Dispersion and time delay effects in synchronized spike–burst networks

We study spike–burst neural activity and investigate its transitions to synchronized states under electrical coupling. Our reported results include the following: (1) Synchronization of spike–burst activity is a multi-time scale phenomenon and burst synchrony is easier to achieve than spike synchrony. (2) Synchrony of networks with time-delayed connections can be achieved at lower coupling strengths than within the same network with instantaneous couplings. (3) The introduction of parameter dispersion into the network destroys the existence of synchrony in the strict sense, but the network dynamics in major regimes of the parameter space can still be effectively captured by a mean field approach if the couplings are excitatory. Our results on synchronization of spiking networks are general of nature and will aid in the development of minimal models of neuronal populations. The latter are the building blocks of large scale brain networks relevant for cognitive processing.     

Balanced networks under spike-time dependent plasticity

The dynamics of local cortical networks are irregular, but correlated. Dynamic excitatory–inhibitory balance is a plausible mechanism that generates such irregular activity, but it remains unclear how balance is achieved and maintained in plastic neural networks. In particular, it is not fully understood how plasticity induced changes in the network affect balance, and in turn, how correlated, balanced activity impacts learning. How do the dynamics of balanced networks change under different plasticity rules? How does correlated spiking activity in recurrent networks change the evolution of weights, their eventual magnitude, and structure across the network? To address these questions, we develop a theory of spike–timing dependent plasticity in balanced networks. We show that balance can be attained and maintained under plasticity–induced weight changes. We find that correlations in the input mildly affect the evolution of synaptic weights. Under certain plasticity rules, we find an emergence of correlations between firing rates and synaptic weights. Under these rules, synaptic weights converge to a stable manifold in weight space with their final configuration dependent on the initial state of the network. Lastly, we show that our framework can also describe the dynamics of plastic balanced networks when subsets of neurons receive targeted optogenetic input.     

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.     

Spike timing dependent plasticity promotes synchrony of inhibitory networks in the presence of heterogeneity

Recently Haas et al. (J Neurophysiol 96: 3305–3313, 2006), observed a novel form of spike timing dependent plasticity (iSTDP) in GABAergic synaptic couplings in layer II of the entorhinal cortex. Depending on the relative timings of the presynaptic input at time t _pre and the postsynaptic excitation at time t _post, the synapse is strengthened (Δt = t _post − t _pre > 0) or weakened (Δt < 0). The temporal dynamic range of the observed STDP rule was found to lie in the higher gamma frequency band (≥40 Hz), a frequency range important for several vital neuronal tasks. In this paper we study the function of this novel form of iSTDP in the synchronization of the inhibitory neuronal network. In particular we consider a network of two unidirectionally coupled interneurons (UCI) and two mutually coupled interneurons (MCI), in the presence of heterogeneity in the intrinsic firing rates of each coupled neuron. Using the method of spike time response curve (STRC), we show how iSTDP influences the dynamics of the coupled neurons, such that the pair synchronizes under moderately large heterogeneity in the firing rates. Using the general properties of the STRC for a Type-1 neuron model (Ermentrout, Neural Comput 8:979–1001, 1996) and the observed iSTDP we determine conditions on the initial configuration of the UCI network that would result in 1:1 in-phase synchrony between the two coupled neurons. We then demonstrate a similar enhancement of synchrony in the MCI with dynamic synaptic modulation. For the MCI we also consider heterogeneity introduced in the network through the synaptic parameters: the synaptic decay time of mutual inhibition and the self inhibition synaptic strength. We show that the MCI exhibits enhanced synchrony in the presence of all the above mentioned sources of heterogeneity and the mechanism for this enhanced synchrony is similar to the case of the UCI.     

Neural coding properties based on spike timing and pattern correlation of retinal ganglion cells

Correlation between spike trains or neurons sometimes indicates certain neural coding rules in the visual system. In this paper, the relationship between spike timing correlation and pattern correlation is discussed, and their ability to represent stimulus features is compared to examine their coding strategies not only in individual neurons but also in population. Two kinds of stimuli, natural movies and checkerboard, are used to arouse firing activities in chicken retinal ganglion cells. The spike timing correlation and pattern correlation are calculated by cross-correlation function and Lempel–Ziv distance respectively. According to the correlation values, it is demonstrated that spike trains with similar spike patterns are not necessarily concerted in firing time. Moreover, spike pattern correlation values between individual neurons’ responses reflect the difference of natural movies and checkerboard; neurons cooperate with each other with higher pattern correlation values which represent spatiotemporal correlations during response to natural movies. Spike timing does not reflect stimulus features as obvious as spike patterns, caused by their particular coding properties or physiological foundation. As a result, separating the pattern correlation out of traditional timing correlation concept uncover additional insight in neural coding.     

Selectivity of stimulus induced responses in cultured hippocampal networks on microelectrode arrays

Sensory information can be encoded using the average firing rate and spike occurrence times in neuronal network responses to external stimuli. Decoding or retrieving stimulus characteristics from the response pattern generally implies that the corresponding neural network has a selective response to various input signals. The role of various spiking activity characteristics (e.g., spike rate and precise spike timing) for basic information processing was widely investigated on the level of neural populations but gave inconsistent evidence for particular mechanisms. Multisite electrophysiology of cultured neural networks grown on microelectrode arrays is a recently developed tool and currently an active research area. In this study, we analyzed the stimulus responses represented by network-wide bursts evoked from various spatial locations (electrodes). We found that the response characteristics, such as the burst initiation time and the spike rate, can be used to retrieve information about the stimulus location. The best selectivity in the response spiking pattern could be found for a small subpopulation of neurones (electrodes) at relatively short post-stimulus intervals. Such intervals were unique for each culture due to the non-uniform organization of the functional connectivity in the network during spontaneous development.     

Microsatellite mapping of genes that determine supernumerary spikelets in wheat (T. aestivum) and rye (S. cereale)

The wheat and rye spike normally bears one spikelet per rachis node, and the appearance of supernumerary spikelets is rare. The loci responsible for the ‘multirow spike’ or MRS trait in wheat, and the ‘monstrosum spike’ trait in rye were mapped by genotyping F₂ populations with microsatellite markers. Both MRS and the ‘monstrosum’ trait are under the control of a recessive allele at a single locus. The Mrs1 locus is located on chromosome 2DS, co-segregating with the microsatellite locus Xwmc453. The placement of flanking microsatellite loci into chromosome deletion bin 2DS-5 (FL 0.47–1.0) delimited the physical location of Mrs1 to the distal half of chromosome arm 2DS, within the gene rich region 2S0.8. The Mo1 locus maps about 10 cM from the centromere on chromosome arm 2RS. The similar effect on phenotype of mo1 and mrs1, together with their presence in regions of conserved synteny, suggest that they may well be members of an orthologous set of Triticeae genes governing spike branching. The practical importance of the MRS spike is that it produces more spikelets per spike, and thereby enhances the sink capacity of wheat, which is believed to limit the yield potential of the crop.     

Directionality of auditory nerve fiber responses to pure tone stimuli in the grassfrog, Rana temporaria. II. Spike timing

We studied the directionality of spike timing in the responses of single auditory nerve fibers of the grass frog, Rana temporaria, to tone burst stimulation. Both the latency of the first spike after stimulus onset and the preferred firing phase during the stimulus were studied. In addition, the directionality of the phase of eardrum vibrations was measured. The response latency showed systematic and statistically significant changes with sound direction at both low and high frequencies. The latency changes were correlated with response strength (spike rate) changes and were probably the result of directional changes in effective stimulus intensity. Systematic changes in the preferred firing phase were seen in all fibers that showed phaselocking (i.e., at frequencies below 500–700 Hz). The mean phase lead for stimulation from the contralateral side was approximately 140° at 200 Hz and decreased to approximately 100° at 700 Hz. These phaseshifts correspond to differences in spike timing of approximately 2 ms and 0.4 ms respectively. The phaseshifts were nearly independent of stimulus intensity. The phase directionality of eardrum vibrations was smaller than that of the nerve fibers. Hence, the strong directional phaseshifts shown by the nerve fibers probably reflect the directional characteristics of extratympanic pathways. Accepted: 23 November 1996     

Competition in the temporal domain among neural activities phase-locked to subthreshold oscillations

 In the presence of a subthreshold membrane oscillation, analog information may be encoded in the timing of spike generation phase-locked to the oscillation. With this spike timing neural code, a competitive network of inhibitory spiking neurons was shown to achieve a novel timing mechanism of neural activity selection: the neurons had higher probabilities of becoming winners if they were stimulated earlier in each oscillatory cycle. Here the timing mechanism and its robustness are studied both numerically and analytically, and the conditions to yield a given number of winners (the inhibitory neurons that remain active after the competition) are investigated. The analysis revealed that activity selection with a small number of winners is ensured for broad ranges of values of the parameters such as the strength and time constant of inhibition. In particular, the number of winners is almost unchanged for various timing differences between stimuli to different neurons. This implies that the timing mechanism is useful for such biological information processing as requires perception of a relatively small number of significant stimulus components. Received: 24 January 1996 / Accepted in revised form: 24 July 1996     

Sensory development of the Antarctic silverfish Pleuragramma antarcticum: a test for the ontogenetic shift hypothesis

In 1996 Montgomery proposed an ontogenetic shift in the use of visual and non-visual senses in Antarctic notothenioid fishes, with visual dominance in larval fishes giving way to non-visual senses in adults. One prediction of the hypothesis is timing differences in the development of the respective sensory systems, with the visual system expected to develop earlier than the other systems. The volume of certain brain centres can be determined from fixed material and should correlate with sensory development. This study determined the relative volumes of visual and lateral line brain areas, and relative eye size as a function of fish length in Pleuragramma antarcticum.The relative volume of optic tectum was largest in larval fish, exhibiting a negative allometry with growth. The eminentia granularis, and crista cerebellaris (lateral line associated areas) were not recognisable in the smallest larvae; they became differentiated at standard lengths of 10–20 mm and their relative volumes continued to increase over the size range of fish studied (up to 150 mm standard length). Relative eye diameter decreased dramatically over the size range 5–25 mm and then increased such that relative eye diameter doubled over the size range 25–30 mm. A similar, but less extreme, pattern was seen over the size range 30–60 mm. Above 60 mm relative eye diameter increased slightly with size. Our interpretation is that eye growth and somatic growth are on separate trajectories, and the breaks in the relative eye diameter curve result from overwinter periods when somatic growth is static, but the eye continues to grow. These results provide support for the ontogenetic shift hypothesis, and indicate that the timing of the shift probably occurs after the second winter. Received: 22 October 1996 / Accepted: 10 January 1997     

Parameters for a model of an oscillating neuronal network in the cochlear nucleus defined by genetic algorithms

Chopper neurons in the cochlear nucleus are characterized by intrinsic oscillations with short average interspike intervals (ISIs) and relative level independence of their response (Pfeiffer, Exp Brain Res 1:220–235, 1966; Blackburn and Sachs, J Neurophysiol 62:1303–1329, 1989), properties which are unattained by models of single chopper neurons (e.g., Rothman and Manis, J Neurophysiol 89:3070–3082, 2003a). In order to achieve short ISIs, we optimized the time constants of Rothman and Manis single neuron model with genetic algorithms. Some parameters in the optimization, such as the temperature and the capacity of the cell, turned out to be crucial for the required acceleration of their response. In order to achieve the relative level independence, we have simulated an interconnected network consisting of Rothman and Manis neurons. The results indicate that by stabilization of intrinsic oscillations, it is possible to simulate the physiologically observed level independence of ISIs. As previously reviewed and demonstrated (Bahmer and Langner, Biol Cybern 95:371–379, 2006a), chopper neurons show a preference for ISIs which are multiples of 0.4 ms. It was also demonstrated that the network consisting of two optimized Rothman and Manis neurons which activate each other with synaptic delays of 0.4 ms shows a preference for ISIs of 0.8 ms. Oscillations with various multiples of 0.4 ms as ISIs may be derived from neurons in a more complex network that is activated by simultaneous input of an onset neuron and several auditory nerve fibers.     

Running as fast as it can: How spiking dynamics form object groupings in the laminar circuits of visual cortex

How spiking neurons cooperate to control behavioral processes is a fundamental problem in computational neuroscience. Such cooperative dynamics are required during visual perception when spatially distributed image fragments are grouped into emergent boundary contours. Perceptual grouping is a challenge for spiking cells because its properties of collinear facilitation and analog sensitivity occur in response to binary spikes with irregular timing across many interacting cells. Some models have demonstrated spiking dynamics in recurrent laminar neocortical circuits, but not how perceptual grouping occurs. Other models have analyzed the fast speed of certain percepts in terms of a single feedforward sweep of activity, but cannot explain other percepts, such as illusory contours, wherein perceptual ambiguity can take hundreds of milliseconds to resolve by integrating multiple spikes over time. The current model reconciles fast feedforward with slower feedback processing, and binary spikes with analog network-level properties, in a laminar cortical network of spiking cells whose emergent properties quantitatively simulate parametric data from neurophysiological experiments, including the formation of illusory contours; the structure of non-classical visual receptive fields; and self-synchronizing gamma oscillations. These laminar dynamics shed new light on how the brain resolves local informational ambiguities through the use of properly designed nonlinear feedback spiking networks which run as fast as they can, given the amount of uncertainty in the data that they process.     

Relative spike time coding and STDP-based orientation selectivity in the early visual system in natural continuous and saccadic vision: a computational model

We have built a phenomenological spiking model of the cat early visual system comprising the retina, the Lateral Geniculate Nucleus (LGN) and V1’s layer 4, and established four main results (1) When exposed to videos that reproduce with high fidelity what a cat experiences under natural conditions, adjacent Retinal Ganglion Cells (RGCs) have spike-time correlations at a short timescale (~30 ms), despite neuronal noise and possible jitter accumulation. (2) In accordance with recent experimental findings, the LGN filters out some noise. It thus increases the spike reliability and temporal precision, the sparsity, and, importantly, further decreases down to ~15 ms adjacent cells’ correlation timescale. (3) Downstream simple cells in V1’s layer 4, if equipped with Spike Timing-Dependent Plasticity (STDP), may detect these fine-scale cross-correlations, and thus connect principally to ON- and OFF-centre cells with Receptive Fields (RF) aligned in the visual space, and thereby become orientation selective, in accordance with Hubel and Wiesel (Journal of Physiology 160:106–154, 1962) classic model. Up to this point we dealt with continuous vision, and there was no absolute time reference such as a stimulus onset, yet information was encoded and decoded in the relative spike times. (4) We then simulated saccades to a static image and benchmarked relative spike time coding and time-to-first spike coding w.r.t. to saccade landing in the context of orientation representation. In both the retina and the LGN, relative spike times are more precise, less affected by pre-landing history and global contrast than absolute ones, and lead to robust contrast invariant orientation representations in V1.     

Modeling Hermissenda: II. Effects of variations in type-B cell excitability, synaptic strength, and network architecture

Because the Hermissenda eye is relatively simple and its cells well characterized, it provides an attractive preparation for detailed computational analysis. To examine the neural mechanisms of learning in this system, we developed multicompartmental models of the type-A and type-B photoreceptors, simulated the eye, and asked three questions: First, how do conductance changes affect cells in a network as compared with those in isolation; second, what are the relative contributions of increases in B-cell excitability and synaptic strength to network output; and third, how do these contributions vary as a function of network architecture? We found that reductions in the type-B cells of two K⁺ currents, I _A and I _C, differentially affected the type-B cells themselves, with I _C reductions increasing firing rate (excitability) in response to light, and I _A reductions increasing quantal output (synaptic strength) onto postsynaptic targets. Increases in either type-B cell excitability or synaptic strength, induced directly or indirectly, each suppressed A-cell photoresponses, and the combined effect of both changes occurring together was greater than either alone. To examine the effects of network architecture, we compared the full network with a simple feedforward B-A pair and intermediate configurations. Compared with a feedforward pair, the complete network exhibited greater A-cell sensitivity to B-cell changes. This was due to many factors, including an increased number of B-cells (which increased B-cell impact on A-cells), A-B feedback inhibition (which slowed both cell types and altered spike timing relationships), and B-B lateral inhibition (which reduced B-cell sensitivity to intrinsic biophysical modifications). These results suggest that an emergent property of the network is an increase both in the rate of information acquisition (“learning”) and in the amount of information that can be stored (“memory”).     

Effects of phase on homeostatic spike rates

Recent experimental results by Talathi et al. (Neurosci Lett 455:145–149, 2009) showed a divergence in the spike rates of two types of population spike events, representing the putative activity of the excitatory and inhibitory neurons in the CA1 area of an animal model for temporal lobe epilepsy. The divergence in the spike rate was accompanied by a shift in the phase of oscillations between these spike rates leading to a spontaneous epileptic seizure. In this study, we propose a model of homeostatic synaptic plasticity which assumes that the target spike rate of populations of excitatory and inhibitory neurons in the brain is a function of the phase difference between the excitatory and inhibitory spike rates. With this model of homeostatic synaptic plasticity, we are able to simulate the spike rate dynamics seen experimentally by Talathi et al. in a large network of interacting excitatory and inhibitory neurons using two different spiking neuron models. A drift analysis of the spike rates resulting from the homeostatic synaptic plasticity update rule allowed us to determine the type of synapse that may be primarily involved in the spike rate imbalance in the experimental observation by Talathi et al. We find excitatory neurons, particularly those in which the excitatory neuron is presynaptic, have the most influence in producing the diverging spike rates and causing the spike rates to be anti-phase. Our analysis suggests that the excitatory neuronal population, more specifically the excitatory to excitatory synaptic connections, could be implicated in a methodology designed to control epileptic seizures.     

The effects of various spatial distributions of weak noise on rhythmic spiking

We consider the response of the classical Hodgkin–Huxley (HH) spatial system in the weak to intermediate noise regime near the bifurcation to repetitive spiking. The deterministic component of the input (signal) is restricted to a small segment near the origin whereas noise, with parameter σ, occurs either only in the signal region or throughout the whole neuron. In both cases small noise inhibits the spiking and there is a minimum in the spike counts at σ ≈ 0.15. At the same value of σ, the variance of the spike counts undergoes a pronounced maximum. For spatially restricted noise, the spike count continues to increase beyond the minimum until σ = 0.5, but in the case of spatially extended noise the spike count begins to decline around σ = 0.35 to give a local maximum. For both spatial distributions of noise, the variance of the spike count is found to also have a local minimum at about σ = 0.4. Examples are given of the probability distributions of the spike counts and the spatial distributions of spikes with varying noise level. The differences in behaviours of the spike counts as noise increases beyond 0.3 are attributable to noise-induced spiking outside the signal region, which has a larger probability of occurrence when the noise is over an extended region. This aspect is investigated by ascertaining the probability of noise-induced spiking as a function of noise level and examination of the corresponding latency distributions. These findings prompt a definition of weak noise in the standard HH model as that for which the probability of secondary phenomena is negligible, which occurs when σ is less than about 0.3. Finally, if signal and weak (σ < 0.3) noise are applied on disjoint intervals, then the noise has no effect on the instigation or propagation of spikes, no matter how large its region of application. These results are expected to apply to type 2 neurons in general, including the majority of cortical pyramidal cells.     

Activity-dependent enhancement in the reliability of correlated spike timings in cultured cortical neurons

To study the use-dependent modification of activity in neural networks, we investigated the spike timing by simultaneously recording activity at multiple sites in a network of cultured cortical neurons. We used dynamical analysis to study the temporal structure of spike trains and the activity-dependent changes in the reliability and reproducibility of spike patterns evoked by a stimulus. We also used cross-correlation analysis to evaluate the interactions of neuron pairs. Our main conclusions are that even when no obvious change in spike numbers can be seen, use-dependent modification occurs, either enhancing or reducing in the reliability and reproducibility of spike trains evoked by a stimulus, and the fine temporal structure of stimulus-evoked spike trains and interactions between neurons are also modified by tetanic stimulation. Received: 25 February 1998 / Accepted in revised form: 24 August 1998     

A versatile ODE approximation to a network model for the spread of sexually transmitted diseases

 We develop a moment closure approximation (MCA) to a network model of sexually transmitted disease (STD) spread through a steady/casual partnership network. MCA has been used previously to approximate static, regular lattices, whereas application to dynamic, irregular networks is a new endeavour, and application to sociologically-motivated network models has not been attempted. Our goals are 1) to investigate issues relating to the application of moment closure approximations to dynamic and irregular networks, and 2) to understand the impact of concurrent casual partnerships on STD transmission through a population of predominantly steady monogamous partnerships. We are able to derive a moment closure approximation for a dynamic irregular network representing sexual partnership dynamics, however, we are forced to use a triple approximation due to the large error of the standard pair approximation. This example underscores the importance of doing error analysis for moment closure approximations. We also find that a small number of casual partnerships drastically increases the prevalence and rate of spread of the epidemic. Finally, although the approximation is derived for a specific network model, we can recover approximations to a broad range of network models simply by varying model parameters which control the structure of the dynamic network. Thus our moment closure approximation is very flexible in the kinds of network models it can approximate. Received: 26 August 2001 / Revised version: 15 March 2002 / Published online: 23 August 2002 C.T.B. was supported by the NSF. Key words or phrases: Moment closure approximation – Network model – Pair approximation – Sexually transmitted diseases – Steady/casual partnership network     

A “Spike-Based” Grammar Underlies Directional Modification in Network Connectivity: Effect on Bursting Activity and Implications for Bio-Hybrids Systems

Developed biological systems are endowed with the ability of interacting with the environment; they sense the external state and react to it by changing their own internal state. Many attempts have been made to build ‘hybrids’ with the ability of perceiving, modifying and reacting to external modifications. Investigation of the rules that govern network changes in a hybrid system may lead to finding effective methods for ‘programming’ the neural tissue toward a desired task. Here we show a new perspective in the use of cortical neuronal cultures from embryonic mouse as a working platform to study targeted synaptic modifications. Differently from the common timing-based methods applied in bio-hybrids robotics, here we evaluated the importance of endogenous spike timing in the information processing. We characterized the influence of a spike-patterned stimulus in determining changes in neuronal synchronization (connectivity strength and precision) of the evoked spiking and bursting activity in the network. We show that tailoring the stimulation pattern upon a neuronal spike timing induces the network to respond stronger and more precisely to the stimulation. Interestingly, the induced modifications are conveyed more consistently in the burst timing. This increase in strength and precision may be a key in the interaction of the network with the external world and may be used to induce directional changes in bio-hybrid systems.     

Temporal correlation based learning in neuron models

We study a learning rule based upon the temporal correlation (weighted by a learning kernel) between incoming spikes and the internal state of the postsynaptic neuron, building upon previous studies of spike timing dependent synaptic plasticity (Kempter, R., Gerstner, W., van Hemmen, J.L., Wagner, H., 1998. Extracting Oscillations: Neuronal coincidence detection with noisy periodic spike input. Neural computation 10, 1987–2017; Kempter, R., Gerstner, W., van Hemmen, J.L., 1999. Hebbian learning and spiking neurons. Physical Reviewm E59, 4498–4514; van Hemmen, J.L., 2001. Theory of synaptic plasticity. In: Moss, F., Gielen, S. (Eds.), Handbook of biological physics. vol. 4, Neuro Informatics, neural modelling, Elsevier, Amsterdam, pp. 771–823. Our learning rule for the synaptic weight w _ij is where the t _j,μ are the arrival times of spikes from the presynaptic neuron j and the function u(t) describes the state of the postsynaptic neuron i. Thus, the spike-triggered average contained in the inner integral is weighted by a kernel Γ(s), the learning window, positive for negative, negative for positive values of the time difference s between post- and presynaptic activity. An antisymmetry assumption for the learning window enables us to derive analytical expressions for a general class of neuron models and to study the changes in input-output relationships following from synaptic weight changes. This is a genuinely non-linear effect (Song, S., Miller, K., Abbott, L., 2000. Competitive Hebbian learning through spike timing dependent synaptic plasticity. Nature Neuroscience 3, 919–926).