Article Figures & Data
Figures
- Figure 1.
Linear and supralinear integration of synaptic inputs in CA1 pyramidal neurons. a, Dendritic recordings showing the random pattern of input (Iinj) and the resulting dendritic depolarization (Vdend) produced by this input. At left (a; blue traces), the input pattern is asynchronous with the number of inputs increasing from 28 to 140 over a time window of 50 ms. At right (b; black traces), the input pattern is a highly synchronous pattern in which the number of inputs, increasing from 12 to 60, are delivered within 1 ms. The dotted lines indicate the region in which the peak amplitude was calculated (average of the last 20% of the current injection). c, Expanded dendritic and somatic recordings from a neuron receiving suprathreshold asynchronous input (50 ms time window) showing that APs are always initiated in the soma/axon region, while synchronous input (d; 1 ms time window) causes dendritic spike generation that precedes somatic AP output. e, Mean input–output relationships for the population of dendritic recordings (n = 9). The curves show that the shift from linear to supralinear summation occurred only for the most synchronous input. The data from suprathreshold 10–100 ms input are shown in dashed lines and are approximate because of bAPs. Error bars indicate SE. f, Representative single neuron integration functions for synchronous (Synch) and asynchronous (Asynch) input patterns (1 and 50 ms input windows from the cell shown in a and b). Input amount expressed as a percentage of the amount of input required to reach output AP threshold. Synchronous input data were fit by a sigmoid-like function in the form of y = 25/(1 + exp(−(n − 88)/5.1)) + (0.38n + 0.4), whereas the asynchronous input data were fit by a linear function in the form of y = 0.24n + 0.1.
- Figure 2.
The spatial distribution of the input pattern determines dendritic integration. a, Image stack of a distal apical dendrite region showing the experimental configuration for clustered (blue dots) and distributed (red dots) uncaging locations (recording pipette at ∼275 μm). w/i, Within. b, Individual glu-EPSPs for the seven different sites with position indicated by associated number. c, Inputs given at positions 1–7 with a 5.1 ms interval at three different laser intensities. d, Inputs given at positions 1–7 with a 0.4 ms interval at four different laser intensities. The bottom traces represent the temporal derivatives of dendritic spikes for clustered (left) and distributed inputs (right). e, Input–output curves recorded at the dendrite for clustered and distributed (distrib.) input patterns. Note that only the synchronous pattern that is also clustered in space produces a strong nonlinearity. Distributing the synchronous input over ∼150 μm reduced or removed the ability of the dendrite to shift into the nonlinear integration mode. Laser intensities produced the equivalent of 51 clustered and 53 distributed synapses in b; 30, 41, and 51 clustered synapses and 28, 40, and 53 distributed synapses in c; and 22, 30, 41, and 51 clustered synapses and 18, 28, 40, and 53 distributed synapses in d.
- Figure 3.
Dendritic integration mode determines input efficacy and spike rate variability. a, Experimental configuration. A dendritic whole-cell electrode was used to inject a random pattern of EPSC-shaped currents while the corresponding voltage deflections were recorded with both dendritic and somatic electrodes. b, Examples of the random patterns of EPSC-shaped currents that were injected into the dendrite in the case of synchronous (≤1 ms; black) and asynchronous (50 ms; red) input patterns. c, d, Dendritic (dend; c) and somatic (soma; d) recordings showing that higher input levels are required for output generation in the case of dispersed synaptic activation. Traces to the right in b–d demonstrate the effect of increasing the amount of input to nearly twice threshold levels. e, Image stack of a CA1 pyramidal neuron showing the experimental configuration. Red dots indicate the approximate locations of the spines that were used for the distributed input pattern. Clustered pattern was given to spines located within an ∼20 μm region near the scale bar. f, Somatic membrane potential recordings showing that the number of inputs required to achieve action potential output differs depending on the spatial and temporal distribution of the input pattern. The patterns that were both synchronous and clustered required the fewest inputs. synch, Synchronous; asynch, asynchronous. g, Plot of the number of synapses required for output generation for synchronous input (all within 3 ms) or asynchronous input that was either clustered (clust), distributed (distrib), or clustered plus 50 nm TTX. The plot shows that the neuron will preferentially respond to clustered and synchronous input, only. Clustered input includes input from current injections, conductance changes, and glutamate uncaging. Distributed was only from glutamate uncaging. TTX condition was for current injections and conductance changes. h, Plot of number of output APs evoked expressed as a function of the amount of input (relative to threshold) for either asynchronous or synchronous input, showing that the number of output APs can significantly vary as a function of input number only for asynchronous input patterns. Error bars indicate SE.
- Figure 4.
The dendritic integration mode determines the output timing and variability. a, b, Dendritic (dend; a) and somatic (b) recordings showing 10 traces obtained for the same just suprathreshold random-patterned dendritic current injections for either synchronous (within 1 ms) or asynchronous (within 50 ms) input. c, Somatic recordings of just suprathreshold stimulation given by two-photon MNI-glu uncaging to spines in either a clustered (∼20 μm; labeled “c”) or distributed (∼150 μm; labeled “d”) spatial pattern for synchronous (within 3 ms; black and gray traces) or asynchronous (within 50 ms; red and blue traces) temporal patterns. d, Plot of the latency to the first spike for either synchronous or asynchronous input delivered as clustered (clust) or distributed (distrib) spatial patterns. Also, the impact of 50 nm TTX application is shown. e, Plot of action potential jitter (defined as the SD of the axonal action potential timing in repeated identical trials) for either synchronous or asynchronous input delivered as clustered or distributed spatial patterns. Also, the impact of 50 nm TTX application is shown. The plots show that the initiation of a dendritic spike for synchronous and clustered input disproportionately decreases latency and the variability of the action potential output timing. f, Plot of AP latency (expressed as relative to the latency at just threshold values; see e) versus the amount of input (relative to the threshold level) for both synchronous input (within 3 ms) and asynchronous input (50 ms). Action potential latency was highly dependent on the level of input only when the input pattern was asynchronous, whereas latency was extremely invariant when synchronous input patterns were delivered. Error bars indicate SE.
- Figure 5.
Linear dendritic integration during theta-like activity. a, Somatic recording (red) obtained as a 10 Hz sine wave was injected in the soma (blue), and a random pattern of EPSC-shaped currents of increasing intensity (from 80 to 400 synapses in increments of 80) was simultaneously injected through a dendritic electrode (b). c, Simultaneous somatic and dendritic recordings of the first three cycles with APs shown at an expanded timescale, demonstrating that the dendrite remained in the linear integration mode with bAPs only. The asterisks indicate the presence of a prolonged bAP duration presumably because of enhanced dendritic Ca2+ channel activation. d, Plot of AP numbers and mean firing phase versus the amount of input delivered to the neuron shown in a, demonstrating that the number of spikes generated at the soma increased with the number of synapses activated. In addition, the coarse timing of the spiking was advanced in relation to the 10 Hz sine wave. e, Average plot of the mean firing rate and the firing phase as a function of the number of inputs (n = 6). Error bars indicate SE.
- Figure 6.
Only supralinear dendritic integration can recreate features of the sharp wave state. a1, Experimental setup showing the synchronous and clustered input that was repeatedly delivered to the dendrite simultaneous with a 200 Hz hyperpolarizing sine wave to the soma. The number of inputs within the pattern was varied between 60 and 100 inputs. a2, Dendritic recordings showing that the synchronous input evoked dendritic spikes and high precision action potential output from the soma/axon region regardless of large changes in input number (a3). a4, a5, Expanded somatic traces (10 consecutive traces) (a4) and spike timing histogram (as a function of the sine phase) (a5) showing the extremely precise spike timing achieved when the nonlinear integrative properties of the dendrite are engaged, even as the amount of input is varied. b, Repeated asynchronous input (4 different random patterns with 180 synapses delivered within 50 ms) that produces a linear integration mode (b2) causes the neuron to initiate output APs (20 consecutive traces) that are spread out over several cycles of the 200 Hz sine (b3). Expanded traces (b4) and spike time histogram (b5) show that, even when aligned to sine wave phase, the precision is much reduced compared with that produced by synchronous input (a). c, A somewhat synchronous (within 4 ms) but still subthreshold for dendritic spike generation input pattern was randomly varied between 50, 75, and 100 inputs. Again, the expanded somatic voltage traces (c4) and spike timing histogram (c5) show the resulting output AP timing to be very imprecise as the number of inputs varied.
- Figure 7.
Nonlinear integration allows discrimination between synchronous inputs. a, Two-photon image stack of a representative neuron showing the approximate locations of spines where glutamate was uncaged to produce either a clustered (green dots) or distributed (red dots) input pattern. b, Individual (single spine uncaging events) somatic glu-EPSPs were summed off-line (see Materials and Methods) for both the clustered and distributed input patterns and combined to show their timing (green traces) relative to the somatic 200 Hz sine wave (blue trace). The red trace is somatic membrane potential during the presentation of first a clustered pattern (5 inputs within 1.5 ms and 20 μm) and then a distributed pattern (the same but spread over ∼150 μm) together with the somatic sine wave. When the clustered input pattern was delivered (arrow labeled “clustered”), a somatic output spike was evoked, but when a similarly sized but distributed input pattern was subsequently delivered during the same 200 Hz event (arrow labeled “distributed”), no output was evoked. c, Shown is the same situation but with the timing of the clustered and distributed patterns reversed. d, Graph of spike probability for clustered or distributed inputs showing that the synchronous and clustered input was much better at producing a well timed output than a synchronous but distributed input under recreated SPW conditions. Error bars indicate SE. e, Experimental setup.
- Figure 8.
Model of state-dependent dendritic computations. A, During theta states (characteristic extracellular population pattern shown), excitatory input (A1) to the dendritic arbor is relatively asynchronous, increasing steadily as the animal moves toward and through the place field of the cell. Inhibitory input to the proximal regions of the neuron (proximal trunk, soma, and axon initial segment) is phasic at 5–10 Hz (blue trace). Inhibition to stratum radiatum dendritic regions is similarly phasic but shifted ∼180°, increasing the phasic profile of dendritic depolarization. A2, A3, During such input conditions, the dendritic arbor will remain in a linear integration mode (A2), and action potential output rate during a single theta cycle will increase and timing will shift forward (phase precession) as the number of inputs increases with the position of the animal (A3). Red ticks on the sine wave below the output trace show the AP number and timing relative to the theta phase. The cartoon neuron shows that, in this behavioral state, dendritic integration is linear (black linear function), allowing it to transfer a level of depolarization that is a linear function of the number of inputs to the soma/axonal output AP generating zone (purple sigmoid function) even as a significant subset of the input is spatially clustered onto one dendritic compartment. B, During sharp-wave states (characteristic extracellular population pattern shown), excitatory input (B1) to the dendritic arbor is ∼10-fold more synchronous and the phasic inhibitory input to the proximal regions is at a much higher rate (200 Hz; blue trace). Dendritic inhibition has similar timing as that of proximal inhibition and should again enhance the phasic nature of the dendritic depolarization. CA1 neurons may receive multiple synchronous inputs (patterns 1 and 2; red and green, respectively) during a single ripple event. B2, B3, During such input conditions, only the dendritic compartment receiving clustered input will shift into a supralinear integration mode (B2), and action potential output will repeatedly occur precisely during the brief time period of least proximal inhibition for only the clustered pattern (B3). The cartoon neuron shows the dendritic compartment receiving clustered input is integrating nonlinearly (light blue sigmoid function), allowing it to transfer a relatively constant amount of rapid depolarization to the soma/axonal output AP generating zone (purple sigmoid function). This increases the temporal output precision while reducing its sensitivity to input strength. Green and red dashed lines represent Schaffer collateral input that is either clustered or distributed, respectively. The blue dashed lines are perforant path.
