manipulations or was intrinsically slow due to immature AP generation mechanisms. Multicompartment conductance-based models reproducing the initiation of spikes in the AIS could encode high frequencies only if AP onset was fast at the initiation site (e.g., attributable to cooperative gating of a fraction of sodium channels) but not when fast onset of somatic AP was produced solely by backpropagation. We conclude that fast-onset dynamics is a genuine property of cortical AP generators. It enables fast computations in cortical circuits that are rich in recurrent connections both within each region and across the hierarchy of areas.
Large amplitude slow waves are characteristic for the summary brain activity, recorded as electroencephalogram (EEG) or local field potentials (LFP), during deep stages of sleep and some types of anesthesia. Slow rhythm of the synchronized EEG reflects an alternation of active (depolarized, UP) and silent (hyperpolarized, DOWN) states of neocortical neurons. In neurons, involvement in the generalized slow oscillation results in a long-range synchronization of changes of their membrane potential as well as their firing. Here, we aimed at intracellular analysis of details of this synchronization. We asked which components of neuronal activity exhibit long-range correlations during the synchronized EEG? To answer this question, we made simultaneous intracellular recordings from two to four neocortical neurons in cat neocortex. We studied how correlated is the occurrence of active and silent states, and how correlated are fluctuations of the membrane potential in pairs of neurons located close one to the other or separated by up to 13 mm. We show that strong long-range correlation of the membrane potential was observed only (i) during the slow oscillation but not during periods without the oscillation, (ii) during periods which included transitions between the states but not during within-the-state periods, and (iii) for the low-frequency (<5 Hz) components of membrane potential fluctuations but not for the higher-frequency components (>10 Hz). In contrast to the neurons located several millimeters one from the other, membrane potential fluctuations in neighboring neurons remain strongly correlated during periods without slow oscillation. We conclude that membrane potential correlation in distant neurons is brought about by synchronous transitions between the states, while activity within the states is largely uncorrelated. The lack of the generalized fine-scale synchronization of membrane potential changes in neurons during the active states of slow oscillation may allow individual neurons to selectively engage in short living episodes of correlated activity—a process that may be similar to dynamical formation of neuronal ensembles during activated brain states.
intracellular recording; cat; sleep; synchrony
Generation of action potentials (APs) is a crucial step in neuronal information processing. Existing biophysical models for AP generation almost universally assume that individual voltage-gated sodium channels operate statistically independently, and their avalanche-like opening that underlies AP generation is coordinated only through the transmembrane potential. However, biological ion channels of various types can exhibit strongly cooperative gating when clustered. Cooperative gating of sodium channels has been suggested to explain rapid onset dynamics and large threshold variability of APs in cortical neurons. It remains however unknown whether these characteristic properties of cortical APs can be reproduced if only a fraction of channels express cooperativity, and whether the presence of cooperative channels has an impact on encoding properties of neuronal populations. To address these questions we have constructed a conductance-based neuron model in which we continuously varied the size of a fraction of sodium channels expressing cooperativity and the strength of coupling between cooperative channels . We show that starting at a critical value of the coupling strength , the activation curve of sodium channels develops a discontinuity at which opening of all coupled channels becomes an all-or-none event, leading to very rapid AP onsets. Models with a small fraction, , of strongly cooperative channels generate APs with the most rapid onset dynamics. In this regime APs are triggered by simultaneous opening of the cooperative channel fraction and exhibit a pronounced biphasic waveform often observed in cortical neurons. We further show that presence of a small fraction of cooperative Na+ channels significantly improves the ability of neuronal populations to phase-lock their firing to high frequency input fluctuation. We conclude that presence of a small fraction of strongly coupled sodium channels can explain characteristic features of cortical APs and has a functional impact of enhancing the spike encoding of rapidly varying signals.
Deep anesthesia is commonly used as a model of slow-wave sleep (SWS). Ketamine-xylazine anesthesia reproduces the main features of sleep slow oscillation: slow, large amplitude waves in field potential, which are generated by the alternation of hyperpolarized and depolarized states of cortical neurons. However, direct quantitative comparison of field potential and membrane potential fluctuations during natural sleep and anesthesia is lacking, so it remains unclear how well the properties of sleep slow oscillation are reproduced by the ketamine-xylazine anesthesia model. Here, we used field potential and intracellular recordings in different cortical areas in the cat, to directly compare properties of slow oscillation during natural sleep and ketamine-xylazine anesthesia. During SWS cortical activity showed higher power in the slow/delta (0.1-4 Hz) and spindle (8-14 Hz) frequency range, while under anesthesia the power in the gamma band (30-100 Hz) was higher. During anesthesia, slow waves were more rhythmic and more synchronous across the cortex. Intracellular recordings revealed that silent states were longer and the amplitude of membrane potential around transition between active and silent states was bigger under anesthesia. Slow waves were largely uniform across cortical areas under anesthesia, but in SWS they were most pronounced in associative and visual areas, but smaller and less regular in somatosensory and motor cortices. We conclude that although the main features of the slow oscillation in sleep and anesthesia appear similar, multiple cellular and network features are differently expressed during natural SWS as compared to ketamine-xylazine anesthesia.
Sleep; oscillations; synchrony; intracellular; anesthesia; ketamine-Xylazine
Sensory and cognitive processing relies on the concerted activity of large populations of neurons. The advent of modern experimental techniques like two-photon population calcium imaging makes it possible to monitor the spiking activity of multiple neurons as they are participating in specific cognitive tasks. The development of appropriate theoretical tools to quantify and interpret the spiking activity of multiple neurons, however, is still in its infancy. One of the simplest and widely used measures of correlated activity is the pairwise correlation coefficient. While spike correlation coefficients are easy to compute using the available numerical toolboxes, it has remained largely an open question whether they are indeed a reliable measure of synchrony. Surprisingly, despite the intense use of correlation coefficients in the design of synthetic spike trains, the construction of population models and the assessment of the synchrony level in live neuronal networks very little was known about their computational properties. We showed that many features of pairwise spike correlations can be studied analytically in a tractable threshold model. Importantly, we demonstrated that under some circumstances the correlation coefficients can vanish, even though input and also pairwise spike cross correlations are present. This finding suggests that the most popular and frequently used measures can, by design, fail to capture the neuronal synchrony.
spike correlations; count correlations; synchrony; correlation coefficient
Slow-wave sleep is characterized by spontaneous alternations of activity and silence in corticothalamic networks, but the causes of transition from silence to activity remain unknown. We investigated local mechanisms underlying initiation of activity, using simultaneous multisite field potential, multiunit recordings, and intracellular recordings from 2 to 4 nearby neurons in naturally sleeping or anesthetized cats. We demonstrate that activity may start in any neuron or recording location, with tens of milliseconds delay in other cells and sites. Typically, however, activity originated at deep locations, then involved some superficial cells, but appeared later in the middle of the cortex. Neuronal firing was also found to begin, after the onset of active states, at depths that correspond to cortical layer V. These results support the hypothesis that switch from silence to activity is mediated by spontaneous synaptic events, whereby any neuron may become active first. Due to probabilistic nature of activity onset, the large pyramidal cells from deep cortical layers, which are equipped with the most numerous synaptic inputs and large projection fields, are best suited for switching the whole network into active state.
intracellular; intrinsic; oscillations; sleep; synaptic; synchronization
Concerted neural activity can reflect specific features of sensory stimuli or behavioral tasks. Correlation coefficients and count correlations are frequently used to measure correlations between neurons, design synthetic spike trains and build population models. But are correlation coefficients always a reliable measure of input correlations? Here, we consider a stochastic model for the generation of correlated spike sequences which replicate neuronal pairwise correlations in many important aspects. We investigate under which conditions the correlation coefficients reflect the degree of input synchrony and when they can be used to build population models. We find that correlation coefficients can be a poor indicator of input synchrony for some cases of input correlations. In particular, count correlations computed for large time bins can vanish despite the presence of input correlations. These findings suggest that network models or potential coding schemes of neural population activity need to incorporate temporal properties of correlated inputs and take into consideration the regimes of firing rates and correlation strengths to ensure that their building blocks are an unambiguous measures of synchrony.
spike correlations; count correlations; population models; synchrony; correlation coefficient
Ongoing learning continuously shapes the distribution of neurons’ synaptic weights in a system with plastic synapses. Plasticity may change the weights of synapses that were active during the induction—homosynaptic changes, but also may change synapses not active during the induction—heterosynaptic changes. Here we will argue, that heterosynaptic and homosynaptic plasticity are complementary processes, and that heterosynaptic plasticity might accompany homosynaptic plasticity induced by typical pairing protocols. Synapses are not uniform in their susceptibility for plastic changes, but have predispositions to undergo potentiation or depression, or not to change. Predisposition is one of the factors determining the direction and magnitude of homo- and heterosynaptic changes. Heterosynaptic changes which take place according to predispositions for plasticity may provide a useful mechanism(s) for homeostasis of neurons’ synaptic weights and extending the lifetime of memory traces during ongoing learning in neuronal networks.
Synaptic plasticity; Homosynaptic; Heterosynaptic; Induction; Synaptic weight normalization; Synaptic homeostasis
The generation of action potentials (APs) is a key process in the operation of nerve cells and the communication between neurons. Action potentials in mammalian central neurons are characterized by an exceptionally fast onset dynamics, which differs from the typically slow and gradual onset dynamics seen in identified snail neurons. Here we describe a novel method of analysis which provides a quantitative measure of the onset dynamics of action potentials. This method captures the difference between the fast, step-like onset of APs in rat neocortical neurons and the gradual, exponential-like AP onset in identified snail neurons. The quantitative measure of the AP onset dynamics, provided by the method, allows us to perform quantitative analyses of factors influencing the dynamics.