Neurons possess highly branched , complex dendritic trees , but the relationship between the structure of the dendritic arbor and underlying neural function is poorly understood 1 ., Recent studies suggest that dendritic branches form independent computational subunits: Individual branches function as single integrative compartments 2 , 3 , generate isolated dendritic spikes 4 , 5 linking together neighbouring groups of synapses by local plasticity rules 6–8 ., Coupling between dendritic branches and the soma is regulated in a branch-specific manner through local mechanisms 9 , and the homeostatic scaling of the neurotransmitter release probability is also regulated by the local dendritic activation 10 ., The computational power of active dendrites had already been demonstrated by several computational studies 11–16 , but how local events influence the output of the neuron remained an open question ., Using the cable equation 17 or compartmental modelling tools one can calculate the current or voltage attenuation between arbitrary points in a dendritic tree 14 , which is in good agreement with in vitro recordings ., However , cortical networks in vivo are believed to operate in a balanced state 18 , 19 , where the inhibitory drive is continuously adjusted such that the mean activity of the population is nearly constant 20 , 21 ., In this case , the firing of an individual neuron is determined , beyond its own input , by the activity distribution of the population ., A simple cascade model 22 incorporating numerous dendritic compartments allowed us the statistical estimation of the activity distribution of neurons within the population ., We used this model to study how localized dendritic computations influence the output of the neuron ., The present study focuses on hippocampal granule cells ., Compared to pyramidal neurons granule cells have relatively simpler dendritic arborization: They lack the apical trunk and the basal dendrites , but are characterized by several , equivalent dendritic branches , extended into the molecular layer 23 ( Figure 1A ) ., Recordings from freely moving rats revealed that like pyramidal neurons , granule cells exhibit clear spatially selective discharge 24 , 25 ., However , granule cells had smaller place fields than pyramidal cells , and had multiple distinct subfields 24 , 26 ., It has also been recently shown that these subfields are independent , i . e . , their distribution was irregular and the transformation of the environment resulted in incoherent rate change in the subfields 26 ., The dendritic morphology of granule cells suggest that parallel dendritic computations could contribute to the generation of multiple , distinct subfields of these neurons ., In the present study we analyzed how synaptic input arriving to dendritic subunits influence the neuronal output ., First , we introduce the model used in this study and we define statistical criteria to measure if a dendritic branch alone is able to trigger somatic spiking ., We show , that generally neurons perform input strength encoding i . e . , input to the whole dendritic tree but not activation of a single branch is encoded in the somatic firing ., Next we demonstrate that if the local response is enhanced by active mechanisms ( dendritic spiking and synaptic plasticity ) then neurons switch to feature detection mode during which the firing of the neuron is usually triggered by the activation of a single dendritic branch ., Furthermore we show that moderately branched dendritic tree of granule cells is optimal for this computation as large number of branches favor local plasticity by isolating dendritic compartments , while reliable detection of individual dendritic spikes in the soma requires low branch number ., Dendritic branches of dentate granule cells could therefore learn different inputs; and the cell , activated through different dendritic branches , could selectively respond to distinct features ( locations ) , participating in different memories ., Finally using spatially organized input we illustrate that our model explains the multiple independent place fields of granule cells and these dendritic computations increase the pattern separation capacity of the dentate gyrus ., Supposing that firing rates of presynaptic neurons ( uj ) are independent and identically distributed we assume that the total input of the dendritic branches Ui\u200a=\u200aΣjwijuj is drawn randomly from a Gaussian distribution with mean μ and variance σ2: ( 5 ) where pU indicates a probability distribution over U ( Figure 1C; see Eq . 17 in Methods for parameters specific to hippocampal granule cells ) ., More specifically , indicates the distribution of the magnitude of possible total inputs to a single dendrite over many different instances ., Based on the distribution of the total input , we can compute the distribution of the somatic activation and determine the firing threshold ( β ) according to the proportion of simultaneously active cells ( the sparseness of the representation , spDG ) in the DG 24 ., First , we rearrange Eq ., 3 using the input distribution to express the distribution of : ( 6 ) where indicates that the inputs of the dendritic branches are randomly sampled from a Gaussian distribution ., We substitute Eq ., 6 into Eq ., 4 , and we get ( 7 ) We can assume again , that the inputs ( Ui ) of the dendritic branches are independent and identically distributed variables ., ( Note , that while the activations are not independent because of the back-propagation of currents from the soma , the inputs are . ), If N is high enough , we can approximate the sum in Eq ., 7 with a Gaussian distribution , and rewrite the equation: ( 8 ) where indicates a probability distribution over , while μF and are the expected value and the variance of the dendritic integration function F ( U ) given the input distribution : ( 9 ) ( 10 ) We calculated the integrals 9–10 with two different forms of dendritic integration of synaptic inputs: a linear and a quadratic function ( Figure 1C ) ., The details of these calculations are in the Supporting Information ( Text S4 ) ., In this paper we do not model inhibitory neurons in the dentate gyrus , however , we assume , that they play a substantial role in continuously adjusting the firing threshold of principal neurons and regulating the activity of the network 20 , 21 ., As a result of this regulation always the most depolarized neurons are able to fire , and the proportion of simultaneously active neurons is characteristic for different hippocampal areas 24 , 29 ., Given that all neurons share a common input statistics and have similar internal dynamics , equation 8 also describes the distribution of across the granule cell population at a given time ., If only the most depolarized 1–5% of the population are able to fire 29 , this also means that only those neurons exceed their firing threshold whose activation is within the uppermost 1–5% of the distribution described by Eq ., 8 ., Therefore , the proportion of simultaneously active neurons within the dentate gyrus spDG 24 , 29 also determine the firing threshold β for granule cells ., We approach the dendritic independence by focusing on the statistical distributions of the input to dendritic branches , as these branches form the basic computational subunits in our model ., We ask whether the input of a single branch could be sufficiently large to significantly depolarize not only the given branch but also the soma of the neuron ., We defined two conditions to study whether the spiking of the neuron is caused by the activation of a single dendritic branch or by the simultaneous depolarization of multiple branches ., First , the conditional probability is the probability of firing given that any branch k has total input Uk\u200a=\u200aΣjwkjuj , while inputs to all other branches are random and independent samples from the distribution of ( Figure 2A ) ., At those Uk values where this probability is close to 1 the cell tends to fire when any of the dendritic branches gets that input ., Second , the conditional distribution is the distribution of the synaptic input of the most active branch at the time the depolarization of the soma exceeds the firing threshold ( β ) , where U* is the total synaptic input arriving to the most active branch ( Figure 2A ) ., K ( U* ) can be regarded as the marginal distribution of above the firing threshold ( Figure 2B ) ., The probability mass of this function shows the typical maximal input ( U* ) values when the neuron fires ., These two conditions together determine whether a single branch can be sufficiently depolarized to trigger somatic spike or not ., If the probability of firing is high ( H ( U ) ≈1 ) at typical input values ( K ( U* ) ) then the firing of the cell is caused by a single branch ., With the definition of Gasparini and Magee 30 we call this form of information processing as independent feature detection ., On the other hand , if the firing probability is low ( H ( U ) ≪1 ) even if one of the branches receive extremely large input ( U* is high ) then the cell mostly fires when the overall dendritic activation is high , and even the most depolarized branch usually fails to make the neuron fire ., We use the expression input strength encoding 30 to denote this second type of computation ., The calculation of the two functions H ( U ) and K ( U* ) is described in the Methods section ., First we chose unstructured synaptic input , i . e . , the firing of entorhinal neurons were independent and the strength of all synapses were equal ., In this case we approximated the total synaptic input U to a branch with a Gaussian distribution ( Eq . 5 , Figure 1C ) ., Given the input distribution we asked whether the excitation of single branches can be sufficiently large to cause significant depolarization in the soma ., The typical largest input values , indicated by the probability mass of K ( U* ) ( Figure 2C–D ) are unable to sufficiently depolarize the soma and determine the neuronal output ( indicated by the low H ( U ) values ) in the case of both the linear ( Figure 2C ) and the quadratic ( Figure 2D ) integration functions ., Wherever K ( U* ) has high values , H ( U ) is low in both cases , which indicate , that these branches are not able to independently influence the output of the neuron ., Only coactivation of several branches could make the neuron fire in this case , and the output of the neuron encodes the strength of all dendritic inputs ., As H ( U ) converges to 1 for high input values extremely high inputs to a single dendrite could reliably trigger somatic firing ., In the next sections , however , we study how synaptic plasticity selectively modifies individual synapses and contributes to the sparse occurrence of extraordinarily high input values ., During Hebbian learning synapses contributing to postsynaptic activation are potentiated while other synapses may experience compensatory depression 31 , 32 ., We simulated the learning process by showing a finite number of uncorrelated samples from the input distribution ( see Methods ) to the model neuron initiated with uniform synaptic weights ., The synaptic weights of those dendritic branches where the activation exceeded a threshold , βd were modified according to the following Hebbian plasticity rule 33 that incorporates heterosynaptic depression 31: ( 11 ) where is the local dendritic activation , uj is the presynaptic firing rate and wij is the synaptic strength ., is the Heaviside function and γ<1 is a constant learning parameter ., Note , that the learning rule is local to the dendritic branches: the synaptic change depends on the local activation but not on the somatic firing ., Next , we calculated the total input to the branches Ui\u200a=\u200aΣjwijuj after modification of synapses ( Figure 3A ) , and recalculated the two functions H ( U ) and K ( U* ) defined previously with the new input distribution ( Eq . 18 ) ., As shown on Figure 3A the total synaptic input in response to a learned pattern increases significantly after learning ( compare blue and grey curves on Figure 3A ) , while untrained patterns generate smaller synaptic inputs ( compare grey and black curves on Figure 3A ) ., The main consequence of synaptic plasticity is that the trained patterns generate much larger local response than untrained patterns , which raise the possibility of their detection in the soma ., Note , that an unspecific increase of synaptic weights would result in an upward shift of both the input distribution ( Eq . 5 ) and the firing threshold , but would not affect the somatic detection of individual dendritic events ., The neuron is able to selectively respond to the dendritically learned patterns if a single branch , when facing with its preferred input , is able to induce significantly more depolarization at the site of the action potential initiation compared with the case when all of the branches get random , not learned input ., Figure 3B–E shows the dendritic input and the activation of the soma after learning ., If the maximal input U* is small ( left bumps on Figure 3B , D ) and none of the branches got its preferred input then the somatic activation is usually small ., If U* is high ( Figure 3B , D; right bumps ) , which means that one of the branches receives its preferred input pattern , then the somatic activation is increased ., The increase of the somatic activation with learned input is only moderate in the linear case ( Figure 3B , C ) resulting in an incomplete separation of learned and not learned inputs by the somatic firing threshold ., However , if synaptic inputs are supra-linearly ( quadratically ) integrated within the dendritic branches , efficient separation is possible: the probability that the presentation of a learned pattern elicits subthreshold somatic response , called dendritic spike detection probability was over 95% ( Figure 3D , E ) ., In this case the output of the neuron encodes whether or not one of the stored features was present in the neurons input and not simply the strength of the total input arriving to the whole dendritic tree ., In other words , if dendritic nonlinearity enhance the response of a given branch to its preferred input , then this branch alone is able to trigger somatic spiking ., In the following sections we use the term dendritic spiking to refer to these supra-linear dendritic events ., Although there is no data available on the synaptic induction of local dendritic spiking in hippocampal granule cells , voltage dependent Ca2+ currents are present in the membrane of granule cells 34 , 35 and whole-cell recordings from these neurons suggest that T-type Ca2+ channels can generate dendritic action potentials at least in young neurons 36 or under hyper-excitable conditions 34 , 37 ., Next , we explored how the independent feature detection ability of the model depends on the resistance between the somatic and dendritic compartments with nonlinear dendritic integration ., In the passive cable model of dendritic trees the space constant of the membrane λm≈ ( Rm/Ri ) 1/2 plays a substantial role in determining the voltage attenuation among two sites ., Consequently , an increase in the intracellular resistivity Ri or a similar decrease in the membrane resistance Rm will contribute to the separation of dendritic subunits by decreasing the membranes space constant λm ., In the present study we used the inverse of the space constant R≈Ri/Rm to characterize the degree of electrical resistivity between the somatic and dendritic compartments ., Indeed , an increased resistivity ( R ) between the compartments ( smaller space constant ) induced larger degree of electrical isolation as the somatic response to the same amount of dendritically applied current decreased ( compare Figure 4A left and right panels ) ., However , this isolation did not modify the dendritic spike detection probability in the soma: Large dendritic spikes localized to a single compartment could be reliably separated from subthreshold events with a somatic firing threshold at a large range of resistances R ( Figure 4A–B ) ., This was also true for the selective alternation of the somatic or the dendritic membrane resistance ( Figure 4B ) ., On the other hand , the resistance parameter had a substantial impact on the isolation of different dendritic compartments which might be necessary for the independence of synaptic plasticity ., To measure the isolation of the dendritic subunits we calculated the influence of other compartments on the activation of a given branch ( external influence ) quantified by the standard deviation of ., Figure 4C shows the activation of a dendritic branch in the function of its input at different R values ., If the resistance is small ( , Figure 4C , left ) , then the local activation depends only slightly on the local input and the external influence is high ( Figure 4D ) ., In this case the local input spread out to the entire dendritic tree and activates similarly all branches ., On the other hand , if the resistance is high ( R\u200a=\u200a1 , Figure 4C , right ) then the external influence is small , and the depolarization of a dendritic branch depends mostly on the local input ., Interestingly , decreasing the resistance of the perisomatic membrane ( ) alone was more efficient in separating the dendritic subunits than decreasing the resistance of the dendritic membrane or both ( Figure 4D ) ., The extensive GABAergic 38 , 39 and glutamatergic 40 innervation of the proximal dendritic and perisomatic region of granule cells may therefore contribute significantly to the isolation of the dendritic compartments ., The impact of a single branch on the somatic activation , and also the coupling between dendritic branches may depend highly on the structure of the dendritic tree ., Therefore we varied the number of dendritic subunits , N , and calculated the probability of detecting dendritic spikes in the soma and the external influence on the dendritic subunits ( Figure 5 ) ., The probability of detecting a dendritic spike in the soma decreased gradually after a few ( N≈30 ) number of branches from 1 to 0 . 3 ( N≈1000 , Figure 5A–B ) ., If the number of branches was low , then the effect of a single branch on the soma was relatively high , and the somatic detection of single dendritic events was reliable ., Conversely , one out of hundreds of branches had relatively low impact on the neurons output even if the local depolarization was significant ., The electrical coupling between the dendritic subunits characterized by the external influence on the local activation also decreased with the number of branches , ( Figure 5C–D ) ., In the model the branches are connected through the somatic compartment , and because the variance of the somatic activation decreases if N increases ( Eq . 8 ) , the external influence will also decrease ., However , in a complex dendritic tree containing higher number of subunits the branches are electronically more isolated which is required for local plasticity ., To keep the probability of dendritic spike detection high and the dendritic coupling low at the same time , the number of branches should therefore be as high as possible , but not higher than N≈60 ., As we showed on Figure 4 , the dendritic coupling depends on the resistance R , as high resistance separates better the subunits ., Therefore we conclude , that a medium number of branches with relatively high resistance is ideal for parallel dendritic computations ., The optimal number of dendritic subunits , however , depends on the size of the dendritic event determined by the local integration of the synaptic inputs ( Figure 5B ) ., Appropriate detection of dendritic responses to learned patterns with linear integration is possible only in very small dendritic trees , whereas supra-linear integration allows the detection of individual dendritic events also in a larger dendritic arbor ., Nonlinear integration by dendritic spiking therefore permits the neuron to selectively respond to a larger number of distinct input pattern ., During the calculation above we assumed , that the activity of the presynaptic neurons are independent and that the samples from the distribution are uncorrelated ., It is known , however , that the firing of entorhinal neurons are not independent: At least half of layer II cells in the medial entorhinal cortex ( EC ) are grid cells , whose firing depend mostly on the position of the animal 27 ., Moreover , in reality animals do not face with discrete uncorrelated samples , but they experience the continuous change of their environment which is mirrored by the activity of the entorhinal neurons ., In order to test our model under more realistic conditions , we simulated the activity of the rodents EC during exploratory behavior as input to our modeled granule cell ., The EC consisted of two neuron population: A population of grid cells ( 1000 neurons , 5 spacing , 5 orientations ) representing a path integrator system 41 and a population of visual cells ( 1200 units ) , representing highly processed sensory information available in the EC 42 ., In these simulations we used the Webots mobile robot simulator 43 ., The firing statistics of the entorhinal neurons was the same as used in the analytical calculation except that the activity of the neurons was location dependent ., Moreover , as we simulated the trajectory of the rat during continuous foraging for randomly tossed food pellets 26 the subsequent input patterns were highly correlated ., We simulated a single granule cell with N\u200a=\u200a20 dendritic branches each of them receiving a total number of M\u200a=\u200a100 synaptic contacts from entorhinal neurons ., The resistance was R\u200a=\u200a1 , we used the quadratic integration function and the neuron was tested in 5 different environments ., During the 5 min . learning period ( while 2000 spatial locations was sampled with an average running speed of 0 . 22 m/s ) 0–8 branches learned usually at different spatial locations in each of the 5 environments ., In most of the time synaptic plasticity in different branches occurred at different places , therefore the subunits were able to learn independently ., Moreover , learning occurred only in naive branches , i . e . , each branch learned only in one environment at a specific location and synapses of trained branches did not engage in learning at a different location ., After the training period the synaptic weights of those branches that were subthreshold for synaptic plasticity ( βd\u200a=\u200a1 . 11 ) in all environments were scaled down manually ., Next we studied the spatial activity pattern of the somatic and dendritic compartments while the robot was moving on a different track in the same environments ., The dendritic branches responded with high activation ( “dendritic spikes” ) to subsequent visit of places close to their preferred locations leading to the formation of dendritic place fields ( Figure 6 ) ., Moreover , since the activation of the soma was substantially increased in each of these dendritic place fields , the neuron had a multi-peaked activity map in several environments ( Figure 6 ) ., Finally we explored the effect of the size of the dendritic tree on the spatial firing pattern of the neuron ( Figure 7 ) ., If there were only a few functional dendritic subunit than the neuron obviously had a small number of dendritic place fields ( Figure 7A ) , but the individual branches had strong influence on the somatic activity ., Therefore the correlation between the somatic activation as and the maximal dendritic input U* was high ( Figure 7B , C ) , as predicted by the analytical calculations ., On the other hand , in neurons with large number of dendritic subunits there were more dendritic place fields ( Figure 7A ) , but a single branch had only a little impact on the activity of the neuron ( Figure 7D ) ., Accordingly , the correlation between the maximal dendritic input and somatic activation was reduced ( Figure 7B ) ., In these cases the cell fired when the overall excitation was high or when more than one branch were simultaneously excited ., Therefore , the moderately branching dendritic tree of granule cells seems optimal for parallel dendritic computations since extensive branching inhibits the detection of individual dendritic events ., We conclude , that clustered plasticity together with dendritic spiking may be an adequate cellular mechanism to explain the generation of multiple place fields in the DG 24 , 26 ., Dendritically generated spikes mediated by voltage-gated Na+ 3 and/or Ca2+ channels 44 as well as glutamate-activated N-methyl-D-aspartate ( NMDA ) channels 45 have been described in a variety of neurons ( for a review see 46 or 47 ) including hippocampal granule cells 34–37 ., We used a quadratic integration function in order to analytically model supra-linear dendritic integration 15 which differs from the sigmoid form of nonlinearity realized by dendritic spiking ( Text S1 , 3 , 4 , 45 ) ., We believe , however , that at this level of abstraction the exact form of nonlinearity does not affect our results: As that is the difference between the dendritic responses to learned and not learned patterns that influence the somatic detection of dendritic events , a sigmoid integration function give qualitatively similar results ( Text S2 ) ., Moreover , we studied only passive interactions between individual dendritic events as the effect of voltage and calcium dependent currents ( including A-type and Ca2+-dependent potassium 48 and the H-current 49 ) regulating the propagation of dendritic spikes were not included in the model ., Future studies using a compartmental model equipped with dendritic spiking could support our results and clarify further details ., Our analysis has revealed that a moderately branched dendritic tree is optimal for the independent branches model , and we have shown that this mechanism could contribute to the spatial firing properties of granule cells in the DG ., The dendritic tree of cerebellar Purkinje cells as well as the apical dendrites of hippocampal and neocortical pyramidal cells is typically larger , and more ramifying 50 ., Their morphology is suitable for local plasticity within single branches 6 , 8 , and although it seems that individual branches may function as single integrative compartments 3 , 4 , 51 , 52 , dendritic spikes localized to these compartments fail to propagate to the soma and directly influence the neurons output 53 ., Larger dendritic events , active spread of dendritic spikes towards the soma or interactions among dendritic subunits could contribute to the generation of somatic action potentials in this case ., The dendritic tree of pyramidal neurons is , however , far more complex than that of granule cells: it has several morphological and functional subregions with different afferent inputs and membrane excitability 50 ., Understanding how their spatial firing characteristics arise from their cellular properties would require at least a different model structure and is beyond the scope of this paper ., Whether individual dendritic events influence the output of the neuron depends - beyond the structure of the dendritic tree - on the size and the frequency of the large dendritic events and the output sparsity ., The size of the events depends on the exact form of the dendritic integration function and the plasticity rule while the input statistics determine the frequency of such events ., We have shown that given the sparseness of the output , sufficiently large , localized dendritic events arriving with appropriate frequency are able to separately determine the output of the neuron ., Whether a local event is sufficiently large depends on the geometry of the dendritic tree: A smaller event may be sufficient if there are only a few subunits , or if the events actively propagate to a large part of the entire dendritic tree ( e . g , the apical tuft in pyramidal neurons , 54 ) ., Conversely , in neurons such as cerebellar Purkinje cells with large , ramifying dendritic tree , where individual events are localized to small branches , very large dendritic spikes would be required to influence the output ., Indeed , detailed compartmental modelling of dendritic morphology revealed that the forward propagation of the action potential initiated in the apical trunk of pyramidal neurons was very effective , while in Purkinje cells dendritic action potentials were rapidly attenuated 53 ., Clustered plasticity allows the neuron to simultaneously learn several different patterns but requires the electrical and/or biochemical isolation of the dendritic compartments 47 , 55 ., However , the intracellular resistance ( ) in dentate granule cells is relatively low and granule cells are usually regarded as electrically compact neurons 28 ., Indeed , signal propagation from somata into dendrites in vitro is more efficient in granule cells compared with CA1 pyramidal cells and distal synaptic inputs from entorhinal fibers can efficiently depolarize the somatic membrane of granule cells 28 ., However , in vitro studies do not take into account that neurons are embedded in a network of spontaneously active cells ., As thousands of synapses bombard the dendritic tree in vivo , the dendritic membrane becomes “leakier” and , consequently , the membranes space constant decreases significantly 56 ., Moreover perisomatic inhibition 57 and feed-back excitation ( via hilar mossy cells 40 ) further decrease the resistance of the proximal membrane contributing to the separation of the somatic and dendritic compartments 54 , 58 ., More specifically , we predict , that the membrane resistance of granule cells is considerably smaller at the perisomatic region than in the distal dendrites ., Indeed , computational studies predict a 7–30 fold increase in the somatic leak conductance due to the synaptic background activity 59 ., On the other hand , large space constant at long terminal branches facilitate interactions among synapses distributed on the same branch ., Therefore the long dendritic branches of dentate granule cells may act as single integrative computational subunits , separated from each other by the perisomatic region of the cell ., Furthermore , in the present paper we used steady-state approximations and we neglected temporal characteristics of the input and the integration ., For rapidly varying inputs the coupling between dendritic sites and the soma is much smaller than for slowly varying currents since the distributed capacitance throughout the tree will absorb the charge before it reaches the soma 14 ., Therefore dendritic compartments in a passive tree are more isolated for transient events such as dendritic spikes than for steady-state current ., Finally , biochemical compartmentalization is likely to play a substantial role in the cooperative induction of LTP in both hippocampal 60 and neocortical neurons 7 ., If , on the other hand , dendritic branches are not isolated during the learning process and synapses across the whole dendritic tree are modified simultaneously then different dendritic branches will be sensitive for different component ( modalities ) of the same episode ., A new episode with partial overlap with the previously learned one may trigger dendritic spiking in the corresponding dendritic branch ., As the somatic detection probability of dendritic spikes does not depend on the degree of electrical isolation ( Figure 4 ) , individual branches trigger somatic spiking , and , in this way the dentate gyrus contributes to the associative recall of the previously encoded episode in the hippocampus ., Since the first description of LTP at perforant path - granule cell synapses 61 synaptic plasticity has become widely accepted as the physiological basis of memory 62 ., As Hebbian plasticity is intrinsically unstable , simply because it is a positive feed-back mechanism multiple stability-promoting mechanisms h
A fundamental question in understanding neuronal computations is how dendritic events influence the output of the neuron ., Different forms of integration of neighbouring and distributed synaptic inputs , isolated dendritic spikes and local regulation of synaptic efficacy suggest that individual dendritic branches may function as independent computational subunits ., In the present paper , we study how these local computations influence the output of the neuron ., Using a simple cascade model , we demonstrate that triggering somatic firing by a relatively small dendritic branch requires the amplification of local events by dendritic spiking and synaptic plasticity ., The moderately branching dendritic tree of granule cells seems optimal for this computation since larger dendritic trees favor local plasticity by isolating dendritic compartments , while reliable detection of individual dendritic spikes in the soma requires a low branch number ., Finally , we demonstrate that these parallel dendritic computations could contribute to the generation of multiple independent place fields of hippocampal granule cells .
Neurons were originally divided into three morphologically distinct compartments: the dendrites receive the synaptic input , the soma integrates it and communicates the output of the cell to other neurons via the axon ., Although several lines of evidence challenged this oversimplified view , neurons are still considered to be the basic information processing units of the nervous system as their output reflects the computations performed by the entire dendritic tree ., In the present study , the authors build a simplified computational model and calculate that , in certain neurons , relatively small dendritic branches are able to independently trigger somatic firing ., Therefore , in these cells , an action potential mirrors the activity of a small dendritic subunit rather than the input arriving to the whole dendritic tree ., These neurons can be regarded as a network of a few independent integrator units connected to a common output unit ., The authors demonstrate that a moderately branched dendritic tree of hippocampal granule cells may be optimized for these parallel computations ., Finally the authors show that these parallel dendritic computations could explain some aspects of the location dependent activity of hippocampal granule cells .
neuroscience/theoretical neuroscience, computational biology/computational neuroscience