Network dynamics and synchronous activity in cultured cortical neurons

Neurons extracted from specific areas of the Central Nervous System (CNS), such as the hippocampus, the cortex and the spinal cord, can be cultured in vitro and coupled with a micro-electrode array (MEA) for months. After a few days, neurons connect each other with functionally active synapses, forming a random network and displaying spontaneous electrophysiological activity. In spite of their simplified level of organization, they represent an useful framework to study general information processing properties and specific basic learning mechanisms in the nervous system. These experimental preparations show patterns of collective rhythmic activity characterized by burst and spike firing. The patterns of electrophysiological activity may change as a consequence of external stimulation (i.e., chemical and/or electrical inputs) and by partly modifying the "randomness" of the network architecture (i.e., confining neuronal sub-populations in clusters with micro-machined barriers). In particular we investigated how the spontaneous rhythmic and synchronous activity can be modulated or drastically changed by focal electrical stimulation, pharmacological manipulation and network segregation. Our results show that burst firing and global synchronization can be enhanced or reduced; and that the degree of synchronous activity in the network can be characterized by simple parameters such as cross-correlation on burst events.     

The dynamics of a neuronal culture of dissociated cortical neurons of neonatal rats

Neuronal networks of dissociated cortical neurons from neonatal rats were cultured over a multielectrode dish with 64 active sites, which were used both for recording the electrical activity and for stimulation. After about 4 weeks of culture, a dense network of neurons had developed and their electrical activity was studied. When a brief voltage pulse was applied to one extracellular electrode, a clear electrical response was evoked over almost the entire network. When a strong voltage pulse was used, the response was composed of an early phase, terminating within 25 ms, and a late phase which could last several hundreds of milliseconds. Action potentials evoked during the early phase occurred with a precise timing with a small jitter and the electrical activity initiated by a localized stimulation diffused significantly over the network. In contrast, the late phase was characterized by the occurrence of clusters of electrical activity with significant spatio-temporal fluctuations. The late phase was suppressed by adding small amounts of d(−)-2-amino-5-phosphonovaleric acid to the extracellular medium, or by increasing the amount of extracellular Mg²⁺. The electrical activity of the network was substantially increased by the addition of bicuculline to the extracellular medium. The results presented here show that the neuronal network may exist in two different dynamical states: one state in which the neuronal network behaves as a non-chaotic deterministic system and another state where the system exhibits large spatio-temporal fluctuations, characteristic of stochastic or chaotic systems. Received: 8 June 1999 / Accepted in revised form: 10 January 2000     

Spike generating dynamics and the conditions for spike-time precision in cortical neurons

Temporal precision of spiking response in cortical neurons has been a subject of intense debate. Using a canonical model of spike generation, we explore the conditions for precise and reliable spike timing in the presence of Gaussian white noise. In agreement with previous results we find that constant stimuli lead to imprecise timing, while aperiodic stimuli yield precise spike timing. Under constant stimulus the neuron is a noise perturbed oscillator, the spike times follow renewal statistics and are imprecise. Under an aperiodic stimulus sequence, the neuron acts as a threshold element; the firing times are precisely determined by the dynamics of the stimulus. We further study the dependence of spike-time precision on the input stimulus frequency and find a non-linear tuning whose width can be related to the locking modes of the neuron. We conclude that viewing the neuron as a non-linear oscillator is the key for understanding spike-time precision.     

Firing responses of bursting neurons with delayed feedback

Thalamic neurons, which play important roles in the genesis of rhythmic activities of the brain, show various bursting behaviors, particularly modulated by complex thalamocortical feedback via cortical neurons. As a first step to explore this complex neural system and focus on the effects of the feedback on the bursting behavior, a simple loop structure delayed in time and scaled by a coupling strength is added to a recent mean-field model of bursting neurons. Depending on the coupling strength and delay time, the modeled neurons show two distinct response patterns: one entrained to the unperturbed bursting frequency of the neurons and one entrained to the resonant frequency of the loop structure. Transitions between these two patterns are explored in the model’s parameter space via extensive numerical simulations. It is found that at a fixed loop delay, there is a critical coupling strength at which the dominant response frequency switches from the unperturbed bursting frequency to the loop-induced one. Furthermore, alternating occurrence of these two response frequencies is observed when the delay varies at fixed coupling strength. The results demonstrate that bursting is coupled with feedback to yield new dynamics, which will provide insights into such effects in more complex neural systems.     

dynamics of responsiveness of cortical neurons towards the repeated combined action of L-glutamate and acetylcholine

The probability, direction, and intensity of changes in mean firing rate of spike activity elicited by application of L-glutamate (Gl) and acetylcholine (ACh) have been compared in a series of successive responses of neuronal units in the sensorimotor cortex of unanesthetized rats; delayed paired application of the above transmitters was used. It is shown that the neurons significantly more often decrease their excitatory responses to the associated action of transmitters, and that responses are not enhanced. In the population of neurons studied, decreases in responsiveness with respect to Gl and ACh occurred with the same probability and in similar fashion over the whole period of testing (60 applications). After long-term transmitter application, potentiation became more typical of the responses to Gl than to ACh.Translated from Neirofiziologiya, Vol. 25, No. 2, pp. 94–97, March–April, 1993.     

Characteristics of cortical inhibitory neurons

Spikes were recorded extracellularly and IPSPs intracellularly from auditory cortical neurons of cats immobilized with D-tubocurarine in response to stimulation of geniculo-cortical fibers. Fibers whose stimulation induces IPSPs in auditory cortical neurons mainly have low thresholds. When two stimuli, each of which separately evoked an IPSP of maximal amplitude, were applied to them the shortest interval at which the second stimulus evoked an effect was 2.5–3 msec. This effect consisted of an increase in the duration of the integral IPSP, the amplitude of which either remained unchanged or increased under these circumstances by only 5–10%. The interval at which a separate IPSP appeared in response to the second stimulus depended on the duration of the ascending phase of the IPSP and varied from 4 to 22 msec for different neurons. The amplitude of the second IPSP in this case depended on the interval between stimuli. Under moderately deep pentobarbital anesthesia the number of neurons responding to stimulation of the geniculo-cortical fibers by spikes fell sharply but the number of neurons responding by primary IPSPs remained almost unchanged. Under very deep pentobarbital anesthesia, when spike responses of the cortical neurons completely disappeared, the IPSPs also were completely suppressed. It is concluded that inhibitory neurons of the auditory cortex are excited by thick low-threshold fibers, they have a short refractory period, and they are resistant to the narcotic action of pentobarbital.     

Regulatory dynamics of synthetic gene networks with positive feedback

Biological processes are governed by complex networks ranging from gene regulation to signal transduction. Positive feedback is a key element in such networks. The regulation enables cells to adopt multiple internal expression states in response to a single external input signal. However, past works lacked a dynamical aspect of this system. To address the dynamical property of the positive feedback system, we employ synthetic gene circuits in Escherichia coli to measure the rise-time of both the no-feedback system and the positive feedback system. We show that the kinetics of gene expression is slowed down if the gene regulatory system includes positive feedback. We also report that the transition of gene switching behaviors from the hysteretic one to the graded one occurs. A mathematical model based on the chemical reactions shows that the response delay is an inherited property of the positive feedback system. Furthermore, with the aid of the phase diagram, we demonstrate the decline of the feedback activation causes the transition of switching behaviors. Our findings provide a further understanding of a positive feedback system in a living cell from a dynamical point of view.     

Excitotoxicity-related endocytosis in cortical neurons

Recent studies showed that endocytosis is enhanced in neurons exposed to an excitototoxic stimulus. We here confirm and analyze this new phenomenon using dissociated cortical neuronal cultures. NMDA-induced uptake (FITC-dextran or FITC or horseradish peroxidase) occurs in these cultures and is due to endocytosis, not to cell entry through damaged membranes; it requires an excitotoxic dose of NMDA and is dependent on extracellular calcium, but occurs early, while the neuron is still intact and viable. It involves two components, NMDA-induced and constitutive, with different characteristics. Neither component involves specific binding of the endocytosed molecules to a saturable receptor. Strikingly, molecules internalized by the NMDA-induced component are targeted to neuronal nuclei. This component, but not the constitutive one, is blocked by a c-Jun N-terminal protein kinase inhibitor. In conclusion, an excitotoxic dose of NMDA triggers c-Jun N-terminal protein kinase-dependent endocytosis in cortical neuronal cultures, providing an in vitro model of the excitotoxicity-induced endocytosis reported in intact tissues.     

Boolean dynamics of biological networks with multiple coupled feedback loops

Boolean networks have been frequently used to study the dynamics of biological networks. In particular, there have been various studies showing that the network connectivity and the update rule of logical functions affect the dynamics of Boolean networks. There has been, however, relatively little attention paid to the dynamical role of a feedback loop, which is a circular chain of interactions between Boolean variables. We note that such feedback loops are ubiquitously found in various biological systems as multiple coupled structures and they are often the primary cause of complex dynamics. In this article, we investigate the relationship between the multiple coupled feedback loops and the dynamics of Boolean networks. We show that networks have a larger proportion of basins corresponding to fixed-point attractors as they have more coupled positive feedback loops, and a larger proportion of basins for limit-cycle attractors as they have more coupled negative feedback loops.     

Calcium imaging of cortical networks dynamics

Studies relating spontaneous network activities to cognitive processes and/or brain disorders constitute a recently expanding field of investigation. They are mostly based either on cellular recordings--usually performed in pharmacologically induced oscillations in brain slices--or on multi-cellular recordings using tetrodes or multiple electrodes. However, these research strategies cannot link the electrical recordings with morphological characterization of the neurons. The progress made in imaging techniques allows for the first time to have simultaneously a dynamic and global characterization of network activity and to determine the single-cell properties of the unitary microcircuits involved in this activity.     

Rabbit visual cortical neurons with simple and complex receptive fields

Receptive fields of neurons of the rabbit visual cortex selective for stimulus orientation were investigated. These receptive fields were less well differentiated than those of the analogous neurons of the cat visual cortex (large in size and circular in shape). Two mechanisms of selectivity for stimulus orientation were observed: inhibition between on and off zones of the receptive field (sample type) and oriented lateral inhibition within the same zone of the receptive field (complex type). Lateral inhibition within the same zone of the receptive field also took place in unselective neurons; "complex" selective neurons differed from them in the orientation of this inhibition. A combination of both mechanisms was possible in the receptive field of the same neuron. It is suggested that both simple and complex receptive fields are derivatives of unselective receptive fields and that "complex" neurons are not the basis for a higher level of analysis of visual information than in "simple" neurons.A. N. Severtsov Institute of Evolutionary Morphology and Ecology of Animals, Academy of Sciences of the USSR, Moscow. Translated from Neirofiziologiya, Vol. 10, No. 1, pp. 13–21, January–February, 1978.     

Cooperative nonlinearities in auditory cortical neurons

Cortical receptive fields represent the signal preferences of sensory neurons. Receptive fields are thought to provide a representation of sensory experience from which the cerebral cortex may make interpretations. While it is essential to determine a neuron's receptive field, it remains unclear which features of the acoustic environment are specifically represented by neurons in the primary auditory cortex (AI). We characterized cat AI spectrotemporal receptive fields (STRFs) by finding both the spike-triggered average (STA) and stimulus dimensions that maximized the mutual information between response and stimulus. We derived a nonlinearity relating spiking to stimulus projection onto two maximally informative dimensions (MIDs). The STA was highly correlated with the first MID. Generally, the nonlinearity for the first MID was asymmetric and often monotonic in shape, while the second MID nonlinearity was symmetric and nonmonotonic. The joint nonlinearity for both MIDs revealed that most first and second MIDs were synergistic and thus should be considered conjointly. The difference between the nonlinearities suggests different possible roles for the MIDs in auditory processing.     

Extra DNA in forebrain cortical neurons

Combined cytochemical and biochemical techniques show that neurons from the forebrain cortex of various mammals (rat, mouse, and rabbit) contain near, but not full, 4c DNA levels (c, DNA content of haploid chromosome set). This extra DNA is predominantly synthesized post-natally. More specifically, in rats a wave of DNA synthesis starts a few hours before birth and extends well into the post-natal period, levelling off after 30 days. Density labelling experiments using [5-³H]-bromo-2′-deoxyuridine (BUdR) suggest that the DNA synthesis proceeds semiconservatively, with the prenatally formed DNA serving as a template for post-natal strand replication. Although all three mammalian DNA polymerases (α, β, and γ) can be detected in the cortical neurons of young rats their developmental course does not allow one to unambiguously identify the enzyme(s) responsible for the observed DNA increase. Density gradient centrifugations of neuronal DNA post-natally labelled with [³H]thymidine give no indication of a preferential enrichment of defined segments of the genome. In spite of this, the present data do not rule out the possibility that functionally important sequences might be selectively replicated.     

On the dynamics of electrically-coupled neurons with inhibitory synapses

We study the dynamics and bifurcations of noise-free neurons coupled by gap junctions and inhibitory synapses, using both delayed delta functions and alpha functions to model the latter. We focus on the case of two cells, as in the studies of Chow and Kopell (2000) and Lewis and Rinzel (2003), but also show that stable asynchronous splay states exist for globally coupled networks of N cells dominated by subthreshold electrical coupling. Our results agree with those of Lewis and Rinzel (2003) in the weak coupling range, but our Poincaré map analysis yields more information about global behavior and domains of attraction, and we show that the explicit discontinuous maps derived using delayed delta functions compare well with the continuous history-dependent, implicitly-defined maps derived from alpha functions. We find that increased bias currents, super-threshold electrical coupling and synaptic delays promote synchrony, while sub-threshold electrical coupling and fast synapses promote asynchrony. We compare our analytical results with simulations of an ionic current model of spiking cells, and briefly discuss implications for stimulus response modes of locus coeruleus and for central pattern generators. Action Editor: F. Skinner     

Representation of binocular surfaces by cortical neurons

Useful representations of the three-dimensional (3D) world go beyond assigning depth to individual points, building maps of surfaces and shapes. Studies in a wide range of extrastriate cortical areas have shown that single neurons show selective responses to 3D surfaces. The extent to which this advances the representation beyond that provided by the earliest binocular signals requires careful evaluation. We conclude that current data are not sufficient to identify distinctive contributions from different cortical areas to the binocular representation of 3D surfaces.     

Monosynaptic inhibitory postsynaptic potentials of cortical neurons

Monopolar intracortical stimulation of the auditory cortex was carried out in cats immobilized with D-tubocurarine. A macroelectrode (tip diameter 100 µ) or a microelectrode (tip diameter 10–15 µ) was used for stimulation. In both cases, besides excitatory responses, primary IPSPs with latent periods of 0.4–1.2 and 1.4–6.0 msec were recorded in cortical neurons close to the point of stimulation. The first group of IPSPs are considered to be generated in response to direct stimulation of bodies or axons of inhibitory cortical neurons, i.e., monosynaptically. The amplitude of these IPSPs varied in different neurons from 3 to 15 mV, and their duration from 4 to 150 msec. Additional later inhibitory responses were superposed on many of them. Of the IPSPs generated in auditory cortical neurons in response to stimulation of geniculocortical fibers 1.5% had a latency of 0.8–1.3 msec. They also are assumed to be monosynaptic. It is concluded that the duration of synaptic delay of IPSPs in cortical neurons and spinal motoneurons is the same, namely 0.3–0.4 msec. Axons of auditory cortical inhibitory neurons may be 1.5 mm long. The velocity of impulse conduction along these axons is 1.6–2.8 m/sec. The genesis of some special features of IPSPs of cortical neurons is discussed.A. A. Bogomolets Institute of Physiology, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Neirofiziologiya, Vol. 7, No. 5, pp. 458–467, September–October, 1975.     

Viewing lip forms: cortical dynamics

Viewing other persons' actions automatically activates brain areas belonging to the mirror-neuron system (MNS) assumed to link action execution and observation. We followed, by magnetoencephalographic cortical dynamics, subjects who observed still pictures of lip forms, on-line imitated them, or made similar forms in a self-paced manner. In all conditions and in both hemispheres, cortical activation progressed in 20-70 ms steps from the occipital cortex to the superior temporal region (where the strongest activation took place), the inferior parietal lobule, and the inferior frontal lobe (Broca's area), and finally, 50-140 ms later, to the primary motor cortex. The signals of Broca's area and motor cortex were significantly stronger during imitation than other conditions. These results demonstrate that still pictures, only implying motion, activate the human MNS in a well-defined temporal order.