Challenges in identifying the biophysical factors underlying neural responses.

A) Somatic Vm response of a biophysical model CA1 pyramidal neuron to distributed naturalistic synaptic inputs. Blue box highlights the portion analyzed in panel C. B) Morphology of the simulated neuron with the location of the synapses (green: excitatory; blue: inhibitory synapses; dark green indicates the location of 12 functional synaptic clusters. See Methods and Fig. 4 for more details.) C) Magnified part of the somatic Vm response. Filled arrowhead highlights a spikelet. D) Visualising the input currents in the model using the currentscape technique (Alonso and Marder, 2019). Top: the magnitude of the total inward current on a logarithmic scale. Since we included the capacitive current to the sum (Eq. (1)), the magnitude of the inward and the outward currents is identical (Kirchhoff’s law). Here membrane currents across the entire dendritic tree were summed. Bottom: Percentage of the different ion channels, including intrinsic and synaptic channels, contributing to outward (inhibitory, top) and inward (excitatory, bottom) currents. Color legend is shown on the right and applies to all subsequent figures. White arrowhead indicates a large Ca2+-current that does not appear in the somatic Vm response. Filled arrow highlights dendritic Na+-channel activation corresponding to spikelet in C. E) Currentscape applied to the somatic currents including currents flowing axially from different dendritic branches (grey).

Glossary

Partitioning the axial current.

A Currentscape analysis of a simple model responding to excitatory synaptic input. Left: Morphology of the model with a soma, an apical trunk and two dendritic branches. Insets show the stimulus and the somatic response, with the period analysed in later panels highlighted. Middle: simplified graph representation of the model with two nodes. Here we used this 2-node graph only for illustration purposes. See panels D and I for larger graphs describing the same biophysical model. Right: currentscape of the somatic compartment of the model. Vertical dotted lines indicate the time points analysed in panels B, J and L, with the corresponding axial current directions shown as insets; arrowhead show the timing of the input. pas: passive leak current. cap: capacitive current. B) The axial current of the target compartment (grey arrow) is partitioned by the membrane currents in the child compartment (coloured arrows). When the axial current flows away from the target, it is partitioned by the outward currents in the child (t1, left). When the direction of the axial current reverses, it is partitioned by the inward currents in the child (t2, right). C) Extended currentscape of the somatic node shown in panel A. D-H) Partitioning recursion. Partitioning begins at the most distal child compartment (3) and moves through its parent towards the target (e.g., 1–soma; D). In the first step, Iaxial,1 is partitioned proportionally to the inward currents in node 3 (E). Next, the partitioned axial currents are added to the membrane currents in the parent (node 2; F). Steps D-F are repeated for the next pair of nodes (F-G) until the target is reached. I-L) Iterative partitioning in a graph. I) Graph representation of a multicompartmental model. The compartments (nodes) are denoted by circles and the axial current flow is indicated by arrows (edges). J) The graph, representing the flow of axial currents at t2 in panel A is pruned at the collision edges, where the direction of the axial current reverses. K) Partitioning algorithm starts from a leaf node and progresses towards the target. L) The structure of the pruned graph is time dependent: each graph shows a pattern of axial current flow at different time points from panels A, O or P. Orange colours highlight the part of the graph behind the colliding edge that can not directly contribute to axial currents towards the target. M) Partitioning with node 3 as the target: inward and outward currents are considered separately for both pruning and partitioning. N-P) Currentscape analysis of the responses of the simple model to strong synaptic input evoking a dendritic Na+-spike triggering a somatic AP (N), coincident excitatory inputs to different dendritic branches (O) and inhibitory input blocking somatic AP after a dendritic Na+-spike (P).

Currentscape analysis of dendritic integration in the CA1 PN model.

A) Dendritic (top) and somatic (bottom) Vm in response to stimulating an increasing number of synapses (N=1-30) on an oblique dendrite (inset in B) with 0.3 ms delay in the model without Ca2+channels. Note the fast dendritic Na+-spike appearing at n=20. B) Expected versus measured somatic response amplitude of the stimulations shown in A. Inset shows the branch used for stimulation and dendritic recordings. C) Extended currentscape analysis of the somatic responses to an increasing number of stimulations (n=8, 10, 15 and 20 shown). Top line: somatic membrane potential (Vm) response. Second line: total outward membrane current on log-scale. Third line: percentage of somatic outward and inward currents partitioned by the current type. Fourth row: somatic currents partitioned by the current origin. D-F) Same as A-D for the model equipped with Ca2+-channels in the apical dendrites. Note the step-like response in the dendritic Vm (D, bottom) and the large Ca2+-currents for n=15 and 20 stimuli (F, right).

Model response to complex synaptic inputs.

A) Activity of the 2000 excitatory (green; ordered by the place field location) and 200 inhibitory synapses (blue). Note the theta oscillation and the theta sequences in the excitatory inputs. Synapse locations are shown in Fig. 1B. Dark green indicates the 240 excitatory synapses with stronger weights and organized to functional clusters (see Methods). B) Somatic (top) and dendritic (from distal apical trunk, bottom) Vm response of the model to the synaptic input pattern shown in A. Grey line (arrow) shows the filtered somatic Vm response used to detect complex spike bursts (CSB). CSBs coincided with large depolarizing events in the dendrite. Dotted line (empty arrowhead): CSB detection threshold. The second CSB event (box) is analyzed further in panel F. C) Average (n=16 laps) cross-correlation of the Vm of the 153 dendritic branches in the model. Branches are ordered by morphology of the cell, not by correlation strength. Soma is shown as branch 153. D) The correlation matrix is low rank: the first two components (orange and blue) explain ∼80% of the variance of the Vm. Error bars show SD across 16 simulations. E) The weights of the first two principal components (PC1 and PC2) in an example simulation: the first component describes a uniform activity across the entire cell, while the second captures activity differences between the perisomatic region and distal apical dendrites. F) Left: location of the dendritic Vm recordings (t: tuft, o: oblique, s: soma). Right: Dendritic Vm during somatic burst firing. Filled arrow indicates a local dendritic Na+ spike, open arrows highlights backpropagating APs. G) Histogram of the time difference between dendritic Vm peaks (reaching -30 mV, with a prominence of 30 mV) and the closest Vm peak at the soma, calculated from 16 simulations and the 153 dendritic branches. H) Histogram of the spatial extent of each dendritic event. The 90% of the events were local (light blue), involving < 20 branches (µ = 1.8). The remaining 10% (dark) were associated with somatic APs. Branch spike prevalence (BSP) of these events is shown on the top. I-J) Fraction of local events (I) and fraction of bAPs detected as a dendritic event (J) as a function of the distance of the branch from the soma. Light color: terminal branches; black dot: apical trunk.

Current dynamics in a place cell.

A) From top to bottom: Somatic Vm; inward somatic currents (log scale) and percentage of different outward and inward currents. Colour legend is shown on the right. Red boxes highlight temporal intervals analyzed in panels B-D. Filled arrowheads in panels B-D indicate local dendritic Na+-spikes, open arrowheads point to bAPs and white arrowheads highlight Ca2+-spikes. Ba-f) Current dynamics outside of the place field. Ba) Total membrane current of the cell during theta oscillation. Bb) Somatic currents, including currents flowing from dendrites (axial currents, grey). Bc) Somatic currents partitioned by current type. White arrowhead highlights that dendritic Ca2+-spike has very little contribution. Bd) Somatic currents partitioned by current source region. Colour legend is shown on the right of panel A. Arrowheads highlights that Ca2+-spike originated in the apical region whereas the Na+-spike came from a basal dendrite. Be) Membrane potential (top), sum of inward currents (middle) and input current types in a tuft branch. The recording location is shown as an inset next to panel Be. Bf Tuft currents partitioned by current region. Ca-f) Same as panel B during action potential (AP) firing. Dendritic Na+-spikes originating in the basal dendrites (Cd) appear as spikelets in the soma (filled arrowhead; inset in Ca). The cell is mostly driven by NMDA inputs (Cc) targeting basal dendrites (Cd) and the tuft is largely decoupled from the rest of the neuron, though APs back-propagate (open arrowhead in Cf). Da-Df) Same as panel B during CSB firing. CSB is preceded by multiple dendritic Na+-spikes, some propagating to the soma (black arrowhead in Dc) from stratum radiatum dendrites (Dd). This facilitates a Ca2+-spike from the oblique-trunk region to propagate to the soma (Da-Dd) leading to the first somatic AP. The back-propagating AP (open arrow in Df) triggers Ca2+-spike in tuft and oblique branches that efficiently propagates to the soma and triggers CSB (white arrowhead in Dc and Dd). Further details are in the legend.

Dendritic Vm dynamics during CSBs and isolated spikes.

A) Average dendritic Vm at somatic CSB firing. Grey lines show average across several branches in a given dendritic domain (tuft, obliques and basal dendrites) during individual CSB events; coloured lines show average across 41 CSB events. B) Average dendritic Vm at temporally isolated action potentials (iAPs) in different dendritic domains. Coloured lines show average across 58 events. Dotted red line shows the average response to CSB. C-D) Probability of Ca2+-spikes in tuft dendrites aligned to the start of CSBs (C) or isolated somatic spikes (D). E) Mean path distance of the active synaptic input clusters from the soma during CSBs and isolated spikes (t-test: p = 10−5.98).

Currents underlying CSBs and isolated spikes.

A) Average currentscape of CSBs, aligned to the first spike of the bursts (n=41 events). Top: average Vm in the soma, the trunk (d=260 µm from soma) and in a tuft branch (d=470 µm). Second row: Somatic total current and currentscapes by current type and current region. Third row: Total current and currentscape by current region in the trunk. Last row: Total current and currentscape by current region in the tuft. Yellow rectangle before the first spike indicates the region used for the analysis in C-F. B) Same as A for isolated spikes (n=58 events). C) Contribution of selected membrane current types to outward (top) or inward (bottom) somatic currents in individual CSBs (circles) or APs (dark diamonds). D) Contribution of different dendritic regions to the somatic currents in individual CSBs (circles) or APs (dark diamonds). E-F) Similar to C-D, calculated for a tuft dendrite.

Structured diversity of the currents preceding CSBs and iAPs.

A) Variance explained as a function of the number of components (factors) considered to reconstruct the magnitude of different current types preceding somatic events (CSBs or iAPs). B) Linear projection of the currents to the 2 factors explaining most of the co-variability across somatic events. The six events highlighted with black outline are shown in D-I. C) Factor loadings (weights) associated with representative inward (open circles) and outward (filled circles) currents of the two factors (F1: factor 1, pink; F2: factor 2, levander) shown in panel B. D-I) Example currentscapes of CSBs (D-F) and iAPs (G-I) with different initiation dynamics.

Biophysical model of burst firing in CA1 PNs.

A) Steady-state activation and inactivation curves (left axis, solid lines) and the time constants (right axis, dotted) of the R-type Ca2+channel used in the model. Dotted lines illustrate sigmoid curves fitted to data in Magee and Johnston (1995). B) Steady-state activation curve (left axis, solid) and time constant (right axis, dashed) of a slowly activating K+ channel. C-D) Dendritic (blue) and somatic (black) Vm response of the model to dendritic (C) and somatic (D) current injections. The model has a lower current-threshold for Na+-spikes in the soma and for Ca2+-spikes in the dendrites. Note, that CSBs can be triggered by stronger somatic current steps in the model (not shown). For similar experimental data see Golding et al. (1999). E: Dendritic and somatic Vm responses of the model to a 300 ms, 400 pA somatic current injection under in vivo-like synaptic input conditions (during theta activity, outside the place field, as in Fig. 5B). The red line indicates the smoothed somatic Vm. Under these conditions, a dendritic Ca2+-spike and an associated somatic CSB can be evoked by somatic current injection. For similar experimental data see Bittner et al. (2015).

Dynamics of dendritic Vm PCA components.

A) Short segment of the z-scored Vm of the dendritic branches (rows; soma is the last) of the simulated neuron during in vivo-like synaptic stimulation. The cell fired an action potential around t = 4300 ms and a CSB around t = 4400. Dendrites are ordered by morphology as in Fig. 4E. B) The weights of the first component (PC1) in an example simulation. Dendritic branches are ordered as in Fig. 4E. C) The temporal activation dynamics of the first component (PC1) in an example simulation on the same segment shown in A. D) Reconstruction of the dendritic membrane potentials using the first PCA components. E-M Similar to A-C for the second (E-G), third (H-J) and fourth (K-M) PCA components. The reconstructions in panels G, J and M used all components up to the given rank. Related to Fig. 4

Further examples of somatic and dendritic Vm dynamics during CSBs and iAPs.

A) Vm response of 5 oblique and 5 tuft branches during 8 different CSB events. The recording locations are the same as in Fig. 4F. The events shown in Fig. 8G-H are indicated above the traces. The timing of the somatic action potentials are marked by dotted vertical lines. B) Vm response of 5 oblique and 5 tuft and 5 basal branches during 4 different iAP events. The events shown in Fig. 8D-E are indicated above the traces. Related to Fig. 4.

Examples of iAPs and CSBs partitioned by current types.

A-C) Somatic (top), distal trunk (middle) and tuft (bottom) currents during iAPs partitioned by current type. The same events are shown as in Fig. 8D-F. D-F) Somatic (top), distal trunk (middle) and tuft (bottom) currents during CSBs partitioned by current type. The same events are shown as in Fig. 8G-I.

Simulating optogenetic inhibition of inputs targeting different dendritic domains.

A) The 75% of the input spikes were removed for N ≈ 300 randomly selected presynaptic inputs targeting the basal (of the Ntotal ≈ 900 inputs), oblique (Ntotal ≈ 700) or tuft (Ntotal ≈ 400) dendrites. In the basal clustered case, the number of synapses in the basal input clusters affected by the inhibition were matched to the number of synapses in tuft input clusters. These manipulations significantly reduced both the average number of output spikes and the complex spike bursts (CSBs) per lap (Wilcoxon signed-rank test compared to control, p < 0.01 in all cases), with the tuft inhibition having the strongest effect on both spikes and CSBs. Moreover, inhibiting the tuft was more specific than that of the oblique of basal domains as it reduced the number of CSBs to a greater extent than the number of spikes. B) The number of CSB events per spikes is most strongly reduced by tuft inhibition. C) Simulated optogenetic inhibition also reduced the number of spikes outside of CSBs. This effect was strongest for basal dendrites. Symbols show mean across 16 laps, error bars indicate SE.

Steady-state activation (solid red line) and inactivation (solid blue line) curves of the voltage-gated ion channels expressed in the detailed model (left axis). Dashed lines indicate the time constants of the channels (right axis).

Summary of synaptic channel kinetics.

A: Time course of excitatory (red) and inhibitory (blue) postsynaptic potentials. We used double exponential kinetics with rise time (τ1) and decay time (τ2) constants presented in milliseconds. The reversal potential of the synaptic currents was Steady-state activation curve of the NMDA channel.