Scene segmentation by spike synchronization in reciprocally connected visual areas. I. Local effects of cortical feedback

 To investigate scene segmentation in the visual system we present a model of two reciprocally connected visual areas using spiking neurons. Area P corresponds to the orientation-selective subsystem of the primary visual cortex, while the central visual area C is modeled as associative memory representing stimulus objects according to Hebbian learning. Without feedback from area C, a single stimulus results in relatively slow and irregular activity, synchronized only for neighboring patches (slow state), while in the complete model activity is faster with an enlarged synchronization range (fast state). When presenting a superposition of several stimulus objects, scene segmentation happens on a time scale of hundreds of milliseconds by alternating epochs of the slow and fast states, where neurons representing the same object are simultaneously in the fast state. Correlation analysis reveals synchronization on different time scales as found in experiments (designated as tower, castle, and hill peaks). On the fast time scale (tower peaks, gamma frequency range), recordings from two sites coding either different or the same object lead to correlograms that are either flat or exhibit oscillatory modulations with a central peak. This is in agreement with experimental findings, whereas standard phase-coding models would predict shifted peaks in the case of different objects. Received: 22 August 2001 / Accepted in revised form: 8 April 2002     

Neural control of interlimb oscillations

How do humans and other animals accomplish coordinated movements? How are novel combinations of limb joints rapidly assembled into new behavioral units that move together in in-phase or anti-phase movement patterns during complex movement tasks? A neural central pattern generator (CPG) model simulates data from human bimanual coordination tasks. As in the data, anti-phase oscillations at low frequencies switch to in-phase oscillations at high frequencies, in-phase oscillations occur at both low and high frequencies, phase fluctuations occur at the anti-phase in-phase transition, a “seagull effect” of larger errors occurs at intermediate phases, and oscillations slip toward in-phase and anti-phase when driven at intermediate phases. These oscillations and bifurcations are emergent properties of the CPG model in response to volitional inputs. The CPG model is a version of the Ellias-Grossberg oscillator. Its neurons obey Hodgkin-Huxley type equations whose excitatory signals operate on a faster time scale than their inhibitory signals in a recurrent on-center off-surround anatomy. When an equal command or GO signal activates both model channels, the model CPG can generate both in-phase and anti-phase oscillations at different GO amplitudes. Phase transitions from either in-phase to anti-phase oscillations, or from anti-phase to in-phase oscillations, can occur in different parameter ranges, as the GO signal increases. Received: 22 August 1994 / Accepted in revised form: 13 May 1997     

Effects of heterogeneity in synaptic conductance between weakly coupled identical neurons

A significant degree of heterogeneity in synaptic conductance is present in neuron to neuron connections. We study the dynamics of weakly coupled pairs of neurons with heterogeneities in synaptic conductance using Wang–Buzsaki and Hodgkin–Huxley model neurons which have Types I and II excitability, respectively. This type of heterogeneity breaks a symmetry in the bifurcation diagrams of equilibrium phase difference versus the synaptic rate constant when compared to the identical case. For weakly coupled neurons coupled with identical values of synaptic conductance a phase locked solution exists for all values of the synaptic rate constant, α. In particular, in-phase and anti-phase solutions are guaranteed to exist for all α. Heterogeneity in synaptic conductance results in regions where no phase locked solution exists and the general loss of the ubiquitous in-phase and anti-phase solutions of the identically coupled case. We explain these results through examination of interaction functions using the weak coupling approximation and an in-depth analysis of the underlying multiple cusp bifurcation structure of the systems of coupled neurons.     

Anti-phase,asymmetric and aperiodic oscillations in excitable cells—I. Coupled bursters

I seek to explain phenomena observed in simulations of populations of gap junction-coupled bursting cells by studying the dynamics of identical pairs. I use a simplified model for pancreatic β-cells and decompose the system into fast (spike-generating) and slow subsystems to show how bifurcations of the fast subsystem affect bursting behavior. When coupling is weak, the spikes are not in phase but rather are anti-phase, asymmetric or quasi-periodic. These solutions all support bursting with smaller amplitude spikes than the in-phase case, leading to increased burst period. A key geometrical feature underlying this is that the in-phase periodic solution branch terminates in a homoclinic orbit. The same mechanism also provides a model for bursting as an emergent property of populations; cells which are not intrinsic bursters can burst when coupled. This phenomenon is enhanced when symmetry is broken by making the cells differ in a parameter.     

Dynamics of two electrically coupled chaotic neurons: Experimental observations and model analysis

Conductance-based models of neurons from the lobster stomatogastric ganglion (STG) have been developed to understand the observed chaotic behavior of individual STG neurons. These models identify an additional slow dynamical process – calcium exchange and storage in the endoplasmic reticulum – as a biologically plausible source for the observed chaos in the oscillations of these cells. In this paper we test these ideas further by exploring the dynamical behavior when two model neurons are coupled by electrical or gap junction connections. We compare in detail the model results to the laboratory measurements of electrically-coupled neurons that we reported earlier. The experiments on the biological neurons varied the strength of the effective coupling by applying a parallel, artificial synapse, which changed both the magnitude and polarity of the conductance between the neurons. We observed a sequence of bifurcations that took the neurons from strongly synchronized in-phase behavior, through uncorrelated chaotic oscillations to strongly synchronized – and now regular – out-of-phase behavior. The model calculations reproduce these observations quantitatively, indicating that slow subcellular processes could account for the mechanisms involved in the synchronization and regularization of the otherwise individual chaotic activities. Received: 28 June 1999 / Accepted in revised form: 30 June 2000     

Activation and inhibition of bimanual movements in school-aged children

The development of motor activation and inhibition was compared in 6-to-12 year-olds. Children had to initiate or stop the externally paced movements of one hand, while maintaining that of the other hand. The time needed to perform the switching task (RT) and the spatio-temporal variables show different agerelated evolutions depending on the coordination pattern (inor anti-phase) and the type of transition (activation, selective inhibition, non selective inhibition) required. In the anti-phase mode, activation perturbs the younger subjects’ responses while temporal and spatial stabilities transiently decrease around 9 years when activating in the in-phase mode. Aged-related changes differed between inhibition and activation in the antiphase mode, suggesting either the involvement of distinct neural networks or the existence of a single network that is reorganized. In contrast, stopping or adding one hand in the in-phase mode shows similar aged-related improvement. We suggest that selectively stopping or activating one arm during symmetrical coordination rely on the two faces of a common processing in which activation could be the release of inhibition.     

Top-down anticipatory control in prefrontal cortex

Summary The prefrontal cortex has been implicated in a wide variety of executive functions, many involving some form of anticipatory attention. Anticipatory attention involves the pre-selection of specific sensory circuits to allow fast and efficient stimulus processing and a subsequently fast and accurate response. It is generally agreed that the prefrontal cortex plays a critical role in anticipatory attention by exerting a facilitatory “top-down” bias on sensory pathways. In this paper we review recent results indicating that synchronized activity in prefrontal cortex, during anticipation of visual stimulus, can predict features of early visual stimulus processing and behavioral response. Although the mechanisms involved in anticipatory attention are still largely unknown, we argue that the synchronized oscillation in prefrontal cortex is a plausible candidate during sustained visual anticipation. We further propose a learning hypothesis that explains how this top-down anticipatory control in prefrontal cortex is learned based on accumulated prior experience by adopting a Temporal Difference learning algorithm.     

Impact of adaptation currents on synchronization of coupled exponential integrate-and-fire neurons

The ability of spiking neurons to synchronize their activity in a network depends on the response behavior of these neurons as quantified by the phase response curve (PRC) and on coupling properties. The PRC characterizes the effects of transient inputs on spike timing and can be measured experimentally. Here we use the adaptive exponential integrate-and-fire (aEIF) neuron model to determine how subthreshold and spike-triggered slow adaptation currents shape the PRC. Based on that, we predict how synchrony and phase locked states of coupled neurons change in presence of synaptic delays and unequal coupling strengths. We find that increased subthreshold adaptation currents cause a transition of the PRC from only phase advances to phase advances and delays in response to excitatory perturbations. Increased spike-triggered adaptation currents on the other hand predominantly skew the PRC to the right. Both adaptation induced changes of the PRC are modulated by spike frequency, being more prominent at lower frequencies. Applying phase reduction theory, we show that subthreshold adaptation stabilizes synchrony for pairs of coupled excitatory neurons, while spike-triggered adaptation causes locking with a small phase difference, as long as synaptic heterogeneities are negligible. For inhibitory pairs synchrony is stable and robust against conduction delays, and adaptation can mediate bistability of in-phase and anti-phase locking. We further demonstrate that stable synchrony and bistable in/anti-phase locking of pairs carry over to synchronization and clustering of larger networks. The effects of adaptation in aEIF neurons on PRCs and network dynamics qualitatively reflect those of biophysical adaptation currents in detailed Hodgkin-Huxley-based neurons, which underscores the utility of the aEIF model for investigating the dynamical behavior of networks. Our results suggest neuronal spike frequency adaptation as a mechanism synchronizing low frequency oscillations in local excitatory networks, but indicate that inhibition rather than excitation generates coherent rhythms at higher frequencies.     

Desynchronization and synchronization of EEG related to stimuli triggering or forbidding sensory-motor reaction in adolescents: II. The peculiarities in case of the attention deficit and hyperactivity syndrome

Evoked desynchronization and synchronization of EEG in θ (4–7.5 Hz), α (7.5–14 Hz) and β (14–20 Hz) ranges were recorded by 19 electrodes in healthy volunteer adolescents and those with attention deficit hyperactivity syndrome in the modified GO/NO-GO test. Two stimuli (high and low tone) were presented in pairs with 1 s intervals inside the pair and 1.5 s intervals between the pairs. Test subjects had to push the button in response to presentation of a pair of high tones and to ignore other stimulus combinations. The components of evoked EEG synchronization in α-θ range that were revealed in the frontocentral and temporoparietal brain regions in connection with inhibition of action (inhibition of movements and making a decision to cancel sensory-motor task performance) were statistically significantly lower in subjects with attention deficit hyperactivity disorder compared with that in healthy subjects.     

Evidence for a slow time-scale of interaction for magnetic fields inhibiting tamoxifen’s antiproliferative action in human breast cancer cells

One critical biophysical feature of environmental-level magnetic field (MF) interactions with biological systems is the time-scale of interaction. A recently proposed fast/slow hypothesis states that a fast mechanism can only sense the instantaneous absolute value of the MF, and that a slow mechanism is potentially capable of sensing features such as frequency and relative orientation and magnitude of the field components. Here we applied the fast/slow hypothesis to a breast cancer model system: A 1.2 μT(rms), 60-Hz field inhibits tamoxifen’s (TAM’s) cytostatic action in MCF-7 cells via a MF interaction. We measured the growth of MCF-7 cells treated with TAM over 7 d, within different MFs: a sinusoidal, 60-Hz, 0.2-μT(rms) field; a sinusoidal, 60-Hz, 1.2-μT(rms) field; and a full-wave rectified version of the 1.2-μT(rms) sinusoidal field. A fast mechanism should not be able to distinguish between the latter two exposures. We observe that the rectified 1.2-μT field does not inhibit TAM’s action, but that the 1.2-μT sinusoidal field does. Therefore, the 1.2-μT MF inhibition of TAM’s cytostatic action operates via a relatively slow mechanism, and we predict that there exists a biologically dynamic complex capable of sensing a 1.2-μT, 60-Hz sinusoidal MF with an intrinsic time-scale of 17 ms or longer, the period of the 60-Hz applied field.     

Sensitivity of firing rate to input fluctuations depends on time scale separation between fast and slow variables in single neurons

Neuronal responses are often characterized by the firing rate as a function of the stimulus mean, or the f–I curve. We introduce a novel classification of neurons into Types A, B−, and B+ according to how f–I curves are modulated by input fluctuations. In Type A neurons, the f–I curves display little sensitivity to input fluctuations when the mean current is large. In contrast, Type B neurons display sensitivity to fluctuations throughout the entire range of input means. Type B− neurons do not fire repetitively for any constant input, whereas Type B+ neurons do. We show that Type B+ behavior results from a separation of time scales between a slow and fast variable. A voltage-dependent time constant for the recovery variable can facilitate sensitivity to input fluctuations. Type B+ firing rates can be approximated using a simple “energy barrier” model.     

Synchronization of neuronal assemblies in reciprocally connected cortical areas

Summary To investigate scene segmentation in the visual system we present a model of two reciprocally connected visual areas comprising spiking neurons. The peripheral area P is modeled similar to the primary visual cortex, while the central area C is modeled as an associative memory representing stimulus objects according to Hebbian learning. Without feedback from area C, spikes corresponding to stimulus representations in P are synchronized only locally (slow state). Feedback from C can induce fast oscillations and an increase of synchronization ranges (fast state). Presenting a superposition of several stimulus objects, scene segmentation happens on a time scale of hundreds of milliseconds by alternating epochs of the slow and fast state, where neurons representing the same object are simultaneously in the fast state. We relate our simulation results to various phenomena observed in neurophysiological experiments, such as stimulus-dependent synchronization of fast oscillations, synchronization on different time scales, ongoing activity, and attention-dependent neural activity.     

A nonlinear dynamics model for simulating long range correlations of cognitive bistability

Simulation results of bistable perception due to ambiguous visual stimuli are presented which are obtained with a behavioral nonlinear dynamics model using perception–attention–memory coupling. This model provides an explanation of recent experimental results of Gao et al. (Cogn Process 7:105–112, 2006a) and it supports their speculation that the fractal character of perceptual dominance time series may be understood in terms of nonlinear and reentrant dynamics of brain processing. Percept reversals are induced by attention fatigue and noise, with an attention bias which balances the relative percept duration. Dynamical coupling of the attention bias to the perception state introduces memory effects leading to significant long range correlations of perceptual duration times as quantified by the Hurst parameter H > 0.5 (Mandelbrot, The fractal geometry of nature, 1991), in agreement with Gao et al. (Cogn Process 7:105–112, 2006a).     

Uncovering the synchronization dynamics from correlated neuronal activity quantifies assembly formation

 Synchronous network excitation is believed to play an outstanding role in neuronal information processing. Due to the stochastic nature of the contributing neurons, however, those synchronized states are difficult to detect in electrode recordings. We present a framework and a model for the identification of such network states and of their dynamics in a specific experimental situation. Our approach operationalizes the notion of neuronal groups forming assemblies via synchronization based on experimentally obtained spike trains. The dynamics of such groups is reflected in the sequence of synchronized states, which we describe as a renewal dynamics. We furthermore introduce a rate function which is dependent on the internal network phase that quantifies the activity of neurons contributing to the observed spike train. This constitutes a hidden state model which is formally equivalent to a hidden Markov model, and all its parameters can be accurately determined from the experimental time series using the Baum-Welch algorithm. We apply our method to recordings from the cat visual cortex which exhibit oscillations and synchronizations. The parameters obtained for the hidden state model uncover characteristic properties of the system including synchronization, oscillation, switching, background activity and correlations. In applications involving multielectrode recordings, the extracted models quantify the extent of assembly formation and can be used for a temporally precise localization of system states underlying a specific spike train. Received: 30 March 1993/Accepted in revised form: 16 April 1994     

Biphasic constitutive laws for biological interface evolution

 A model of tissue differentiation at the bone–implant interface is proposed. The basic hypothesis of the model is that the mechanical environment determines the tissue differentiation. The stimulus chosen is related to the bone–implant micromotions. Equations governing the evolution of the interfacial tissue are proposed and combined with a finite element code to determine the evolution of the fibrous tissue around prostheses. The model is applied to the case of an idealized hip prosthesis. Received: 28 May 2002 / Accepted: 10 November 2002     

Two dynamic processes for the induction of long-term potentiation in hippocampal CA1 neurons

This work sets out to investigate fast and slow dynamic processes and how they effect the induction of long-term potentiation (LTP). Functionally, the fast process will work as a time window to take a spatial coincidence among various inputs projected to the hippocampus, and the slow process will work as a temporal integrator of a sequence of dynamic events. Firstly, the two factors were studied using a “burst” stimulus and a “long-interval patterns” stimulus. Secondly, we propose that, for the induction of LTP, there are two dynamic processes, fast and slow, which are productively activated by bursts and long-interval patterns. The model parameters, a time constant of short dynamics and one of long dynamics, were determined by fitting the values obtained from model simulation to the experimental data. A molecular factor or cellular factors with these two time constants are likely to be induced in LTP induction. Received: 3 November 1997 / Accepted in revised form: 18 August 1999     

A dynamical system model of neurofilament transport in axons

We develop a dynamical system model for the transport of neurofilaments in axons, inspired by Brown's "stop-and-go" model for slow axonal transport. We use fast/slow time-scale arguments to lower the number of relevant parameters in our model. Then, we use experimental data of Wang and Brown to estimate all but one parameter. We show that we can choose this last remaining parameter such that the results of our model agree with pulse-labeling experiments from three different nerve cell types, and also agree with stochastic simulation results.     

A comparative electrophysiological study of regulatory components of working memory in adults and seven- to eight-year-old children: An analysis of coherence of EEG rhythms

Coherence at the frequency of θ, α, and β EEG rhythms was analyzed in 14 adults and 23 children of 7–8 years old while they performed cognitive tasks requiring an involvement of working memory (WM). We used the pair matching paradigm in which subjects had to match a pair of stimuli shown in succession in the central visual field. The pairs of verbal and visuo-spatial stimuli were mixed together and presented in a pseudo random order. Each pair was preceded by a warning signal that did not specify a modality of upcoming stimuli. We analyzed EEG segments recorded (i) in the rest condition, (ii) prior to the first (reference) stimulus (maintenance of nonspecific voluntary attention), and (iii) prior to the second (test) stimulus (retention of information in WM). In the present study we focused on the regulatory functional components of WM, and therefore, the stimulus modality has not been taken into account. In adults, maintaining nonspecific voluntary attention was accompanied by an increase of the strength of θ-related functional coupling between medial areas of the frontal cortex and temporal cortical zones and by a strengthening of local β-related functional connectivity in the fronto-central areas of the cortex. In children, no such increase was found for θ rhythm; for β rhythm the increase was limited to several short-range functional links. In adults, the retention of information in WM was accompanied by the growth in α coherence in distant fronto-parietal links, predominantly in the right hemisphere, while in children information retention was accompanied by the growth of θ coherence in the inferio-temporal and parietal cortical regions. The results of the study point to a relative immaturity of the mechanisms of executive control of WM in children of 7–8 years old.     

Emergence of donor control in patchy predator—prey systems

We study a general predator—prey system in a spatially heterogeneous environment. The predation process, which occurs on a behavioural time-scale, is much faster than the other processes (reproduction, natural mortality and migrations) occurring on the population dynamics time-scale. We show that, taking account of this difference in time-scales, and assuming that the prey have a refuge, the dynamics of the system on a slow time-scale become donor-controlled. Even though predators may control the prey density locally and on a behavioural fast time-scale, nevertheless, both globally and on a slow time-scale, the prey dynamics are independent of predator density: the presence of predators generates a constant prey mortality. In other words, in heterogeneous environments, the prey population dynamics depend in a switch-like manner on the presence or absence of predators, not on their actual density.     

Cluster associative memory formation in a three-layer network of phase oscillators

A three-layer network model of oscillatory associative memory is proposed. The network is capable of storing binary images, which can be retrieved upon presenting an appropriate stimulus. Binary images are encoded in the form of the spatial distribution of oscillatory phase clusters in-phase and anti-phase relative to a reference periodic signal. The information is loaded into the network using a set of interlayer connection weights. A condition for error-free pattern retrieval is formulated, delimiting the maximal number of patterns to be stored in the memory (storage capacity). It is shown that the capacity can be significantly increased by generating an optimal alphabet (basis pattern set). The number of stored patterns can reach values of the network size (the number of oscillators in each layer), which is significantly higher than the capacity of conventional oscillatory memory models. The dynamical and information characteristics of the retrieval process based on the optimal alphabet, including the size of “attraction basins“ and the input pattern distortion admissible for error-free retrieval, are investigated.