Cellularly-Driven Differences in Network Synchronization Propensity Are Differentially Modulated by Firing Frequency
[['Neuronal synchronization is thought to underlie spatiotemporal pattern formation in the healthy [1]–[4] and pathological brain [5]–[9] .', 'The propensity for synchronization in a neuronal network is determined by both cellular and network properties .', 'An important experimentally obtainable measure of cellular properties is the neuronal phase response curve ( PRC ) [10] .', 'The PRC characterizes the change in spike timing of a periodically firing neuron in response to brief , weak external stimulation .', 'PRCs have been classified into two general categories: Type I , which display only phase advances in response to excitatory stimuli , and Type II , which respond with both phase advances and delays .', 'Type I cells exhibit relatively poor propensity for synchronization under excitatory coupling , while Type II cells synchronize better [10]–[17] .', 'Furthermore , the PRC characteristics thought to be responsible for synchronization propensity change differentially as a function of frequency for Type I and Type II cells [18] .', 'In this study , we explain the differential effects of frequency modulation on neuronal response properties and exploit these effects to investigate differential changes in the capacity for synchronization of excitatory networks consisting of Type I or Type II neurons .', 'To demonstrate the universality of the frequency-dependent effects on the neuronal PRC , we consider a reduced model neuron described by the Morris-Lecar equations [19] which can display either a Type I or Type II PRC in different parameter regimes [20] .', 'Then , to present the effects within a physiological context , we turn to the results of a recent experimental study which showed that cholinergic modulation of cortical pyramidal neurons switches the neuronal PRC from Type II to Type I [21] .', 'In a Hodgkin-Huxley-based cortical pyramidal neuron model , the switch in PRC type was shown to depend on a slow , low-threshold potassium current which is targeted by cholinergic modulation [22] .', 'Using these two neuronal models , we explain the underlying cellular basis of the differential frequency effects on the PRC .', "We show that the relative timing of hyperpolarizing , potassium currents in relation to the model's depolarizing currents ( a calcium current in the Morris-Lecar model and a sodium current in the cortical pyramidal cell model ) plays a crucial role in shaping the phase response of a neuron .", 'We then investigate the influence of the frequency-dependent cellular effects on network activity by analyzing network synchronization as a function of underlying neuronal spike frequency near firing threshold in large-scale , excitatory networks composed of either Morris-Lecar neurons or cortical pyramidal model neurons .', 'As expected , the neuronal PRC type profoundly affects network propensity for synchronization [17] .', 'We show that , in general , increasing firing frequency near firing threshold has little effect upon synchrony in Type I networks , while it severely suppresses synchrony in Type II networks .', 'We show these results to be robust to neuronal heterogeneity , network connectivity parameters and whether neuronal activity is driven by constant or stochastic inputs .', 'Our results provide important insight into differential changes in the propensity for network synchronization induced by the external modulation of neuronal frequency .', 'As neuronal firing frequency changes , the changes in network spatiotemporal patterns depend upon the response characteristics of the individual cells in the network .'], ['We used the Morris-Lecar model [19] as a generic neuronal model to initially explore frequency-dependent PRC effects .', 'The model contains two active ionic currents: an inward current whose dynamics are instantaneous and an outward current gated by the dynamic variable .', 'The current balance equation for the cell is ( 1 ) where , is in millivolts , is in milliseconds , is an externally applied current measured in , and is the synaptic current received by neuron .', 'The current is governed by the steady-state activation function , while dynamics of the current gating variable are given by , with and .', 'The Type I and Type II neuronal models share the parameter values , , , , , , and .', 'Type I cells are modeled with , , , and , while Type II cells are modeled with , , , and .', 'These values were taken from [20] .', 'The cortical pyramidal model neuron we employed was motivated by recent computational and experimental findings , as reported in [22] .', 'Varying the maximum conductance of a -mediated adaptation current , , from to effectively switches the response characteristics of the cortical pyramidal model neuron from Type II to Type I , a phenomenon which has been observed in situ and simulates the effects of cholinergic neuromodulation [21] .', 'The model also features a fast , inward current , a delayed rectifier current , and a leakage current , in addition to the aforementioned slow , low-threshold current responsible for spike-frequency adaptation [22] , [23] .', 'The current balance equation for the cell is ( 2 ) with , in millivolts , and in milliseconds .', 'is an externally applied current measured in , and is the synaptic current received by neuron .', 'Activation of the current is instantaneous and governed by the steady-state activation function .', 'Dynamics of the current inactivation gating variable are given by ( 3 ) with and .', 'The delayed rectifier current is gated by , whose dynamics are governed by ( 4 ) with and .', 'The slow , low-threshold current targeted by cholinergic modulation is gated by , which varies in time according to ( 5 ) where .', 'The parameters and in the current gating equations are varied in the investigation of the underlying cellular basis of the differential frequency effects on the PRC , but they are set to in the network simulations .', 'The slow , low-threshold current loosely models the muscarine-sensitive M-current observed in cortical neurons .', "It has been shown in silico that eliminating this current is sufficient to switch the model neuron's PRC from Type II to Type I [22] .", 'This is intended to model cholinergic neuromodulation , which has been shown experimentally to switch cortical pyramidal neurons between Type I and Type II phase responses [21] .', 'This switching of PRC profile is demonstrated in Fig . 1 , and is obtained by setting to obtain a Type I response ( simulated cholinergic modulation ) and to obtain a Type II response ( simulated absence of cholinergic modulation ) .', 'All other parameter values are the same for both types of neurons: , , , , , and .', 'For both neuronal models , is set to a fixed value to elicit repetitive firing in a single , synaptically isolated neuron , and the model equations are time evolved using a fourth-order Runge-Kutta numerical scheme until the oscillatory period stabilizes .', 'Then , using initial conditions associated with spike peak , brief current pulses are administered at different phases of the oscillation , and the perturbed periods are used to calculate the corresponding phase shifts .', 'The current pulses are administered at 100 equally-spaced time points throughout the period of the neuronal oscillation .', 'The current pulses have a duration of 0 . 06 ms and an amplitude of 3 . 0 for the Type I cortical pyramidal neuron , a duration of 0 . 06 ms and an amplitude of 10 . 0 for the Type II cortical pyramidal neuron , and a duration of 0 . 50 ms and an amplitude of 100 . 0 for both the Type I and Type II Morris-Lecar neurons .', 'In all network simulations , the number of neurons is 200 , and the synapses are exclusively excitatory .', 'The network connectivity pattern is constructed using the Watts-Strogatz architecture for Small World Networks [24] .', 'Starting with a 1-D ring network with periodic boundary conditions , each neuron is at first directionally coupled to its nearest neighbors , and then every connection in the network is rewired with probability to another neuron selected at random .', 'In this way , results in a locally-connected network and in a randomly connected network .', 'The radius of connectivity therefore determines the density of connections in the network , while the re-wiring parameter determines the network connectivity structure .', 'Network connectivity is set to 4 in all simulations .', 'Synaptic current is transmitted from neuron at times when its membrane voltage breaches −20 mV .', 'The synaptic current delivered from neuron to a synaptically connected neuron at times is given by .', 'The total synaptic current to a neuron is simply given by , where is the set of all neurons which synapse onto neuron .', 'The synaptic weight s is the same for all synapses within a given simulation , and we set and .', 'All simulations are run for 10 , 000 ms , with the first 3000 ms disregarded in order to eliminate initial transient effects .', 'The dynamics are numerically integrated in Matlab using a fourth-order Runge-Kutta method with a time step of 0 . 05 ms for the cortical pyramidal neuron networks and 0 . 10 ms for Morris-Lecar neuron networks .', 'We employ two different methods to modulate network firing frequency in our simulations .', 'The first is to simply modulate the supra-threshold value of for all neurons in the network .', 'In order to prevent the networks from trivially synchronizing , we do not supply each neuron with exactly the same level of current , but instead sample from a Gaussian distribution of current values .', 'The mean value of the distribution determines the average firing frequency of the network , and the standard deviation of the Gaussian is chosen such that the standard deviation in natural neuronal frequencies is 1 Hz .', 'In order to model more biologically relevant environmental inputs , we also run simulations of cortical pyramidal neuronal networks in which frequency is modulated by stochastic input .', 'All neurons are given the same constant sub-threshold baseline current , plus square current pulses randomly delivered to each neuron at a specified frequency , so that .', 'The delivery of the square current pulses is a Poisson process .', 'Modulation of this noise frequency thereby modulates the average frequency of the network .', 'In our simulations of stochastically-driven cortical pyramidal neuronal networks , consists of square current pulses with amplitude 30 and duration 0 . 2 msec .', 'With these values , at least two successive pulses are required to elicit neuronal firing .', 'The baseline currents are for Type I networks and for Type II networks .', 'We monitor phase-synchronization of neuronal firing in our simulations using the mean phase coherence ( MPC ) measure , [25] .', 'This measure quantifies the degree of phase locking between neurons , assuming a value of 0 for completely random spiking and 1 for complete phase locking .', 'Note that MPC may be attained for locking of phases at any value , not just zero .', 'The MPC between a pair of neurons , , is defined by: ( 6 ) ( 7 ) where is the time of the spike of neuron 2 , is the time of the spike of neuron 1 that is largest while being less than , is the time of the spike of neuron 1 that is smallest while being greater than or equal to , and is the number of spikes of neuron 2 .', 'The MPC of the entire network , , is calculated by averaging over all pairs of neurons , excluding .', 'Note that this measure is not symmetric .', 'We quantify phase-zero synchronization of a network by calculating the bursting measure B , which is 0 for random spiking and approaches 1 for perfect locking at phase zero between all neurons , for a large number of total spikes and neurons .', 'Calculation of B requires a time-ordered list of the spike times of all neurons over the duration of the entire simulation [26] .', 'Denoting as the time difference between spikes i and i+1 , which do not necessarily ( and probably do not ) correspond to spikes of the same neuron , B is then defined as ( 8 ) where represents averaging over all spikes .', 'This measure makes use of the fact that an ensemble of spike time intervals will have a larger standard deviation in a synchronous signal than in an asynchronous signal .', 'In our simulations , both the mean phase coherence and the bursting parameter are calculated for neuronal activity from 3000 ms to 10 , 000 ms , unless otherwise noted .'], ['Fig . 1 displays the response properties of the model neurons in our simulations , with Fig . 1A , D showing the frequency-current curves of the model neurons and Fig . 1B , C , E , F showing the PRCs of the model neurons .', 'Type I PRCs in both the Morris-Lecar and the cortical pyramidal neuron models exclusively display phase advances ( positive PRC values ) in response to excitatory perturbations ( Fig . 1B , E ) while Type II PRCs show phase delays ( negative PRC values ) at earlier phases and advances at later phases ( Fig . 1C , F ) .', '( Note that the presence of small negative regions early in Morris-Lecar PRCs and the absence of such regions in cortical pyramidal cell PRCs is a consequence of the fact that spikes consume a much larger portion of the interspike interval in the Morris-Lecar model than in the cortical pyramidal cell model [20] . We therefore ignore these early regions in Morris-Lecar PRCs . )', 'The switch from Type I to II is induced by changes in the steady state activation function of the current in the Morris-Lecar model and by the presence of the slow , low-threshold current in the cortical pyramidal cell model .', "A categorization of Type I and Type II can also be applied to a neuron's frequency-current ( f-I ) relation , with Type I f-I curves exhibiting arbitrarily low frequencies at firing thresholds and Type II f-I curves showing a finite , non-zero firing frequency at threshold .", "While the categorization of a neuron's PRC and f-I curve are not necessarily the same , and the relationship between the curves has not been completely determined [27] , for both models considered here , PRC and f-I curve types coincide ( Fig . 1A , D ) .", 'In both models , increasing frequency by increasing the constant applied current results in an attenutation of phase responses ( Fig . 1 ) .', 'This attenuation occurred in qualitatively different ways for Type I and Type II neurons .', 'In the Type I model neurons , increased firing frequency led to diminished phase advances but did not change the relative shape of the curves–they all remained distinctly Type I ( Fig . 1B , E ) .', 'In the Type II model neurons , however , there was much greater attenuation of the phase-delay region compared to the phase-advance region ( Fig . 1C , F ) .', 'This asymmetric attenuation can affect synchronization properties because the phase-delay region contributes to the increased propensity for synchronization in Type II excitatory networks [12] .', 'Previously , the emergence of phase delay regions at low firing frequencies was attributed to decreased activation of -mediated adaptation currents at low frequencies [12] , [18] , but this explanation cannot apply to the Morris-Lecar model , since it contains no adaptation currents .', "Below we discuss the properties of a cell's hyperpolarizing and depolarizing currents that are responsible for its phase response , and which explain the observed frequency-dependent attenuation .", 'In both models , phase delays exist in the Type II parameter regimes because there is a voltage interval in which activation of an outward , hyperpolarizing current is greater than activation of the inward , depolarizing current .', 'In the Type II Morris-Lecar model , the steady state activation curve of the current , , is shifted to the left and steeper compared to that of the current , , thus providing for this voltage interval .', 'In the Type II cortical pyramidal neuron model , the steady state activation curve , , of the slow , low-threshold current ( which is absent in the Type I neuron ) , is similarly shifted to the left relative to the steady-state activation curve of the current , .', 'In either model , as the voltage trajectory passes through the early part of the interspike interval , a brief , excitatory stimulus will induce a larger response from the lower-threshold current than from the inward current , resulting in negative values of the PRC at early phases .', 'At higher voltage levels later in the interspike interval , the inward current dominates the response to the brief stimulus due to its faster ( instantaneous ) activation dynamics , thus leading to advances in the cycle , and positive values of the PRC at later phases .', 'As firing frequency increases , the cycle trajectory passes through this -dominant voltage interval at a faster rate , thus preventing the full response from developing before reaching voltage levels where the instantaneous inward current can respond .', 'The delaying response to the brief stimulus is thus diluted by the advance-promoting inward current response , and phase delays are attenuated .', 'This attenuation of phase delays is therefore the result of a disparity between the fixed dynamics of the delay-inducing current and the time afforded that current to act by the shrinking interspike interval .', 'Phase advances are less sensitive to frequency modulation since the instantaneous dynamics of the inward currents in both models can directly track the faster cycle trajectory .', 'We further illustrate this point by modulating the speed of the gating variable controlling the delay-inducing potassium current in each model .', 'Fig . 2A demonstrates that in the Morris-Lecar model , increasing , which increases the rate of the gating variable , results in an increase in the amplitude of PRC phase delays , while decreasing has the opposite effect .', 'Faster dynamics allow for faster development of the delaying response to the excitatory stimulus .', 'In this model , modulating also changes the voltage levels during the interspike interval , which can shift the dominant voltage interval to different phases .', 'We systematically quantify the contribution of dynamics to the generation of the phase delay by measuring the changes in the PRC delay depth as a function of for neurons receiving different driving currents and thus exhibiting different intrinsic frequencies ( Fig . 2B ) .', 'The depth of the PRC delay region increased with increasing for all levels of external current , and faster-firing neurons could display similar delay depths as slower-firing neurons with appropriate increases in .', 'While increasing also acted to increase firing frequency ( Fig . 2C ) , phase delay amplitudes nonetheless increased , indicating that speeding up the rate of dynamics exerts a stronger effect on the phase delay than does the accompanying frequency increase .', 'A similar dependence of phase delay amplitude on the rate of the gating variable for the slow , low-threshold current in the cortical pyramidal cell model is shown in Fig . 2D , E .', 'As the rate of dynamics increased ( i . e . , as increased in Eq . 5 ) , depths of the PRC delay increased due to the ability of the current to develop a delaying response before voltage levels were reached where the current activated .', 'Again , increasing the rate of dynamics caused an increase in frequency ( Fig . 2F ) , but the faster development of the response to the perturbation could overcome a frequency-induced attenuation of phase delays .', 'In this model , voltage levels during the interspike interval also changed with the changes in , but they did not greatly influence the phase of maximal delays .', 'In the cortical pyramidal neuron model , the amplitude of phase delays also depended on the rate of the current inactivation ( Fig . 2G–I ) , gated by the variable in Eq .', '2 .', 'Slower inactivation , induced by lower values of in Eq .', '3 , allowed larger responses to the perturbing stimulus , which diluted the delaying effect of the response and therefore attenuated phase delays .', 'The rate of inactivation had little effect on voltage levels as a function of phase during the interspike interval , and only slightly affected the frequency .', 'Increasing the rate of inactivation did induce a decrease in firing frequency , which would promote the observed increase in delay depth , but these changes to firing frequency were too slight to be the primary cause of the enlarged delay amplitude .', 'These results imply that appropriate selection of the rate of variables gating the intracellular currents mentioned above permits the recovery of specified PRC delay depths for different levels of external current .', 'Fig . 3 illustrates this effect for both models .', 'From the curves in Fig . 2B , E , H , appropriate rates of the gating variables were separately selected for each level of external current to induce delay depths of 0 . 04 in the Morris-Lecar neuron and 0 . 025 in the cortical pyramidal neuron .', 'In the Morris-Lecar model , the maximal phase delay region was shifted to the left as the external current increased because the voltage trace was similarly shifted ( Fig . 3A , D ) .', 'However , in the cortical pyramidal cell model , the PRC profiles were virtually identical for different levels of external current , both when the slow potassium current was modified and when the sodium inactivation was modified ( Fig . 3B , C ) .', 'This was due to the fact that the voltage traces ( plotted as a function of oscillatory phase ) were not shifted when either of these intracellular currents were altered ( Fig . 3E , F ) .', 'The invariance of the voltage traces in the cortical pyramidal cell model is an interesting phenomenon , but it is beyond the scope of this paper .'], ['We have shown that excitatory networks composed of neurons with either Type I or Type II PRC properties respond very differently to frequency modulation near firing threshold , with Type I network synchrony remaining largely unaffected by frequency modulation and Type II networks synchronizing much better at lower frequencies .', 'This result is robust in virtually all network parameter regimes in which the network is capable of attaining any appreciable level of synchronization .', 'While both Type I and Type II PRCs are modified by changes in frequency , only Type II PRCs change in qualitative profile .', 'Specifically , the phase delay region , which is known to be critical in promoting synchrony , is severely attenuated .', "Increased frequency therefore tends to have little effect upon Type I networks , since there is no change in the PRC's contribution to synchrony , while in Type II networks it leads to depressed synchrony via the diminished phase delay region of the PRC .", 'It should be noted that our simulations agreed with a large body of previous work showing that neurons with Type II membrane dynamics ( as defined by the frequency-current curve ) tend to synchronize better than neurons with Type I membrane dynamics , when coupled with excitation .', 'Previous theoretical work indicates that when excitatory networks are driven with constant current , those composed of Type I neurons will not synchronize as well as those composed of Type II neurons [10] , , a phenomenon which we observed in our simulations , since much larger synaptic coupling values were required in Type I networks to evoke levels of synchrony equivalent to those in Type II networks ( Fig . 6 ) .', 'Previous theoretical [29] and experimental [30] work has also shown that neurons with Type I membrane dynamics respond to excitatory noisy input with much higher spike-time variability than do neurons with Type II membrane dynamics .', 'This accords with the results of our simulations of networks stimulated by noisy current pulses , where again we saw that greater synaptic coupling was needed for Type I networks to synchronize as well as Type II networks ( Fig . 10 ) .', 'In this study , we focused on the implications for network synchronization of the observed frequency-dependence of PRCs .', 'Our results suggest that the severe attenuation of the phase-delay region of Type II PRCs at increased firing frequencies contributes to the observed decline in network synchronization at such frequencies .', 'Frequency-dependent modification of PRCs has been investigated before in complex , multi-compartment neuronal models [31] , [32] , but such results rely on dendritic effects and hence do not apply to our results using single-compartment neurons .', 'It has been shown in a simple -neuron model that low-threshold adaptation currents can produce negative regions in the PRC at low frequency [18] , an effect which is probably due to the change in bifurcation structure induced by such currents [12] .', 'From this perspective , the delay region of the PRC develops only at low frequency because the adaptation current is saturated at high frequency , resulting in its responding to excitatory stimulation with relatively smaller transient increases .', 'Our work extends this insight by explaining the emergence and attenuation of delay regions in the PRCs of Morris-Lecar neurons , which have no adapting current .', 'Our explanation applies to the cortical pyramidal model neuron , which does feature an adapting current , as well: it is the speed of low-threshold , hyperpolarizing currents relative to the interspike interval which determines the depth of the PRC delay region in Type II cells .', 'For a fixed level of external current , the faster we made the current in the Morris-Lecar neuron and the adapting current in the cortical pyramidal neuron , the larger their PRC delay depths grew .', 'It is therefore not only the saturation level of low-threshold , hyperpolarizing currents that is important , but also the speed with which they can respond to brief stimulation .', 'In addition , our simulations showed that the PRC delay depth is not exclusively controlled by the effects of hyperpolarizing currents , but can be greatly affected by depolarizing currents as well .', 'The faster we made the deactivation of the sodium current , the larger the delay depth grew , underscoring once again the importance of the speed of intracellular currents relative to the interspike interval .', 'The frequency-dependent synchronization which we have described in this paper could potentially be involved in any cognitive process , functional or pathological , which involves spatiotemporal pattern formation of neuronal populations .', 'For example , cholinergically-induced switching between sensitivity and insensitivity to frequency modulation could be important in proper memory consolidation during slow wave and REM sleep , two states that are characterized by differing levels of acetylcholine in cortical and hippocampal regions .', 'Frequency-mediated synchrony could also play a part in the binding of signals from multiple sensory modalities .', 'Gamma oscillations ( 20–80 Hz ) in cortical networks are believed to be generated by synchronous activity of fast-spiking interneurons [33] , which generally exhibit Type II frequency-current relations and PRC profiles [27] , [30] .', 'While excitatory and inhibitory synaptic connections and gap junctions may participate in the synchronous firing of interneuron networks [34]–[37] , our results suggest the importance of the cellular properties of the fast-spiking interneurons in generating synchrony .', 'Additionally , the frequency-dependence of synchronization may provide a means to restrict synchronization to specific frequency bands .', 'Finally , frequency modulation could contribute to the onset of epileptiform activity , and our results might help to explain recent evidence that synchrony decreases during seizures [38] , [39] .', 'At the same time , the importance of our results is not confined to these examples alone .', 'Our findings point to the possibility that Type I and Type II excitatory networks function in two separate coding regimes , with Type I networks functioning in the rate coding regime and Type II networks functioning in the temporal coding regime , effectively acting as low-pass filters .', 'Further experimental investigation into the interplay between cellular properties , frequency , and network synchronization is clearly required .']]
['Introduction', 'Methods', 'Results', 'Discussion']
['Spatiotemporal pattern formation in neuronal networks depends on the interplay between cellular and network synchronization properties .', 'The neuronal phase response curve ( PRC ) is an experimentally obtainable measure that characterizes the cellular response to small perturbations , and can serve as an indicator of cellular propensity for synchronization .', 'Two broad classes of PRCs have been identified for neurons: Type I , in which small excitatory perturbations induce only advances in firing , and Type II , in which small excitatory perturbations can induce both advances and delays in firing .', 'Interestingly , neuronal PRCs are usually attenuated with increased spiking frequency , and Type II PRCs typically exhibit a greater attenuation of the phase delay region than of the phase advance region .', 'We found that this phenomenon arises from an interplay between the time constants of active ionic currents and the interspike interval .', 'As a result , excitatory networks consisting of neurons with Type I PRCs responded very differently to frequency modulation compared to excitatory networks composed of neurons with Type II PRCs .', 'Specifically , increased frequency induced a sharp decrease in synchrony of networks of Type II neurons , while frequency increases only minimally affected synchrony in networks of Type I neurons .', 'These results are demonstrated in networks in which both types of neurons were modeled generically with the Morris-Lecar model , as well as in networks consisting of Hodgkin-Huxley-based model cortical pyramidal cells in which simulated effects of acetylcholine changed PRC type .', 'These results are robust to different network structures , synaptic strengths and modes of driving neuronal activity , and they indicate that Type I and Type II excitatory networks may display two distinct modes of processing information .']
['Synchronization of the firing of neurons in the brain is related to many cognitive functions , such as recognizing faces , discriminating odors , and coordinating movement .', 'It is therefore important to understand what properties of neuronal networks promote synchrony of neural firing .', 'One measure that is often used to determine the contribution of individual neurons to network synchrony is called the phase response curve ( PRC ) .', 'PRCs describe how the timing of neuronal firing changes depending on when input , such as a synaptic signal , is received by the neuron .', "A characteristic of PRCs that has previously not been well understood is that they change dramatically as the neuron's firing frequency is modulated .", 'This effect carries potential significance , since cognitive functions are often associated with specific frequencies of network activity in the brain .', 'We showed computationally that the frequency dependence of PRCs can be explained by the relative timing of ionic membrane currents with respect to the time between spike firings .', 'Our simulations also showed that the frequency dependence of neuronal PRCs leads to frequency-dependent changes in network synchronization that can be different for different neuron types .', 'These results further our understanding of how synchronization is generated in the brain to support various cognitive functions .']
['biology', 'computational biology', 'neuroscience']