Category: Dynamics

Empirical evidence from human resting state networks has shown a tendency for multiple brain areas to synchronise for short amounts of time, and for different synchronous groups to appear at different times. In dynamical systems terms, this behaviour resembles metastability — an intrinsically driven movement between transient, attractor-like states. However, it remains an open question what the underlying mechanism is that gives rise to these observed phenomena. Recent theories suggest that transient periods of synchronisation and desynchronisation provide a mechanism for dynamically integrating and forming coalitions of functionally related neural areas, and that at these times conditions are optimal for information transfer. Hence such seemingly metastable dynamics could facilitate versatile exploration, integration, and communication between functionally related neural areas, and thereby support sophisticated cognitive processing in the brain.

This is the second of my post on basic concepts in brain science.

Synchrony is to do with oscillations in the brain. I posted about what oscillations are here. To recap, a population of neurons that repeatedly, fire together (burst) and then go quiet and then fire together again, are said to oscillate. The speed of the oscillation is called the frequency and is measured in Hertz (Hz). When two distinct populations oscillate at different frequencies they are desynchronised, but when they both oscillate at the same frequency they are said to be synchronous.

Synchrony is a different concept to resonance. Resonance is where one thing is oscillating and a second thing is not, but then the second starts to oscillate at the same frequency as the first. Resonance is therefore when one thing oscillates in sympathy with another. The reason the second oscillates in sympathy is due to some connection between the two. For example, one object oscillating may be causally linked to another by the gas in our atmosphere and these vibrations my effect the second so it too starts oscillating.

Synchrony is also caused by a connection between two objects. Unlike resonance, where one object is originally oscillating and one is not, with synchrony both objects are originally oscillating. The key is that the frequencies at which each is originally oscillating are different. When they synchronise they may synchronise to a frequency that is different from either of the original frequencies. So for example, you may have two pendulums connected together by the beam they are both hung upon. One may be swinging at 20 Hz and the other at 40 Hz. The beam connecting the two creates a causal interaction. After a while and much interaction both may end up oscillating at 30 Hz. Both are synchronised to the same frequency, but at a different frequency than either was at originally. The reason they may have ended up at a different frequency is that the causal interaction is going both ways. The oscillation from one is effecting the oscillation of the other, and vice versa. With resonance the causal effect is one way, hence the second object oscillating in sympathy at the frequency of the first.

Now back to synchrony in the brain. In the brain you may have one population of neurons oscillating at one frequency and another population oscillating at another frequency. The neurons in one population are causally connected to the other by synapses, and vice versa. Over time the oscillation in each synchronises so that the bursts of firing in each population are at the same frequency. This can be likened two two people hitting a drum at the same tempo. Not only that but also they may have same phase. The phase refers to when the beats happen. Imagine two people drumming at the same tempo. Even though each is at the same tempo one person may hit the drum when the other person is quiet, and vice versa. If this is so they are said to be completely out of phase. If they hit the drum at the same time and therefore quiet moments also happen at the same time they are said to be in phase. Similarly if the two neural populations are synchronous and the burst of firing and moments of quiet occur at the same time then they are in phase.

Gamma-band oscillations (a population of neurons firing together at the rate of 30-80 Hz) can emerge in a population of excitatory and inhibitory neurons. The inhibition causes the moments of quiet in the oscillation. This provides windows for interaction at the moment inhibition wears off and there is a burst of firing. Excitatory signals from a different oscillating population can then take advantage of this because gamma band oscillations are sufficiently regular to allow prediction of the next burst. As long as the travelling time from the sending to the receiving group is also reliable, their communication windows for input and output are open at the same times (i.e. when the bursts occur). Packages of spiking signals from one population of neurons can therefore arrive at the other neuronal group in precise synchronization and enhance their impact. In short, synchronisation between two populations allows two populations to work together and provides the optimal conditions for transferring information. Pascal Fries discusses the mechanistic consequences of neuronal oscillations and calls this hypothesis ‘communication through coherence’. You can read a more technical report by him here.

I am going to write a few post on basic concepts in brain science. This first one is about oscillations.

A group of neurons that are close together is referred to as a population or cluster. A population will have a specific role, e.g. responding to a particular stimulus such as for example a cat.

When the neurons in a population fire at roughly the same time, then go quiet, and then fire again and repeat this process this is called an oscillation. The time when they fire is called a burst of firing. The number of bursts in a second is the frequency of the oscillation. A frequency of 1 Hertz or for short ‘Hz’ is 1 oscillation a second, which means that there will be one burst of firings and one period of silence. 10 Hz is 10 oscillations a second, 50 Hz is 50 oscillations a second etc.

Different names are given to different ranges of the frequency (Hz) of the oscillation (also called rhythms). The delta band rhythm ranges from 0.1−3.5 Hz. Theta rhythm ranges from 4−7.5 Hz. Alpha band is 8−13 Hz. Beta is 14−30 Hz, and gamma is 30-80 Hz.

The amplitude or power of the oscillation/rhythm is dictated by the number of neurons in a population that fire during a burst. If there is a population of 200 neurons and 10 fire in the burst that will have a lower power than if 150 neurons fire. 200 neurons firing during the burst in a population of 200 neurons will have the maximum possible amplitude/power.

The various rhythms have diverse associations. Thalamocortical networks display increased delta band power during deep sleep. Theta activity is increased during memory encoding and retrieval. Alpha band changes are associated with attentional demands. Beta oscillations have been related to the sensorimotor system. Of all the frequency bands the role of gamma is thought to be most extensive and is hypothesized to provide a mechanism that underlies many cognitive functions such as: attention, associative learning, working memory, the formation of episodic memory, visual perception, and sensory selection.

So for example, a population that responds to a cat with a gamma oscillation of very high power may indicate that you attending to a very strong visual perception of a cat.

A localised group of neurons firing synchronously at 30-100 hz is referred to as a local field potential gamma oscillation. These are important for spike-timing-dependent plasticity to occur. Synchronized activity of 10–30 ms in the gamma frequency create a narrow time window for the coincident activation of pre-synaptic and post-synaptic cell used for STDP (for more details read here). Slower oscillations do not provide a narrow enough window and faster oscillations, having more than one cycle in the STDP window, cause the post-synaptic cell to receive inputs both before and after having generated a spike.

However, STDP occurs if pre-synaptic and post-synaptic action potentials are correlated. Notably this occurs even if two cells with equally weak inputs correlate, which is not the kind of result that is useful to learning as we wish to learn strong coincidences. Gamma synchronization is not necessarily time-locked to a stimulus. Due to these two reasons long term potentiation (strengthening) of synapses induced by synchronized gamma activity alone does not attain the specificity of memory encoding, but an additional mechanism is required.

The hippocampus is considered to play a major role in memory. Learning-dependent synchronization of hippocampal theta activity is associated with large event-related potentials with frequency in the theta (4-8 hz) and delta (0-4 hz) range that appear to result from phase the reset of theta activity occurring at a fixed interval after presentation of a stimulus. Theta reset determines the theta phase at which a given stimulus affects a cell. Theta band learning is non-Hebbian and only involves pre-synaptic and not post-synaptic spikes. If the stimuli arrive during the peak of the theta oscillation long term potentiation (strengthening of synapses) occurs, inputs arriving at a trough of the theta cycle induce long term depression (weakening of synapses). Axmacher et al note that a combination between theta and gamma learning dynamics my provide the required specificity for memory learning:

‘Whereas gamma-dependent plasticity alone may not distinguish between correlated weak and strong inputs and occurs not necessarily time-locked to a given stimulus, plasticity during theta reset has these features. Theta-dependent plasticity alone, on the other hand, is too coarse to encode stimulus features with a high temporal resolution: at least Hebbian LTP requires precise spike timing. Moreover, sequence encoding (sequences of items as well as spatial paths) has been suggested to depend on action potentials during subsequent theta phases, with gamma periods binding each item.’

I recently reported here on feed forward models of spiking neurons. Here is a follow up about an interesting recurrent system.

The computational power of a reciprocally connected group are likely to entail population codes rather than singular neurons encoding for stimuli. As the spiking neurons are either in a state of firing or not, they are not as easy to decode at a specific moment in time as a rate based model which contain an average of time spread information at one moment. Hosaka et al demonstrate a recurrent network organized to generate a synchronous firing according to the cycle of repeated external inputs. The timing of the synchrony depends on the input spatio-temporal pattern and the neural network structure. They conclude that network self-organizes its transformation function from spatio-temporal to temporal information. spike timing dependant plasticity makes the recurrent neural network behave as a filter with only one learned spatio-temporal pattern able to go through the filtering network in synchronous form (for more information on synchrony read here). Although their work includes a Monte-Carlo significance test for the synchrony, the synchrony is based on a global metric. Clearly distributed synchrony in which different cell assemblies in the network synchronise a different times due to the influence of stimuli would have to be considered if the network is to respond to multiple stimuli.

Synaptic inputs that are often active together are strengthened during learning so that statistical regularities in synaptic input lead to the post-synaptic neuron being selective to particular stimuli whilst also rendering it invariant to accidental features.Neural hierarchies allow neurons at higher level to capture information gained by many neurons at lower levels. A stimulus that drives a neuron at a high-level in a network hierarchy will almost always be part of a (visual or other) scene together with other stimuli. So although invariance aids object recognition when there are changes to irrelevant aspects of the stimulus, it also causes a problem because a given stimulus will never cover the complete receptive field of a high-level neuron but leave room for competing stimuli. This selective efficacy of subsets of a neuron’s input may be aided if converging neuronal inputs to higher-level neurons are functionally segmented and if only a relevant segment is selected at a time. Pascal Fries believes that whist connectivity provides selectivity and invariance, synchronisation provides the required segmentation and selection of a segment.

Gamma-band synchronization (a group or groups of neurons pulse firing together at the rate of 40-80 Hz) can emerge in a network of excitatory and inhibitory neurons. Inhibitory neurons provide shunting inhibition that stops other neurons from firing. This provides windows for synchrony at the moment inhibition wears off. Excitatory signals can then take advantage. Gamma band oscillations are sufficiently regular to allow prediction of the next excitability peak. As long as the travelling time from the sending to the receiving group is also reliable, their communication windows for input and output are open at the same times. Conduction delays between neurons are typically and order of magnitude shorter than the cycle length of the oscillation allowing sending and receiving to occur within one excitability peak. Packages of spikes can therefore arrive at other neuronal groups in precise synchronization and enhance their impact. Rhythmic inhibition therefore provides rhythmic modulation of excitatory input gain. Fries considers the mechanistic consequences of neuronal oscillations and calls this hypothesis ‘communication through coherence’.

Coincidence detection and rhythmic gain modulation create an exclusive communication link between a target group and a strongly synchronised source group. If there is a synchronization among the neurons in groups A and among the neurons in group B but not between A and B then a down stream group C will either synchronise to A or B but not both at the same time. Strong and precise gamma band synchronisation within group A will trigger many spikes in C and entrain C to the rhythm of A. Once entrained a winner-takes-all effect occur as the result of input gain. A competitive advantage is therefore given to one group of neurons.(read here for more details)

Uhlhaas et al note that the fast switching between synchronized and de-synchronized states observed in the data seems at odds with: the coupling strength that can be achieved through synaptic plasticity, the speed of changes in the functional topology, and mechanisms that could cause changes in transmission delays. Hence they conclude that the most likely option for the modulation of synchrony is to change the dynamical states of the coupled neuronal populations, such as the balance between excitation and inhibition. So in addition to the firing rates, precise timing of individual discharges may be used to gate transmission and synaptic plasticity, to selectively route activity across the cortical network and to define particular relations in distributed activity patterns.

Singer notes that such synchro­nous events are statistically improbable so their information content is high. Therefore they are likely to be very effective in eliciting responses in target populations. For the system to work, individual cells need to be able to rapidly change their synchronisation partners if new associations are required due to a change in Gestalt properties of the scene, and if more than one object is present in a scene several distinct assemblies should form.


When an image appears to the visual system, rapid feedforward processing (within about 120ms) leads to an activity patterns called base-groupings that are distributed across many cortical areas. Base-groupings are coded by single neurons tuned to multiple features. The question arises as to how more complex structures are bound together from a combination of base groupings from many cortical areas. For example, a line contour may require base-groupings that code for many smaller line segments that make up  part of the contour to be bound together as a whole. The combined pattern may not be catered for by an explicitly wired base-grouping. Opinions are polarized as to what methods the brain uses to bind disparate activations together. I will here outline two contenders.

Some suggest that groups of neurons across the cortex synchronise their firing patterns binding disparate parts of brain activation together (e.g. a population encoding for red and a population encoding for circle synchronize to encode for a red circle). This is said to explain rhythmic oscillations in the brain, particularly in the gamma band (30-40 hertz). Others believe this to be a mere epiphenomenon. In the 2006 Annual Review of Neuroscience Roelfsema points out that some recent studies on monkeys observed no direct relationship between synchrony and perceptual grouping, and in some instances, grouping is even associated with a reduction in synchrony.

Incremental grouping proposed my Roelfsema et al are said to make use of horizontal and feedback connections to enhances the responses of neurons coding features that are bound in perception. ‘By the time that the base representation has been computed, neurons that respond to features of the same object are linked by the interaction skeleton. This also holds for neurons that respond to widely separated image elements, although these are only indirectly connected through a chain of cells responsive to interspersed image elements. A rate enhancement has to spread through the interaction skeleton in order to make these additional groupings explicit.’

However, this does not blow synchronization theory out of the water. Firing rate labelling proposed by Roelfsema begs for an explanation of how the rate encodes the label bacause a simply higher rate of firing does not seem to say enough unless the rate itself shares a code between populations or unless we are to believe in some kind of threshold beyond which binding occurs. In addition, Pascal Fries explains how oscillatory rhythmic excitability fluctuations produce temporal windows for communication due to relaxation time needed between firing and when the a neuron is ready to again receive signals. ‘Only coherently oscillating neuronal groups can interact effectively, because their communication windows for input and for output are open at the same times’. A detail which adds an extra level of depth for the synchronization camp.

Groups of neurons firing in unison across the cortex synchronise at many different time scales. The most notable phase time scales are the gamma band (30-40 hertz) and the beta band (15-25 hertz). There is much debate in the community as to the role of phase synchronisation. Many think they are a mere epiphenomenon whilst others believe they play a vital role such as binding disparate parts of brain activation together (e.g. a population encoding for red and a population encoding for circle synchronize to encode for a red circle). Opinions are very polarized and I will not enter that debate right now.

What I would like to mention is Pascal Fries talk at the Brain Connectivity Workshop today. In his work studying phase synchrony in monkey’s brains he states that topologically higher areas in the visual hierarchy exhibit attentive influence on lower areas and in doing so they also manipulate synchrony. In his recent research he uses Granger causality, an analysis technique that can give you a metric for how much one part of a system at a particular time affects another at a later time. His results show that top down processes in the visual cortex have a causal synchronizing effect on lower areas but not the other way round. The implication of this is that higher level areas may facilitate the binding with or between lower areas through attentive modulation. For more details read here.