A Developmental Switch for Hebbian Plasticity
[['Functional circuits in the brain are rapidly established during early development and are fine-tuned by experience throughout life .', 'In the rodent neocortex , for example , cortical columns form in the first three weeks after birth [1 , 2] .', 'During this period , thalamo-cortical input is essential for columnar formation [3] and stimulus-evoked activity patterns further refine cortical connectivity [4] .', 'Activity-dependent forms of synaptic plasticity , in particular Hebbian plasticity , guide the cortical refinement and are required for functional maturation of cortical circuits [5] .', 'Although the postsynaptic pathways involved in the developmental stages of synaptic plasticity are well characterized ( e . g . [6 , 7] ) , the cellular mechanism on the presynaptic side that triggers the onset of Hebbian plasticity is still unclear [7] .', 'Early in development , pre- and postsynaptic structures are co-localized , even in the absence of any action potential activity [8] , while functional connectivity emerges later in development [8] .', 'Initially , synapses are thus established , but functional communication between neurons is lacking .', 'During this initial phase , spontaneous vesicle exocytosis can help to maintain synapses [9 , 10] .', 'Reduced vesicle release during development reduces the rate of synapse formation ( for review see [11] ) .', 'Here we studied the role of vesicle exocytosis for maturation of associative plasticity .', 'We propose that a switch in vesicular exocytosis mode ensures a discrete onset for Hebbian plasticity and triggers the activity-dependent neural circuit formation during neurodevelopment .', 'The mode of vesicular exocytosis changes rapidly during early development [12] .', 'In immature synapses , neurotransmitter vesicles spontaneously fuse with the membrane whether or not there was a preceding action potential ( spontaneous vesicle exocytosis , SVE ) , whereas in mature synapses evoked vesicle exocytosis ( EVE ) dominates synaptic communication [12] .', 'EVE can occur within an interval of several milliseconds ( synchronously evoked vesicle exocytosis ( sEVE ) ) or delayed up to several hundred milliseconds ( asynchronous evoked vesicle exocytosis ( aEVE ) ) after the action potential ( Fig 1A ) .', 'Each mode of vesicle exocytosis has the ability to coordinate activity across a synapse , potentially leading to associative plasticity in neural networks .', 'Immature neurons , due to their high input resistance , small size , slow membrane time constant and prolonged decay constant of the excitatory postsynaptic potential ( EPSP ) [13 , 14] , have a relatively high probability to generate an action potential resulting from postsynaptic integration of uncorrelated synaptic inputs ( SVE ) .', 'The impact of vesicle exocytosis on synaptic communication changes with development .', 'With reduced input resistance and a faster decay of EPSP [13 , 14] the postsynaptic window of opportunity for coincidence detection is shortened such that only temporally correlated presynaptic activity ( EVE ) can be efficiently integrated by the postsynaptic neuron .', 'While the molecular mechanisms for the three principal modes of vesicle exocytosis ( SVE , aEVE , sEVE ) have been characterized [15] , the functional role for SVE and aEVE is currently not clear [15–17] .', 'Here , by modeling the developmental changes in exocytosis mode , we show that SVE optimally prepares neural circuits for learning by maintaining synaptic weights in the appropriate dynamic range and homogenizing the synaptic weights into a tight homogeneous distribution .', 'A switch to EVE initiates a period of rapid synaptic plasticity where synaptic input can be efficiently stored in the network .', 'The SVE-EVE balance regulates the rate of Hebbian plasticity in the synapse and learning in neuronal networks .', 'Besides the role of asynchronous exocytosis in gain modulation [18] , we show that increased locking of vesicle exocytosis to the action potential causes maturation of the STDP rule [19] .', "These results argue that SVE , often considered as 'synaptic noise' , plays an important role in synaptic plasticity during neurodevelopment and predict that a developmentally regulated switch in the mode of vesicular exocytosis contributes to the activity dependent organization of the developing circuits ."], ['Most computational studies of synaptic plasticity with spiking neurons use a spike-timing dependent plasticity ( STDP ) rule [20 , 21] , implicitly assuming that a presynaptic action potential leads to correlated vesicle exocytosis within a short interval .', 'We focus on the timing of vesicular exocytosis , irrespective of whether it is preceded by presynaptic action potentials , leading to vesicle-timing dependent plasticity ( VTDP model ) .', 'Vesicles that are exocytosed within a canonical STDP time window contribute to time-dependent weight changes as described by the STDP model ( Eq ( 7 ) ) .', 'Vesicle exocytosis can occur in three different modes ( Fig 1A and 1B ) .', 'For SVE , exocytosis is independent of the arrival of an action potential at the presynaptic terminal [15] .', 'For aEVE , exocytosis depends on the calcium concentration and the timing of exocytosis is therefore only loosely coupled to an action potential; each action potential induces a presynaptic calcium influx , whose intracellular concentration exponentially decays .', 'For sEVE , exocytosis immediately follows an action potential .', 'To study synaptic competition using the VTDP model , we simulated a network model comprised of feed-forward connections from 500 presynaptic neurons to 10 postsynaptic neurons .', 'A subset of the presynaptic neurons ( 20% ) had a higher firing rate ( 8 Hz ) compared to the rest ( 4 Hz ) .', 'We used a Poisson process to generate action potentials at these rates .', 'In turn , vesicle exocytosis from the presynaptic terminal was modeled as Poisson processes for SVE , aEVE and sEVE .', 'In the model the probability of exocytosis depended on proteins that are available to support each of the different exocytosis modes .', 'The switch from SVE to EVE is implemented by reducing the fraction of vesicles that are available for SVE and increasing the fraction of vesicles that are available for aEVE or sEVE such that the sum of the fractions remains constant .', 'The probability for vesicle exocytosis also depended on the fraction of available vesicles at the synapse ( Eq ( 3 ) ) .', 'The rate of vesicle release for sEVE was directly related to the firing rate of each neuron .', 'The release rate of SVE was scaled with the mean firing rate of all presynaptic neurons to obtain the same mean release rate as EVE .', 'The rate of asynchronous release depended on the amount of residual Ca2+ , which decays exponentially ( Eq ( 4 ) ) .', 'The total amount of Ca2+ entering the presynaptic terminal in response to a single action potential was also scaled to yield the same mean release rate as the other exocytosis modes .', 'Thus , to effectively titrate the differential contribution of the release rate to synaptic plasticity , the cumulative release was normalized such that the mean and total vesicle release rates were equal for the three modes of neurotransmission .', 'An exocytosed vesicle was moved from the active pool to the recycling pool .', 'Recovery from the recycling pool to the active pool was modeled as an exponential process ( Eq ( 5 ) , [22] ) .', 'The neurotransmitters released from each vesicle induced an excitatory postsynaptic current that decayed within several ms . We used leaky integrate-and-fire neurons with an adaptive spike threshold for the postsynaptic neurons .', 'A homeostatic rule kept the firing rate of the postsynaptic neurons at the desired dynamic range ( ~5 Hz ) by scaling the synaptic weights accordingly ( Eq ( 8 ) ) .', 'Thus , for SVE , vesicle exocytosis was spatially ( across synapses belonging to the same neuron ) and temporally ( across time within individual synapses ) random and was not coupled to the onset of presynaptic action potential ( Fig 1B ) .', 'For aEVE , vesicle exocytosis was spatially biased to synapses belonging to presynaptic neurons with higher firing rates , but it was temporally diffuse ( Fig 1B ) .', 'For sEVE the vesicle exocytosis was both temporally and spatially linked to the spiking activity of the neurons ( Fig 1B ) .', 'Synaptic plasticity leads to competition between synapses when presynaptic cells are active at different rates [20] .', 'In the VTDP model , synapses that were active prior to a postsynaptic action potential were strengthened whereas the others were weakened .', 'We used the VTDP model to study how the three vesicle exocytosis modes contribute to synaptic competition .', 'When synaptic communication was mediated by SVE alone , the chemical neurotransmission did not lead to competition between synapses onto the same postsynaptic neuron , and maintained synaptic weight distribution to a homogeneous distribution , also referred to as a unimodal distribution ( Fig 1C ) .', 'Introducing a ( partial ) switch to either aEVE or sEVE caused divergence between synaptic weights for the synapses of the high and low firing rate neurons .', 'The gradual change in synaptic efficacy results in a heterogeneous synaptic efficacy distribution in the network , with synapses that were either weak or strong , but fewer of the intermediate strength ( referred to as multimodal ) .', 'The amount of divergence ( the degree of separation between high and low synaptic weights ) between synapses of the low- and high firing rate neurons depended on the SVE-EVE balance ( Fig 1D ) .', 'When vesicle exocytosis was dominated by EVE we found that asynchronous exocytosis resulted in a moderate , and synchronous exocytosis resulted in a strong drive to increase the synaptic weights of the higher firing presynaptic neurons at the expense of synapses of the lower firing rate neurons ( Fig 1E ) .', 'The SVE-EVE balance regulated the rate at which synaptic competition occurred ( Fig 1F ) .', 'Correlated input could thus shape the structure of the network via EVE .', 'As the rates of vesicle exocytosis onto the postsynaptic neuron were normalized such that they are equal for the three modes , this difference in outcome is caused by their spatiotemporal structure of the synaptic inputs to the postsynaptic neuron .', 'This model of vesicle-timing dependent plasticity shows that the SVE-EVE balance can regulate the rate with which new patterns of action potentials are imprinted into synaptic weights .', 'A switch from SVE to EVE enables a discrete onset for Hebbian plasticity and initiates a period at which synaptic weights rapidly rewire to represent dominant sensory activity .', 'The SVE-EVE balance can control the rate of Hebbian plasticity .', 'In addition to the above described functional role for SVE to control the rate of Hebbian plasticity , we explored other functional roles for SVE .', 'We first compared the effect of SVE ( Fig 2A ) to that of EVE with uncorrelated spiking activity ( Fig 2B ) on the distribution of synaptic weights .', 'We found that SVE homogenizes the synaptic weights into a tighter weight distribution compared to EVE ( Fig 2C ) .', 'SVE events occur more diffusely compared to EVE , and furthermore the larger EPSC inputs from EVE result in stronger correlations between pre- and postsynaptic spiking .', 'Thus , an additional functional role of SVE is homogenization into a tight synaptic weight distribution and increased stability against synaptic weight fluctuations compared to EVE .', 'Homogenization is also important for synaptogenesis , because newly formed synapses with small initial weights grow stronger and become incorporated into the synaptic pool ( Fig 2D ) .', 'Next we asked whether SVE during early development was necessary at all; and what would happen for a gradual increase in EVE in the absence of SVE .', 'Synaptic fluctuations as well as divergence in synaptic weights due to differences in firing rate can be prevented by completely abolishing vesicle release ( no SVE , no EVE ) .', 'If neither SVE nor EVE are present , synaptic weights become saturated due to the homeostatic mechanism ( Fig 2E , Eq ( 8 ) ) .', 'If EVE increases gradually during development , synaptic weights also increase due to the homeostatic mechanism , while remaining heterogeneously distributed ( Fig 2F ) .', 'Thus SVE is necessary to maintain synaptic weights in the appropriate dynamic range .', 'SVE and EVE release mechanisms thereby both serve a biological role in synapse formation and synaptic maintenance [9–11] .', 'After the switch from SVE to EVE and subsequent changes in synaptic weight distribution across synapses occurred , the network now consists of a few strong synapses among many other weak ones [20 , 23] .', 'This change in synaptic weight distribution shapes the network’s ability to encode patterns of action potentials and translate them into memory traces .', 'We aimed to establish the differential roles of the exocytosis modes in the activity dependent organization of cortical circuits .', 'The VTDP model implements the plasticity terms and vesicle exocytosis times separately for each synapse .', 'Such operations are on matrices of size Ni x No ( number of input neurons x number of output neurons ) , which is computationally more demanding than the classical STDP modeling which generates spike times and thus works with operations on vectors of size Ni and No .', 'We therefore used a rate model that represents vesicle-timing dependent plasticity , consisting of a similar structure and that can be implemented with better computational efficiency ( Fig 3A ) .', 'The rate model will help other computational studies that want to conduct follow-up studies to implement our model efficiently .', 'The exocytosis rates are a combination of SVE ( randomly distributed across synapses ) and EVE ( strong for the subset of highly active presynaptic neurons ) .', 'The evolution of synaptic weights is then followed over time .', 'Synaptic efficacy is potentiated for synapses with high vesicle exocytosis rates at the expense of synapses that have lower rate of exocytosis ( Fig 3B ) .', 'Each network was initialized either without any particular structure , with each synaptic strength set randomly according to a unimodal distribution , or with a previously encoded weight pattern , comprised of a bimodal distribution of low and high values , that is different from the pattern presented ( Fig 3C ) .', 'While no pattern of action potentials could be stored during SVE , synaptic communication through EVE introduces competition that enables storage of the patterns of action potentials ( Fig 3D ) .', 'A switch from SVE to EVE thus generates a window of opportunity for a cortical network to rewire as instructed by experience .', 'Rewiring an established circuit after the switch takes significantly more time than starting from a homogeneous state without patterns of action potentials imprinted ( Fig 3E ) .', 'SVE can thus be used to maintain baseline network activity and unspecific network connectivity , and the SVE-EVE balance regulates the rate at which time neural circuits are shaped by patterns of action potentials .', 'How is the SVE-EVE balance regulated ?', 'An initial suggestion that SVE and EVE might utilize distinct vesicle pools [24] was accompanied by a concerted research effort to characterize the differential regulatory pathways that impact vesicle exocytosis ( for reviews , see [15 , 25] ) .', 'Optical recordings from developing neurons in vitro demonstrated a switch from SVE to predominantly EVE as neurons matured [12] .', 'The switch to EVE at the synaptic terminal occurs independent from whether there is functional communication with a postsynaptic neuron , suggesting a cell-autonomous process [12] .', 'Investigations in cell-autonomous regulation of vesicle exocytosis focus on the functional properties of the proteins involved in the docking of vesicles to the presynaptic membrane such as the SNARE proteins Syntaxin , SNAP-25 , and VAMP2/Synaptobrevin and a core set of SNARE-binding proteins: Synaptotagmin , Munc13 , Munc18 , Doc2 and Complexin [25] .', 'Exocytosis of vesicles docked at the active zone in the presynaptic terminal is mediated by calcium-sensitive proteins .', 'Calcium sensitivity and kinetics of vesicle exocytosis depends on the calcium sensors expressed .', 'The presence of high-affinity calcium sensor Doc2b increases the fraction of SVE exocytosis [26] , which might also act completely independent of presynaptic action potential induced calcium entry [27] .', 'Doc2a on the other hand facilitates aEVE [28] .', 'sEVE is mediated by Synaptotagmin1 , which is selectively enhanced by Complexin that can act as a fusion clamp or adaptor to inhibit SVE and aEVE [29 , 30] ( Fig 4A ) .', 'The expression of these calcium sensors varies across time , which is reflected in the corresponding mRNA expression levels .', 'We re-analyzed the human transcriptome [31] for mRNA expression profiles of the calcium sensitive proteins during neurodevelopment and found high Doc2b expression early in development was followed by a peak in Doc2a , while Synaptotagmin1/Complexin1 became prominent during early childhood ( Fig 4B ) .', 'These profiles are consistent with a switch from high SVE to aEVE early in development and dominant sEVE at later developmental stages .', 'To study the developmental learning rate , the SVE , aEVE and sEVE ratio profiles were used to mimic a biological situation .', 'The synapses belonging to the higher firing rate neurons strengthen at the expense of the synapses belonging to the lower firing rate neurons ( for EVE , not for SVE ) .', 'The learning rate ( see Eq ( 9 ) in the Materials & Methods ) diminishes if the synaptic weights approach their upper and lower bounds , which resulted in a learning rate peak around infancy ( Fig 4C ) .', 'During development , new synapses were formed [32] and weak synapses were pruned ( [33] , see Materials & Methods ) .', 'Early in development the rate of synaptogenesis was larger than the rate of synaptic pruning , which caused a rise in synaptic density ( Fig 4D ) .', 'After EVE became more dominant , the rate of synaptic pruning became larger than synaptogenesis , which caused a decrease in synaptic density .', 'The SVE-EVE switch thus coincides in time with the early stages in human neurodevelopment [34 , 35] .', 'There is a rapid increase in synaptogenesis around the time of birth for all cortical areas , while a burst of synapse formation occurs at different ages in cortical regions [36] .', 'In the visual cortex , for example , synapse formation is accelerated between 3 and 4 months and the maximum density is reached between 4 and 12 months , while synaptogenesis in the prefrontal cortex reaches its peak well after the first year [34] .', 'After the peak in synaptic density , corresponding to about 150% of adult levels , a sensitive period with high levels of associative plasticity occurs , whereas plasticity that occurs beyond the end of this sensitive period alters connectivity patterns within the architectural constraints established during the sensitive period [34 , 35] .', 'These developmental patterns are highly conserved throughout many species [36] .', 'A transition from an immature to mature STDP rule is observed during early cortical development of the rat somatosensory cortex ( Fig 5C , [19] ) .', 'The transition coincides in time with a critical period in circuit formation in the barrel cortex , during which extensive activity-dependent pruning occurs , confining neuronal arborizations to the columnar structure in the barrel cortex ( [1] , Fig 5A ) .', 'At the same time , a functional transition occurs from predominantly spontaneous , stimulus-indepedent activity early in development to stimulus-dependent activity later in development ( [2] , Fig 5B ) .', 'The action potential-dependent responses in the intermediate stages are typically prolonged and with high variability , which matures to responsiveness that is tightly synchronized to the stimulus .', 'By modeling the corresponding changes in exocytosis using the VTDP model ( see above ) , we found that STDP expression matures because of the switch to vesicle exocytosis that is increasingly time-locked to the stimulus ( [19] , Fig 5C ) .'], ['At the presynaptic terminal , proteins involved in the exocytotic machinery determine the SVE-EVE balance .', 'The expression of the relevant calcium sensitive proteins can be genetically regulated , and evidence for a cell-autonomous switch from SVE to EVE has previously been shown in vitro [8 , 12] .', 'Despite the fact that both SVE and EVE have the potential to drive Hebbian plasticity across the synapse , it is unclear how , where and when Hebbian plasticity develops in the first place [7] .', 'The model presented here mechanistically links the mode of vesicular exocytosis to Hebbian plasticity during neural development .', 'As the switch from SVE to EVE is genetically regulated , it is an ideal candidate mechanism to initiate region , layer and cell specific onset of Hebbian plasticity .', 'Specific regulation of the onset of Hebbian plasticity is , for example , important for a hierarchical system in order to optimally deal with the input statistics , such that sensitivity to low-level features ( i . e . orientation ) develop prior to rewiring the circuits that deal with high-level features ( i . e . object recognition ) [42] .', 'Neural circuits dealing with sensory information first establish diffuse connectivity with broad receptive fields , followed by selection and refinement of the projections ( Fig 5A , [1 , 5] ) .', 'Whereas electrophysiological recordings of neural circuit development can be biased towards characterizing high firing rate neurons , the role of the SVE-EVE balance is optimally studied with optical and molecular techniques that can assess specific cell activity and collect large population statistics without bias [53] .', 'Further development of molecular techniques to regulate and track the cellular content of the SVE-EVE balance together with optical recording techniques is necessary for fundamental insights in the role of vesicular exocytosis on the structural and functional aspects of synapse maturation and maintenance during neural development .', 'Our results predict that SVE plays a permissive role in the expression of synaptic plasticity and is important for the maintenance of synaptic strengths by disconnecting the action potential-dependent activity during early neurodevelopment .', 'In agreement with this proposition , selective disturbance of SVE release in Drosophila neuromotor junction alters the structural organization of the synapses during development [54] .', 'Understanding the specificity of cell-autonomous regulation of the SVE-EVE balance across time and brain region will provide important insight into the maturation of synaptic wiring and creation of functional networks during brain development .', 'An SVE-EVE imbalance might result in learning deficits because functional circuits would not be appropriately formed by sensory experience in the absence of the regulated switch in the mode of neurotransmitter release .', 'As such , deregulation of the molecular pathways of the three modes of vesicle exocytosis might contribute to the etiology of neurodevelopmental disorders .', 'For example , the expression of Complexin1 , a protein that suppresses SVE and enhances EVE , is dysregulated in patients with schizophrenia , depression and bipolar disorder [55] .', 'Complexin1 knock-out mice show developmental deficits [55] .', 'Hence understanding the molecular mechanisms underlying vesicle exocytosis in relation to developmental regulation of Hebbian plasticity may lead to the rational design of treatments that could alleviate learning deficits early in neural development .'], ['To study Hebbian plasticity in a feed-forward network architecture we use leaky integrate-and-fire neurons:', 'dVdt=− ( V−Vrest ) τm+IvesCm', '( 1 )', 'The neurons have a resting membrane potential Vrest , a membrane time constant τm and a capacitance Cm ( for parameter values see Table 1 ) .', 'Each vesicle induces a postsynaptic current Ives ( See Eq ( 6 ) below ) .', 'Refractoriness was modeled with the adaptive action potential threshold:', 'dθmdt=− ( θm−θrest ) τθ', '( 2 )', 'The adaptive threshold θm is reset to θmax directly after an action potential and returns with a time constant τθ to the threshold value at rest θrest ( for parameter values see Table 1 ) .', 'We describe vesicle exocytosis in terms of the rate of Poisson processes for SVE , aEVE and sEVE .', 'The resulting probability of exocytosis depends on the number of molecules that are available to support each of the different exocytosis modes , described here in terms of the fraction ξSVE , ξaEVE , and ξsEVE , the sum of which is one per synapse .', 'The switch from SVE to EVE is implemented by reducing ξSVE and increasing ξaEVE or ξsEVE , for which ξSVE = 1- ξaEVE - ξsEVE .', 'The probability of exocytosis ( v ) during a short interval ( we used the Euler Method to solve the differential equations with time steps of Δt = 1 ms ) , from presynaptic neuron i to postsynaptic neuron j , depends on the fraction of the available ( Pa , ij , see Eq ( 5 ) ) over the total ( Pc ) vesicle pool:', 'vSVE , ij=n⋅rm⋅ξSVEPa , ijPcΔtvaEVE , ij=Caij⋅ξaEVEPa , ijPcΔtvsEVE , ij=n⋅ri⋅ξsEVEPa , ijPcΔt', '( 3 )', 'For a fair comparison of the different exocytosis modes and have the same average release rate , vSVE is scaled by the mean firing rate that would drive the number of vesicles released through sEVE ( rm = Σri /N ) averaged across all N presynaptic neurons and vaEVE depends on the amount of residual Ca2+ , which decays exponentially with time constant τCa ( parameter values in Table 1 ) :', 'τCadCa ( t ) dt=−Ca ( t )', '( 4 )', 'The total amount of Ca2+ entering the presynaptic terminal in response to a single action potential is given by A = n dt / τCa , such that each action potential is modeled to exocytose 4 vesicles for ξaEVE = 1 .', 'Likewise , the same number ( n = 4 ) vesicles is released by sEVE for each action potential .', 'Firing rate is high ( 8 Hz ) for a subpopulation ( 20% ) of the presynaptic neurons compared to the other neurons ( 4 Hz ) .', 'The release probabilities are normalized such that for each release mode the average rate of vesicles release is the same , only the spatiotemporal structure of the synaptic inputs onto the postsynaptic neuron is different .', 'Most synapses in the brain maintain a single active zone [59] with vesicles for docked exocytosis [60] , while an axon can make multiple connections between cells .', 'The active zone increases in size during development [61] , and the number of docked vesicles is linked to the size of the active zone [62] .', 'We study vesicle pool utilization in the different modes , and set the total vesicle pool per synapse ( Pc ) to 100 .', 'A vesicle that is exocytosed , is moved from the active pool ( Pa ) to the recycling pool ( Pr ) and returns to the active pool according to:', 'τrecdPadt=Pr', '( 5 )', 'With τrec being the vesicle recycling rate ( parameter value in Table 1 ) .', 'The postsynaptic current ( Ives ( j ) ) on neuron j is the sum of currents caused by vesicles released from the presynaptic neurons i at time tves , i .', 'Each vesicle caused a current Ives ( i , j ) which is described by:', 'Ives ( i , j ) =wij⋅e− ( t−tves ) τα for tves<t<tves+twindow', '( 6 )', 'With time constant τα = 3 ms . For computational efficiency only the currents generated by recently exocytosed vesicles are used , with twindow = 20 ms , after which only less than 0 . 2% of the initial current remains .', 'Synaptic weights are modified according to the Hebbian learning rules:', 'dwij+=λw01−μwijμe−|Δs|τ ifΔs>0dwij-=−λαwije−|Δs|τ ifΔs<0', '( 7 )', 'With μ = 0 . 4 , w0 = 5% of mean initial weights ( wij ( 0 ) ) , λ = 0 . 1 , α = 0 . 11 , τ = 20 ms [58] , and here Δs denotes the delay between vesicle exocytosis and the postsynaptic action potential , rather than the integration time step in the preceding text .', 'We use homeostatic scaling to maintain the overall firing rate of the postsynaptic neuron at a fixed level across longer periods [57] .', 'This results in competition because strongly activated synaptic connections undergo potentiation at the expense of other synaptic connections projecting to the same postsynaptic neuron , balancing the total incoming synaptic activity to maintain the desired output firing rate [63]:', 'τhdwijdt= ( rm−rj ) ⋅wij', '( 8 )', 'With τh the timescale of homeostatic scaling , rm the desired firing rate ( which we set to the mean input firing rate ) and rj the firing rate of postsynaptic neuron j ( the running average is across the last 12 spikes ) .', 'For parameter values see Table 1 .', 'The network consists of 500 input neurons that are connected to 10 output neurons .', 'A subset of neurons that has high firing rates represent neurons with receptive fields that are strongly activated by external stimuli .', 'The presynaptic neurons produce Poisson distributed action potentials according to a probability ps = ri * Δt .', 'Initially , SVE equilibrates the network to the desired firing rate ( rm ) , leading to a mean synaptic weight wij ( 0 ) .', 'Synaptic strength has hard bounds at 0 and 8 * wij ( 0 ) , when it exceeds these extreme values it is reset to 0 or 8 * wij ( 0 ) , as appropriate .', 'Learning has occurred when the distribution of synaptic weights has become bimodal .', 'We quantified the learning rate as the time change of the ratio of the median synaptic weight of the higher firing rate synaptic connections ( Mhigh ) over that of the lower firing rate synaptic connections ( Mlow ) :', 'Λ ( t ) =dD ( t ) Δt', '( 9 )', 'Here Λ ( t ) is the learning rate , D ( t ) = Mhigh ( t ) / Mlow ( t ) .', 'We used median synaptic weights because it is more robust than the mean and we used a ratio to make the measure independent of the overall scale of M . To mimic a biological developmental profile , we used mRNA expression levels for Doc2b ( SVE ) , Doc2a ( aEVE ) and Synaptotagmin1 * Complexin1 ( sEVE ) from a database of experimentally measured mRNA expresssion levels [31] .', 'During maturation , in the model new synapses were formed with strength wij and probability ( P ) :', 'Pij=k⋅Δt', '( 10 )', 'New synapses form between unconnected neurons i and j at a rate of 8% newly formed synapses per 2 weeks for early development ( k = 6 . 6 x 10−8 ) , 5% during early childhood ( k = 5 . 0 x 10−8 ) and 3% during adolescence and later ( k = 2 . 5 x 10−8 ) [32] .', 'The generation rates were increased by a factor 106 for computational efficiency , while the relative duration of each developmental stage was preserved [31] .', 'Synaptic stabilization is activity-dependent and involves the formation of PSD-95 [64] , and weak synapses are in general easily pruned [33] .', 'Hence , weak synapses with strength wij < 0 . 7 wij , were eliminated and large synapses were limited to strength 8 * wij .', 'We used a rate model incorporating the dynamics due to vesicle-timing-dependent plasticity to study the effect of the initial weight distribution on the ability to encode patterns of action potentials .', 'It incorporates competition between the exocytosis rates from all presynaptic neurons i that project to the same postsynaptic neuron j:', 'ddtwij=γ ( xij−x¯j ) ⋅s', '( 11 )', 'Where wij is the synaptic strength , xij is the rate of vesicle exocytosis ( see Eq ( 12 ) below ) , x¯j is the average input rate to postsynaptic neuron j , γ the rate constant and s is defined below ( parameter values in Table 1 ) .', 'We use homeostatic scaling to maintain the overall firing rate of the postsynaptic neurons at a fixed level across longer periods ( see Eq ( 8 ) , [57] ) .', 'To keep synaptic weights within a specific range , the rate at which weights change is scaled [65] , here by choosing s = wij2 for LTD ( xij < xj ) and s = wij − wij2 for LTP ( xij > xj ) .', 'Hence large synapses undergo stronger depression during periods of little activity , whereas medium sized synapses are most strongly potentiated in times of correlated activity [66] .', 'This scaling factor affects the overall magnitude of the rate of change of dwij , but the direction of change , whether it gets weakened or strengthened , depends on the rate of exocytosis at each synapse , which i
['Introduction', 'Results', 'Discussion', 'Materials and Methods']
['Hebbian forms of synaptic plasticity are required for the orderly development of sensory circuits in the brain and are powerful modulators of learning and memory in adulthood .', 'During development , emergence of Hebbian plasticity leads to formation of functional circuits .', 'By modeling the dynamics of neurotransmitter release during early postnatal cortical development we show that a developmentally regulated switch in vesicle exocytosis mode triggers associative ( i . e . Hebbian ) plasticity .', "Early in development spontaneous vesicle exocytosis ( SVE ) , often considered as 'synaptic noise' , is important for homogenization of synaptic weights and maintenance of synaptic weights in the appropriate dynamic range .", 'Our results demonstrate that SVE has a permissive , whereas subsequent evoked vesicle exocytosis ( EVE ) has an instructive role in the expression of Hebbian plasticity .', 'A timed onset for Hebbian plasticity can be achieved by switching from SVE to EVE and the balance between SVE and EVE can control the effective rate of Hebbian plasticity .', 'We further show that this developmental switch in neurotransmitter release mode enables maturation of spike-timing dependent plasticity .', 'A mis-timed or inadequate SVE to EVE switch may lead to malformation of brain networks thereby contributing to the etiology of neurodevelopmental disorders .']
['Neurotransmitter release is the principal form of chemical communication in the brain .', 'When an action potential reaches a synapse , calcium influx activates the machinery for neurotransmitter release .', 'During early neuronal development this machinery matures such that neurotransmitter release becomes time-locked to action potentials .', 'By modeling this change in neurotransmitter release , we mechanistically show that the maturation process can be solely responsible for switching on associative ( i . e . Hebbian ) plasticity in the brain .', 'The relevant proteins of the release machinery can thereby regulate the rate at which neural circuits represent sensory input , providing a novel mechanism to control the learning rate and onset .', 'Appropriately timing of the onset of Hebbian plasticity is important because during early development sensory experience fine-tunes , often irreversibly , the neural wiring in our brain .']
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