Many neurons receive excitatory glutamatergic input almost exclusively onto dendritic spines. In the absence of spines, the amplitudes and kinetics of excitatory postsynaptic potentials (EPSPs) at the site of synaptic input are highly variable and depend on dendritic location. We hypothesized that dendritic spines standardize the local geometry at the site of synaptic input, thereby reducing location-dependent variability of local EPSP properties. We tested this hypothesis using computational models of simplified and morphologically realistic spiny neurons that allow direct comparison of EPSPs generated on spine heads with EPSPs generated on dendritic shafts at the same dendritic locations. In all morphologies tested, spines greatly reduced location-dependent variability of local EPSP amplitude and kinetics, while having minimal impact on EPSPs measured at the soma. Spine-dependent standardization of local EPSP properties persisted across a range of physiologically relevant spine neck resistances, and in models with variable neck resistances. By reducing the variability of local EPSPs, spines standardized synaptic activation of NMDA receptors and voltage-gated calcium channels. Furthermore, spines enhanced activation of NMDA receptors and facilitated the generation of NMDA spikes and axonal action potentials in response to synaptic input. Finally, we show that dynamic regulation of spine neck geometry can preserve local EPSP properties following plasticity-driven changes in synaptic strength, but is inefficient in modifying the amplitude of EPSPs in other cellular compartments. These observations suggest that one function of dendritic spines is to standardize local EPSP properties throughout the dendritic tree, thereby allowing neurons to use similar voltage-sensitive postsynaptic mechanisms at all dendritic locations.

The inability of spines to significantly shape EPSPs recorded in dendrites or at the soma has led some authors to question whether spines provide electrical advantages to neurons [20] . Yet, from the point of view of the synaptic membrane, where numerous voltage-sensitive mechanisms may exist [21] – [24] , spine necks play a critical role in shaping EPSPs. In this paper we use computational models of simplified and morphologically realistic dendritic trees to directly compare synaptic responses in spines and dendritic shafts to test the hypothesis that spines act to limit location-dependent variability of EPSP properties at the site of synaptic input. Such comparisons in real neurons are not possible given technological limitations of electrical recording and imaging techniques [25] , and the rarity of excitatory inputs onto dendritic shafts in spiny neurons [26] . By simulating identical synaptic inputs onto spines and shafts at all dendritic locations, we demonstrate that spine morphologies standardize the amplitude and kinetics of local EPSPs, limiting their dependence on synapse location within the dendritic tree, and allowing more uniform activation of voltage-sensitive conductances at the site of synaptic input. Because spines reduce the impact of local dendritic geometry on EPSP properties, they may allow neurons to use similar voltage-sensitive postsynaptic mechanisms at all excitatory synapses, regardless of their location in the dendritic tree.

A) Diagram of a dendritic spine consisting of a spine “head" attached to a dendrite by a narrower spine “neck". B) Spines can be modeled as a series of electrical compartments, each having membrane conductance (g head , g neck , and g dendrite ) and capacitance (C head , C neck , and C dendrite ) determined by the surface area of the compartment. Internal “axial" resistance between compartments reflects the conductivity of the cytoplasm and the morphology (cross-sectional area and length) of the communicating compartments. The small surface area of spines minimizes their membrane resistance and conductance, allowing simplification of the electrical structure of spines (C), in which synaptic current (I synapse ) is illustrated in green, and where dendritic electrical properties, including dendritic connectivity with the rest of the neuron, are represented in aggregate as “input impedance" (Z N ; blue), a measure analogous to input resistance, but also incorporating capacitive influences on non-steady-state voltage signals such as synaptic potentials. EPSPs in spines approximate the product of I synapse and the “in series" sum of R neck and Z N (R head being a negligible “in parallel" resistance to synaptic current). On the other hand, shaft EPSPs, whether generated by synaptic current originating in spine heads or from synapses located on the dendritic shaft, will vary with the product of I synapse and Z N . D) Plot of Z N (calculated for 100 Hz input) and Z N +R neck (for 200 MΩ spine necks) verses distance along a tapering (5 µm to 1 µm) 1000 µm-long dendrite (cartoon at top not to scale) attached to a 40 µm by 40 µm soma (not shown). Spines with neck resistances of 200 MΩ were placed every 10 µm along the dendrite. Coefficients of variation (CV) for Z N and Z N +R neck values indicated in green. EPSPs shown in part C are from the simulations depicted in Figure 2A for a spine input at the distal end of the dendrite.

In spiny neurons, excitatory synapses occur on dendritic spines. Spines have distinct electrical properties that shape synaptic responses locally at the site of synaptic input, but have little impact on EPSPs recorded in dendrites or at the soma [16] – [19] . Spines consist of a spine “head", onto which excitatory synapses are made, and a spine “neck" that attaches the spine head to the dendritic shaft ( Figure 1A ). Each of these “compartments" can be modeled as electrical circuits ( Figure 1B ) having conductance and capacitance determined by the surface area of the surrounding plasma membrane. The small surface area of spines (<1 µm 2 ) provides negligible local membrane conductance and capacitance, and as such almost all the synaptic current entering a spine is transferred to the dendritic shaft via the spine neck resistance ( Figure 1C ) [16] . Because EPSPs are the product of synaptic current and resistance to that current (Ohm's law), the amplitude of synaptic responses in the spine head will depend in large part on the “in series" sum of spine neck resistance and dendritic input impedance (Z N ; see Figure 1 legend). Z N varies with dendritic geometry and topography, and at most dendritic locations is expected to be much lower than spine neck resistance ( Figure 1D ). This could limit the influence of dendritic location on spine EPSP amplitudes. On the other hand, EPSPs in dendrites have amplitudes determined by the product of the synaptic current and Z N alone, which should generate EPSPs that are smaller and more location-dependent than those occurring in synaptically activated spine heads. Finally, since spines have little impact on the synaptic current entering dendrites [16] , dendritic EPSPs generated by spine synapses will appear similar to those generated by synapses located directly on the dendritic shaft.

Excitatory postsynaptic potentials (EPSPs) are shaped locally by the dendritic geometry at the site of synaptic input [13] , [14] . EPSPs tend to have larger amplitudes and faster kinetics when generated in neuronal compartments with higher input impedance and smaller local capacitance, as typically occurs at distal locations within dendritic trees. As a result, local EPSPs at the site of synaptic input can be highly variable in their amplitude and kinetics [15] .

Spines are prominent postsynaptic morphological features found on the dendrites of many neurons. Many functions for spines have been proposed, including electrical filtering and isolation of synaptic inputs [1] – [5] , chemical compartmentalization [6] – [10] , and maximization of the number of potential synaptic connections [11] , [12] . However, despite more than a century of research, a definitive role for dendritic spines remains elusive.

Results

Spines standardize EPSP properties in a simplified model neuron We initially tested the electrical consequences of spines in a simplified “ball-and-stick" model (see Methods) in which AMPA-like synaptic conductances were generated on spines (200 MΩ neck resistance) or onto the neighboring dendritic shaft at evenly spaced dendritic locations (Figure 2). Voltage responses were recorded locally at the site of synaptic input (i.e., in the spine head for spinous inputs or in the adjacent dendritic shaft for dendritic inputs), at the soma, and, in the case of spine inputs, in the shaft below the spine. As expected [15], the amplitude and kinetics of local EPSPs occurring on dendritic shafts were highly location-dependent, tending to be larger and faster at locations distal from the soma (Figure 2A). In contrast, local EPSPs occurring on dendritic spines were more uniform in their amplitude and kinetics across dendritic locations (Figure 2A). This effect of spines on EPSPs was restricted to the site of synaptic input, as spine EPSPs measured within the dendritic shaft or at the soma were similar, although slightly smaller, than shaft EPSPs generated at the same dendritic locations (Figure 2A and B). Spine-dependent standardization of EPSP properties at the site of synaptic input persisted even when the resistance of individual spine necks was varied around a mean value using Gaussian or uniform distributions (Figure 2C). PPT PowerPoint slide

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larger image TIFF original image Download: Figure 2. Spines reduce location-dependent variability of EPSP properties. A) Top, diagram of a “ball-and-stick" model neuron. Synapses were placed onto the dendritic shaft or onto spines (200 MΩ spine neck resistance) at the locations indicated (synapses 1 to 6). Local EPSPs generated in the dendritic shaft (synapses 1 to 3, lower traces) or in spines (synapses 4 to 6, upper traces) are color-coded by location. Bottom left, somatic EPSPs resulting from inputs to the shaft (1 to 3) and spines (4 to 6). Bottom right, local shaft (1 to 3) and spine (4 to 6) EPSPs normalized and superimposed to allow comparison of EPSP kinetics. The time course of the underlying synaptic conductance is indicated by a dashed line. B) Plots of EPSP amplitudes for spine (red) and shaft (blue) inputs as measured in the dendritic shaft. C) Plot of the coefficients of variation (CVs) (mean ± standard deviation) for spine (red) and shaft (blue) EPSP amplitudes for inputs having variable spine neck resistances determined from Gaussian or uniform distributions, as indicated (n = 5 trials per group). D, E) Left, plots of local EPSP amplitude (D) and EPSP half-width (E) versus distance from the soma for inputs onto the dendritic shaft (blue) and spines (red) with the indicated spine neck resistances. Right, plots of the coefficient of variation (CV) for EPSP amplitude (D) and half-width (E) versus spine neck resistance. https://doi.org/10.1371/journal.pone.0036007.g002 Variability in EPSP properties was quantified by calculating the coefficient of variation (CV) of local EPSP amplitudes and half-widths for inputs on shafts or onto spines having a range of spine neck resistances (Figure 2D and E). EPSPs on spines were less variable than were EPSPs generated on dendritic shafts at the same dendritic locations over a range of spine neck resistances. The influence of spines on local EPSP properties was largely independent of synaptic conductance (range examined: 250 pS to 2 nS) or spine head diameter, but depended heavily on spine neck resistance (range examined: 1 to 1000 MΩ). Higher spine neck resistances generated larger and faster local EPSPs in spines at all dendritic locations, leading to reduced location-dependent variability of local EPSP properties (Figure 2D and E). Yet, even with relatively low spine neck resistances (as low as 10 MΩ), the CVs of spine EPSP amplitude (0.65) and half-width (0.22) were lower for inputs onto spines when compared to those onto dendritic shafts at the same dendritic locations (0.82 and 0.33, respectively). Spine-dependent standardization of EPSP properties at the site of synaptic input was not dependent on the increased variability evident at distal dendritic locations (Figure 3). When considering inputs onto the entire dendrite, the CVs of EPSP amplitude and half-width equaled 0.09 for spine inputs (spine neck resistance = 200 MΩ), but were approximately 9 fold (CV [EPSP amplitude] = 0.82) and 3 fold (CV [EPSP half-width] = 0.33) higher for shaft inputs. When considering only those inputs occurring along the first 70% (700 µm) of the dendrite, CVs for EPSP amplitude and half-width were 0.02 and 0.03, respectively, for spine inputs, and 0.29 and 0.20 for shaft inputs; differences of almost 15 and 7 fold, respectively. On the other hand, for the most distal 30% (300 µm) of the dendrite, CVs calculated for EPSP amplitudes and half-widths were 0.09 and 0.05, respectively, for spine inputs, and 0.43 and 0.13, respectively, for shaft inputs; differences of almost 5 and 3 fold, respectively. We conclude that spine-dependent reductions in the variability of EPSP properties occurs over the entire dendrite, and does not depend upon “end effects" occurring at the tips of dendrites. PPT PowerPoint slide

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larger image TIFF original image Download: Figure 3. Spine-dependent reduction of EPSP variability does not depend on dendritic location. Comparisons of the CVs for EPSP properties calculated over the entire dendritic population, or for inputs restricted to the first 700 µm (70% of inputs) or last 300 µm (30% of inputs) of the dendrite. Left, local EPSPs at spine (red traces) or shaft (blue traces) inputs along the first 700 µm (∼100 µm intervals). Middle, local spine and shaft EPSPs generated along the last 300 µm of dendrite. Right, local EPSPs along the entire dendrite. CVs for EPSP amplitude (indicted in light blue) and half-width (indicated in green) were calculated for all inputs located within the dendritic subregions (n = 70, 30, and 100, respectively, for first 70%, last 30%, and entire synapse population). https://doi.org/10.1371/journal.pone.0036007.g003

Spines standardize EPSP properties in morphologically realistic models To test whether spines standardize EPSP properties in morphologically realistic neurons, we utilized 3-dimensional reconstructions of several types of spiny neurons (Figure 4). In each model, spines (200 MΩ neck resistance) were placed at ∼10 µm intervals along all spiny dendrites and EPSPs generated either in spine heads or on dendritic shafts adjacent to spines. As was found in the ball-and-stick model, spines decreased the location-dependent variability of local EPSP amplitude and kinetics in the apical and basal dendrites of a layer 5 pyramidal neuron from the prefrontal cortex (Figure 4A), as well as in the dendrites of a hippocampal dentate granule cell (Figure 4B), a cerebellar Purkinje neuron (Figure 4C), and a striatal medium-spiny neuron (Figure 4D). The CVs of EPSP properties were measured across all shaft and spine synapses for each of the different dendritic morphologies. This analysis indicated that spines significantly (p<0.001; repeated measures ANOVA) reduced distance-dependent variability in local EPSP amplitude and half-width, confirming that spines act to standardize EPSP amplitudes and kinetics at the site of synaptic input in morphologically realistic dendritic trees. PPT PowerPoint slide

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larger image TIFF original image Download: Figure 4. Spines standardize EPSP properties in morphologically realistic neurons. A 1 –D 1 ) Morphology of reconstructed neurons: A 1 ) layer 5 pyramidal neuron from the medial prefrontal cortex, B 1 ) hippocampal dentate granule cell, C 1 ) cerebellar Purkinje neuron, and D 1 ) striatal medium spiny neuron. Synaptic inputs were placed onto shafts and spines of the colored dendrites at proximal, intermediate, and distal locations as indicated by the numbered locations (1 to 3). A 2 –D 2 ) Left, local EPSPs recorded in spines (top traces) or in dendritic shafts (lower traces) at the locations indicated in the different morphologies. Normalized and superimposed traces, expanded in time and shaded at far right, allow comparison of EPSP kinetics. The time course of the underlying synaptic conductance is indicated by dashed lines. https://doi.org/10.1371/journal.pone.0036007.g004

Spines standardize activation of voltage-gated calcium channels Synaptic transmission can involve postsynaptic voltage-sensitive processes that may benefit from spine-dependent standardization of EPSP amplitude and kinetics. One mechanism present at many synapses are low-threshold (i.e.,“T-type") voltage-gated calcium-channels (VGCCs) that provide a source of postsynaptic calcium and depolarization. We first tested the ability of EPSPs to activate T-type VGCCs at synapses occurring on spines or onto the dendritic shaft in a ball-and-stick model (Figure 5A). The equivalent of ten Ca v 3.1 (T-type) channels (50 pS maximum combined conductance) was placed at spine and shaft synapses localized at ∼10 µm intervals along the dendrite. Synapses on spines generated larger and less variable postsynaptic calcium currents than did synapses occurring on the dendritic shaft, with current amplitude, time-to-peak, and half-width all having lower variation when inputs occurred on spines (Figure 5C). Since Ca v 3.1 channels are known to be localized to spines in cerebellar Purkinje neurons [21], we tested synaptic T-type channel activation in a Purkinje neuron model having shaft and spine inputs placed at ∼10 µm intervals from the soma (Figure 5B). As was found in the ball-and-stick model, EPSPs occurring in spines generated larger and less variable calcium currents than did EPSPs on dendritic shafts (Figure 5B and C). Similar results were observed in models of a medium-spiny neuron, a dentate granule cell, and a layer 5 pyramidal neuron (not shown). PPT PowerPoint slide

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larger image TIFF original image Download: Figure 5. Spines standardize synaptic activation of voltage-gated calcium channels. A) Top, ball and stick model neuron. Local EPSPs (bottom) and calcium currents (middle) generated by inputs onto spines (left) or dendritic shafts (right) located at ∼100 µm intervals along the dendrite, each synapse contains the equivalent of ten Ca v 3.1 (T-type) calcium channels (total maximum conductance, 50 pS). B) Local EPSPs (bottom) and calcium currents (top) generated by inputs onto spines (left) and shafts (right) located at ∼10 µm intervals along a spiny dendrite (red) of a cerebellar Purkinje neuron (inset). C) Average calcium current amplitude, time-to-peak, and half-width for all spine (red) and shaft (blue) inputs in the ball and stick (n = 100 inputs) and Purkinje neuron (n = 367 inputs) models. Asterisks indicate p<0.0001 (paired t-tests). CVs are indicated in light blue at base of each bar. https://doi.org/10.1371/journal.pone.0036007.g005

Spines facilitate and reduce the variability of AMPA-dependent NMDA currents Another important postsynaptic mechanism present in many cell types is the NMDA-type glutamate receptor, which is voltage sensitive due to block by magnesium at hyperpolarized membrane potentials. By standardizing local AMPA EPSP amplitude and kinetics, spines might be expected to generate more uniform NMDA-mediated responses within dendritic trees. However, the kinetics of NMDA receptors are much slower than those of AMPA receptors (Figure 6A; see also [27]), limiting the potential influence of fast AMPA-mediated responses on NMDA currents. To test the impact of spines on NMDA receptor currents, we simulated NMDA-like conductances in spines and shafts, either alone, or together with an AMPA-like conductance, in a ball-and-stick model (Figure 6B and C) and in a model of a dentate granule cell (Figure 6D and E). Placing inputs onto spines led to small but significant increases in total NMDA currents, and standardized the amplitude and half-width of the AMPA-dependent component of NMDA currents (Figure 6B–E). In both the simplified ball-and-stick model (not shown) and the dentate granule cell (Figure 6D and E), we measured AMPA-dependent NMDA currents at several resting membrane potentials (−79, −70, −60, and −50 mV). AMPA-dependent NMDA currents in spines were larger and more uniform than were those generated at shaft synapses over this range of membrane potentials. These simulations indicate that spines boost and standardize local AMPA-driven activation of NMDA conductances during synaptic transmission. PPT PowerPoint slide

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larger image TIFF original image Download: Figure 6. Spines enhance and standardize AMPA-dependent NMDA currents. A) Time courses of AMPA and NMDA receptor-mediated conductances. Green dashed line indicates the peak of the slower NMDA conductance. B) NMDA currents generated in a ball-and-stick model neuron when both AMPA and NMDA conductances are activated (top) or when the NMDA conductance is activated alone (middle). Subtraction allows isolation of the AMPA-dependent NMDA current (bottom). Traces show responses at ∼100 µm intervals. C) Comparison of total NMDA current (left) and AMPA-dependent NMDA current (right) in spines (red) and shafts (blue) for the ball-and-stick neuron resting at −79 mV. CVs shown in light blue. D) Local (spine or shaft) EPSPs (top traces) and AMPA-dependent NMDA currents (lower traces) simulated in a dentate granule neuron (inset). Traces show responses at inputs occurring at ∼20 µm intervals along the dendrite indicated in red in the inset morphology. CVs for EPSP or AMPA-dependent NMDA current amplitudes (light blue) or half-widths (green) shown for all 211 inputs (∼10 µm intervals) throughout the granule cell dendritic tree. E) Comparison of AMPA-dependent NMDA current amplitudes for inputs onto spines (red) and shafts (blue) in a dentate granule cell at the indicated resting membrane potentials. CVs shown in light blue. Data shown as mean ± standard deviation. Asterisks indicate p<0.05. https://doi.org/10.1371/journal.pone.0036007.g006

Active dendritic conductances enhance spine-dependent standardization of EPSPs The dendrites of many neurons express voltage-gated ion channels that dynamically regulate neuronal excitability and synaptic integration. We investigated the impact of active dendritic conductances on spine-dependent standardization of EPSP properties in a model of a somatosensory layer 5 pyramidal neuron (Figure 9A) having well characterized dendritic properties [32]. Synaptic inputs activating AMPA and NMDA receptors were placed onto spines or on the dendritic shaft at ∼10 µm intervals throughout the dendritic tree, and inputs along an apical dendrite were individually activated. In the absence of dendritic voltage-gated ion channels, CVs for EPSP amplitude and half-width were lower for spinous inputs than for inputs made at the same locations on the dendritic shaft (Figure 9B; “Passive model"). The addition of dendritic voltage-gated sodium and potassium channels at densities similar to those reported experimentally for these neurons [33]–[36] had little impact on spine or shaft EPSP variability (Figure 9B; “Na+ and K+ channels"). On the other hand, adding dendritic hyperpolarization-activated cyclic-nucleotide-gated (HCN) channels [37], [38], either alone or in combination with voltage-gated sodium and potassium channels, reduced the CVs of local spine EPSP amplitude and half-width by about 38% and 35%, respectively (Figure 9B; “Na+, K+, and HCN" and “HCN only"). Dendritic HCN channels had only a small impact on the variability of shaft EPSPs, reducing the CV for EPSP amplitudes by ∼5%, and actually increasing the CV of EPSP half-widths by ∼10%. These data indicate that dendritic HCN channels, but not voltage-gated sodium and potassium channels, act synergistically with spine morphology to preferentially reduce location-dependent variability of local EPSPs occurring in dendritic spines. PPT PowerPoint slide

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larger image TIFF original image Download: Figure 9. Dendritic HCN channels enhance spine-dependent standardization of EPSPs. A) Reconstructed layer 5 pyramidal neuron from the somatosensory cortex with spines at ∼10 µm intervals throughout the dendritic tree. Inset, action potential generated in an “active model" containing sodium, potassium, and HCN channels. B) EPSPs generated in spines (red) or shafts (blue) at ∼50 µm intervals along the apical dendrite (red dendrite in A) in models with different passive and active properties. Numbers in light blue and green indicate coefficients of variation (CVs) for EPSP amplitudes and half-widths, respectively, for all local responses (10 µm intervals) to spine and shaft inputs in the various models. https://doi.org/10.1371/journal.pone.0036007.g009 Dendritic expression of HCN channels has two important and related effects on dendritic properties. HCN channels increase dendritic membrane conductance while at the same time depolarizing the dendritic membrane potential [37]–[40]. To test the relative impact of these two consequences of dendritic HCN expression on EPSP properties, we constructed two additional models: one in which the reversal potential of the HCN conductance was set to the somatic resting membrane potential (−79 mV), which eliminates HCN-mediated distance-dependent depolarization (Figure 9B; “HCN-only, E HCN = −79 mV"), and another model lacking active channels, but where dendritic compartments were artificially depolarized to the same extent as occurs when HCN channels are present (Figure 9B; “Passive, HCN-like depolarization"). Setting the reversal potential for the HCN conductance to −79 mV effectively eliminated HCN-dependent reduction in spine EPSP amplitude variability, but enhanced the standardization of EPSP half-width (Figure 9B). On the other hand, depolarizing dendritic compartments in the absence of HCN mimicked the HCN-induced reduction in EPSP amplitude variability, but eliminated the influence of HCN channels on EPSP half-widths (Figure 9B). These results indicate that dendritic HCN channels reduce local spine EPSP amplitude variability via a depolarization-dependent reduction in EPSP driving force at distal locations, whereas the variability of spine EPSP half-width is reduced primarily via an HCN-mediated increase in distal dendritic membrane conductance.