Experimental analysis of neuronal dynamics in cultured cortical networks and transitions between different patterns of activity

A general method for developing data-based, stochastic nonlinear models of neurons by means of extended functional series expansions was applied to neural activities of pigeon auditory nerve fibers responding to Gaussian white noise stimuli. To determine Wiener series representations of the investigated neurons the fast orthogonal search algorithm was used. The results suggest that nonlinearities are only instantaneous and that the signal transduction of the investigated sensory system can be described by cascades of dynamic linear and static nonlinear devices. However, only slight improvements result from the nonlinear terms. Considerable improvements are, nevertheless, possible by generalizing the ordinary Wiener series, so that prior neural activity can be taken into account. These extended series were used to develop stochastic models of spiking neurons. The models are able to generate realistic interspike interval distributions and rate-intensity functions. Finally, it will be shown that the irregularity in real and modeled action potential trains has advantages concerning the decoding of neural responses. Received: 16 April 1996 / Accepted in revised form: 23 October 1996     

Statistical analysis and stochastic modeling of neuronal spike-train activity

Considerable attention has been paid in the literature to the development of biologically interpretable mathematical models of spontaneous stationary neuronal spike-train activity. However, these models work poorly in applied spike-train analysis. In order to improve matters, we need (1) to select appropriate statistical techniques, and (2) to fit the models into the semialternating renewal (SAR) framework. In the present study, biologically interpretable models, the SAR framework, and relevant statistical techniques are integrated in a form which suits the practical research worker. The theory is illustrated with reference to the analysis of a number of spike trains.     

An analysis of spontaneous human cortical EEG activity to odours

Using single trial presentation of odours, mapping of spontaneousEEG was made in naive subjects. Systematic increases in EEGamplitudes for alpha (8–13 Hz) frequency were shown forthe odours used and discrimination of odours was shown by specificelectrodes. These were mainly in the area bounded by International10/20 scalp locations CP1, PZ, CP2, TCP2 and C4. It was alsoshown that EEG recordings from more anterior electrodes couldbe related to psychometric responses. The findings showed thatstatistically reliable electrical amplitudes to odour presentationswere discernible in the noisy EEG environment on the surfaceof the brain.     

Epidermal growth factor induces oxidative neuronal injury in cortical culture

Recently, we have demonstrated that certain neurotrophic factors can induce oxidative neuronal necrosis by acting at the cognate tyrosine kinase-linked receptors. Epidermal growth factor (EGF) has neurotrophic effects via the tyrosine kinase-linked EGF receptor (EGFR), but its neurotoxic potential has not been studied. Here, we examined this possibility in mouse cortical culture. Exposure of cortical cultures to 1-100 ng/ml EGF induced gradually developing neuronal death, which was complete in 48-72 h; no injury to astrocytes was noted. Electron microscopic findings of EGF-induced neuronal death were consistent with necrosis; severe mitochondrial swelling and disruption of cytoplasmic membrane occurred, whereas nuclei appeared relatively intact. The EGF-induced neuronal death was accompanied by increased free radical generation and blocked by the anti-oxidant Trolox. Suggesting mediation by the EGFR, an EGFR tyrosine kinase-specific inhibitor, C56, attenuated EGF-induced neuronal death. In addition, inhibitors of extracellular signal-regulated protein kinase 1/2 (Erk-1/2) (PD98056), protein kinase A (H89), and protein kinase C (GF109203X) blocked EGF-induced neuronal death. A p38 mitogen-activated protein kinase inhibitor (SB203580) or glutamate antagonists (MK-801 and 6-cyano-7-nitroquinoxaline-2,3-dione) showed no protective effect. The present results suggest that prolonged activation of the EGFR may trigger oxidative neuronal injury in central neurons.     

Lateralization of perception of short time intervals and cortical evoked activity in man

Recognition of short time intervals (10, 60, and 180 ms) between visual stimuli presented to the left or right hemisphere was studied in adult healthy people. The interval of 180 ms is recognized better than that of 10 or 60 ms. Learning with repeated tests with 180 ms intervals proceeds better than that with short intervals. The predominance of the left hemisphere has been revealed only for perception of 10 ms interval. The other time intervals asymmetry is not observed. It is suggested that the left hemisphere is predominant in estimation of short (less than 60 ms) time intervals. In formation of time nervous model a significant role is played by local activation of the cortical zone where the standard stimulus is addressed.     

Experimental generation and computational modeling of intracellular pH gradients in cardiac myocytes

It is often assumed that pH(i) is spatially uniform within cells. A double-barreled microperfusion system was used to apply solutions of weak acid (acetic acid, CO(2)) or base (ammonia) to localized regions of an isolated ventricular myocyte (guinea pig). A stable, longitudinal pH(i) gradient (up to 1 pH(i) unit) was observed (using confocal imaging of SNARF-1 fluorescence). Changing the fractional exposure of the cell to weak acid/base altered the gradient, as did changing the concentration and type of weak acid/base applied. A diffusion-reaction computational model accurately simulated this behavior of pH(i). The model assumes that H(i)(+) movement occurs via diffusive shuttling on mobile buffers, with little free H(+) diffusion. The average diffusion constant for mobile buffer was estimated as 33 x 10(-7) cm(2)/s, consistent with an apparent H(i)(+) diffusion coefficient, D(H)(app), of 14.4 x 10(-7) cm(2)/s (at pH(i) 7.07), a value two orders of magnitude lower than for H(+) ions in water but similar to that estimated recently from local acid injection via a cell-attached glass micropipette. We conclude that, because H(i)(+) mobility is so low, an extracellular concentration gradient of permeant weak acid readily induces pH(i) nonuniformity. Similar concentration gradients for weak acid (e.g., CO(2)) occur across border zones during regional myocardial ischemia, raising the possibility of steep pH(i) gradients within the heart under some pathophysiological conditions.     

On the dynamics of the spontaneous activity in neuronal networks

Most neuronal networks, even in the absence of external stimuli, produce spontaneous bursts of spikes separated by periods of reduced activity. The origin and functional role of these neuronal events are still unclear. The present work shows that the spontaneous activity of two very different networks, intact leech ganglia and dissociated cultures of rat hippocampal neurons, share several features. Indeed, in both networks: i) the inter-spike intervals distribution of the spontaneous firing of single neurons is either regular or periodic or bursting, with the fraction of bursting neurons depending on the network activity; ii) bursts of spontaneous spikes have the same broad distributions of size and duration; iii) the degree of correlated activity increases with the bin width, and the power spectrum of the network firing rate has a 1/f behavior at low frequencies, indicating the existence of long-range temporal correlations; iv) the activity of excitatory synaptic pathways mediated by NMDA receptors is necessary for the onset of the long-range correlations and for the presence of large bursts; v) blockage of inhibitory synaptic pathways mediated by GABA(A) receptors causes instead an increase in the correlation among neurons and leads to a burst distribution composed only of very small and very large bursts. These results suggest that the spontaneous electrical activity in neuronal networks with different architectures and functions can have very similar properties and common dynamics.     

SYCAMORE--a systems biology computational analysis and modeling research environment

SYCAMORE is a browser-based application that facilitates construction, simulation and analysis of kinetic models in systems biology. Thus, it allows e.g. database supported modelling, basic model checking and the estimation of unknown kinetic parameters based on protein structures. In addition, it offers some guidance in order to allow non-expert users to perform basic computational modelling tasks. AVAILABILITY: SYCAMORE is freely available for academic use at http://sycamore.eml.org. Commercial users may acquire a license. CONTACT: ursula.kummer@bioquant.uni-heidelberg.de.     

Exploring the spectrum of dynamical regimes and timescales in spontaneous cortical activity

Rhythms at slow (<1 Hz) frequency of alternating Up and Down states occur during slow-wave sleep states, under deep anaesthesia and in cortical slices of mammals maintained in vitro. Such spontaneous oscillations result from the interplay between network reverberations nonlinearly sustained by a strong synaptic coupling and a fatigue mechanism inhibiting the neurons firing in an activity-dependent manner. Varying pharmacologically the excitability level of brain slices we exploit the network dynamics underlying slow rhythms, uncovering an intrinsic anticorrelation between Up and Down state durations. Besides, a non-monotonic change of Down state duration is also observed, which shrinks the distribution of the accessible frequencies of the slow rhythms. Attractor dynamics with activity-dependent self-inhibition predicts a similar trend even when the system excitability is reduced, because of a stability loss of Up and Down states. Hence, such cortical rhythms tend to display a maximal size of the distribution of Up/Down frequencies, envisaging the location of the system dynamics on a critical boundary of the parameter space. This would be an optimal solution for the system in order to display a wide spectrum of dynamical regimes and timescales.     

Spatial range of autocrine signaling: modeling and computational analysis

Autocrine loops formed by growth factors and their receptors have been identified in a large number of developmental, physiological, and pathological contexts. In general, the spatially distributed and recursive nature of autocrine signaling systems makes their experimental analysis, and often even their detection, very difficult. Here, we combine Brownian motion theory, Monte Carlo simulations, and reaction-diffusion models to analyze the spatial operation of autocrine loops. Within this modeling framework, the ability of autocrine cells to recapture the endogenous ligand and the distances traveled by autocrine ligands are explicitly related to ligand diffusion coefficients, density of surface receptors, ligand secretion rate, and rate constants of ligand binding and endocytic internalization. Applying our models to study autocrine loops in the epidermal growth factor receptor system, we find that autocrine loops can be highly localized--even at the level of a single cell. We demonstrate how the variations in molecular and cellular parameters may "tune" the spatial range of autocrine signals over several orders of magnitude: from microns to millimeters. We argue that this versatile regulation of the spatial range of autocrine signaling enables autocrine cells to perceive a broad spectrum of environmental information.     

Effects of memory-modulating neuropeptides on spontaneous and evoked cortical electrical activity in rabbits

Encephalographic correlates of behavioral activity were demonstrated for oligopeptides belonging to the group of memory neuromodulators and of a similar nature: arginine-vasopressin, corticotrophic fragment ACTH_4–7 and its four analogs, leu-enkephalin, and a melanostatin analog. The compounds activated the EEG, the number of low-frequency components in the spectrum was reduced and the number of high-frequency components increased, and the amplitude of the waves was reduced in most cases, The results of a study of the effect of ACTH_4–7 and vasopressin on the parameters of the visual global evoked potential show that, depending on their dose, neuropeptides can reduce the latent period and increase the amplitude of the global potential or, conversely, in a substantially increasing dose they may inhibit these parameters. Effects of vasopressin are long-term in nature and may continue for weeks, whereas the effect of ACTH fragments and leuenkephalin are limited to a few hours.S. M. Kirov Military Medical Academy, Leningrad. Translated from Neirofiziologiya, Vol. 14, No. 6, pp. 578–584, November–December, 1982.     

Insulin-induced oxidative neuronal injury in cortical culture: mediation by induced N-methyl-D-aspartate receptors

While effectively attenuating neuronal apoptosis in mouse cortical culture, insulin paradoxically induced neuronal necrosis with 48 h of exposure. The insulin neurotoxicity was blocked by an antioxidant but not by caspase inhibitors. Exposure to insulin led to tyrosine phosphorylation of the insulin receptor and the insulin-like growth factor-1 (IGF-1) receptor and activation of protein kinase C (PKC) and phosphoinositide 3-kinase (PI3-kinase). Inhibitors of tyrosine kinase and PKC, but not PI3-kinase, attenuated the insulin neurotoxicity. Conversely, the inhibitor of PI3-kinase but not PKC reversed the antiapoptotic effect of insulin. Suggesting that the gene activity-dependent emergence of excitotoxicity contributed to insulin neurotoxicity, macromolecule synthesis inhibitors and N-methyl-D-aspartate (NMDA) antagonists blocked it. Consistently, exposure to insulin increased the level of the NR2A subunit of the NMDA receptor without much altering NR1 or NR2B levels. The present study suggests that insulin can be both neuroprotective and neurotoxic in the same cell system but by way of different signaling cascades.     

Mechanobiological modeling of endochondral ossification: an experimental and computational analysis

Long bone formation starts early during embryonic development through a process known as endochondral ossification. This is a highly regulated mechanism that involves several mechanical and biochemical factors. Because long bone development is an extremely complex process, it is unclear how biochemical regulation is affected when dynamic loads are applied, and also how the combination of mechanical and biochemical factors affect the shape acquired by the bone during early development. In this study, we develop a mechanobiological model combining: (1) a reaction–diffusion system to describe the biochemical process and (2) a poroelastic model to determine the stresses and fluid flow due to loading. We simulate endochondral ossification and the change in long bone shapes during embryonic stages. The mathematical model is based on a multiscale framework, which consisted in computing the evolution of the negative feedback loop between Ihh/PTHrP and the diffusion of VEGF molecule (on the order of days) and dynamic loading (on the order of seconds). We compare our morphological predictions with the femurs of embryonic mice. The results obtained from the model demonstrate that pattern formation of Ihh, PTHrP and VEGF predict the development of the main structures within long bones such as the primary ossification center, the bone collar, the growth fronts and the cartilaginous epiphysis. Additionally, our results suggest high load pressures and frequencies alter biochemical diffusion and cartilage formation. Our model incorporates the biochemical and mechanical stimuli and their interaction that influence endochondral ossification during embryonic growth. The mechanobiochemical framework allows us to probe the effects of molecular events and mechanical loading on development of bone.     

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