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. 2023 Jan 10;14(1):131.
doi: 10.1038/s41467-022-35747-8.

Introducing the Dendrify framework for incorporating dendrites to spiking neural networks

Michalis Pagkalos  1   2 , Spyridon Chavlis  1 , Panayiota Poirazi  3
Affiliations

Introducing the Dendrify framework for incorporating dendrites to spiking neural networks

Michalis Pagkalos et al. Nat Commun. .

Abstract

Computational modeling has been indispensable for understanding how subcellular neuronal features influence circuit processing. However, the role of dendritic computations in network-level operations remains largely unexplored. This is partly because existing tools do not allow the development of realistic and efficient network models that account for dendrites. Current spiking neural networks, although efficient, are usually quite simplistic, overlooking essential dendritic properties. Conversely, circuit models with morphologically detailed neuron models are computationally costly, thus impractical for large-network simulations. To bridge the gap between these two extremes and facilitate the adoption of dendritic features in spiking neural networks, we introduce Dendrify, an open-source Python package based on Brian 2. Dendrify, through simple commands, automatically generates reduced compartmental neuron models with simplified yet biologically relevant dendritic and synaptic integrative properties. Such models strike a good balance between flexibility, performance, and biological accuracy, allowing us to explore dendritic contributions to network-level functions while paving the way for developing more powerful neuromorphic systems.

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Conflict of interest statement

The authors declare no competing interests.

Figures

Fig. 1
Fig. 1. The main characteristics of dendrify.
a Dendrify stemmed from our efforts to bridge the gap between detailed biophysical models and reduced I&F models. The result is a modeling framework for developing simplified compartmental models that balance efficiency and biological accuracy by capturing the most important characteristics of both worlds. b Dendrify facilitates the development of SNNs comprising reduced compartmental neurons (ball and sticks) and known dendritic phenomena, such as various types of local spikes (Color code; teal: Na+ spikes, red: Ca2+ spikes, orange: NMDA spikes. Scale bar: 20 mV/10 ms).
Fig. 2
Fig. 2. A basic compartmental neuron model with passive dendrites.
a Schematic illustration of a compartmental model consisting of a soma (spiking unit) and two dendrites (passive integrators). The apical dendrite can integrate excitatory synapses comprising AMPA and NMDA currents. b Membrane voltage responses to current injections of the same amplitude are applied individually to each compartment. Notice the electrical segregation caused by the resistance between the three neuronal compartments. c Somatic responses to a varying number of simultaneous synaptic inputs (5–35 synapses). Left: control EPSPs, right: EPSPs in the presence of NMDA blockers. d) Input-output function of the apical dendrite as recorded at the soma. The dotted line represents a linear function. Notice the shift from supralinear to the sublinear mode when NMDARs are blocked. The simulations and analysis code related to the above figure can be executed in any browser by following this link: https://github.com/Poirazi-Lab/dendrify/blob/main/paper_figures/Fig2_notebook.ipynb.
Fig. 3
Fig. 3. A reduced compartmental model that replicates active dendritic properties.
a Schematic illustration of a compartmental model consisting of a soma (leaky I&F) and three dendritic segments (trunk, proximal, distal) equipped with Na+-type VGICs. The distal and proximal segments can also receive AMPA and NMDA synapses. b–d Rheobase current injections (5 ms square pulses) for dSpike generation were applied individually to each dendritic segment. Shaded areas: location of current injection and dSpike initiation. Top: stimulation protocol showing the current threshold for a single dSpike (rheobase current). e First temporal derivative of dendritic (left) and somatic (right) voltage traces from panels (b–d). f Input–output function of the distal (left) and proximal (right) segment as recorded from the corresponding dendritic locations. We also indicate the number of quasi-simultaneously activated synapses (ISI = 0.1 ms) needed to elicit a single dSpike in each case. OFF: deactivation of Na+ dSpikes. Dashed lines: linear input–output relationship. g Left: Backpropagating dSpikes are generated in response to somatic current injections. The short-amplitude spikelets detected in the distal branch are subthreshold voltage responses for dSpike initiation. Right: Magnified and superimposed voltage traces (top) from the dashed box (left). Bellow: dendritic voltage-activated currents responsible for dSpikes generation in each dendritic segment. The simulations and analysis code related to the above figure can be executed in any browser by following this link: https://github.com/Poirazi-Lab/dendrify/blob/main/paper_figures/Fig3_notebook.ipynb.
Fig. 4
Fig. 4. CA1 pyramidal model validation.
a Schematic illustration of the reduced CA1 PC model consisting of a somatic and eight dendritic segments (2× basal, 1× proximal trunk, 1× distal trunk, 2× radial oblique, 2× distal tuft). Grey numbers: distance of the indicated points from the soma. Red axons: EC layer III input, orange axons: CA3 input. Horizontal dotted lines: borders of the four CA1 layers (slm: stratum lacunosum-moleculare, sr: stratum radiatum, sp: stratum pyramidale, so: stratum oriens). b Somatic voltage responses to various (1000 ms long) current injections used for model validation. c F–I curves comparing the model with actual superficial and deep PCs located in the CA1b area. Shaded area: SEM. d Steady-state, distance-dependent voltage attenuation of a long current pulse injected at the soma. G15: data for three detailed biophysical models adapted from. e The attenuation of postsynaptic currents propagating along the apical dendrite as a function of distance from the soma. M18: biophysical modeling data adapted from, Exp: experimental data adapted from. Shaded area: two standard deviations. f Simultaneous somatodendritic recordings in response to a somatic current injection showing the emergence of BPAPs. T1/T2: start/end of current injection (duration = 500 ms). g Main panel: Input-output function of the reduced model’s oblique dendrite (the interval between inputs is 0.1 ms). P03: biophysical modeling data adapted from. Arrows: indicate a different number of co-active synapses (grey = 13, pink = 14, blue = 24). Inset: dendritic voltage responses from the three highlighted cases. h Main panel: peak dV/dt of somatic voltage responses as a function of synaptic inputs (data aligned to their respective thresholds for dSpike initiation). M18: biophysical modeling data adapted from. Exp: experimental data adapted from. Shaded areas: SEM. Inset: First temporal derivative of the reduced model’s somatic EPSPs. Numbers indicate the number of co-active synapses on the apical oblique dendrites. The simulations and analysis code related to the above figure can be executed in any browser by following this link: https://github.com/Poirazi-Lab/dendrify/blob/main/paper_figures/Fig4_notebook.ipynb.
Fig. 5
Fig. 5. Pathway interaction in a reduced CA1 network model.
a Schematic illustration of a pool of reduced compartmental CA1 PCs (N = 10,000). The arrows represent the two streams of input (independent Poisson-distributed spike trains) projecting to distinct dendritic segments. Each neuron represents a repetition of the same experiment with independent Poisson-distributed inputs of the same average frequency. Bottom: table describing the conditional activation of CA1 PCs requiring coincident EC and CA3 input. b Probability distribution of somatic spike count, with (ON) or without (OFF) dendritic spikes, when both EC and CA3 input is applied to the network. c Summary of the results shown in panel (b). Active neurons: PCs that fired ≥1 somatic spike. Notice the reduction of the active population size when dendritic spiking is turned off. d Repeating the coincidence detection experiment for a broad range of input intensities. Left: Mean neuronal firing rate (MFR) for each combination of EC/CA3 input amplitudes. Centre: same as in Left but with dSpikes turned off. The highlighted squares indicate the initial experimental conditions for the data shown in panels (b, c. Right: quantifying the decrease in coincidence detection efficacy by measuring the MFR percentage decrease (dSpikes ON vs. dSpikes OFF). Deactivation of dendritic spiking results in reduced MFR in all cases tested. The white squares (bottom left) represent cases with very low initial MFR (<0.1 Hz or <5% network activity) that were excluded from the analysis. The highlighted squares indicate the experimental conditions of the data shown in panel (f). e Distribution of the results shown in panel (d) (right). f Comparing the ISI distributions between the dSpikes ON and OFF conditions, using the highlighted cases in panel (d) (right). The circles represent the distribution medians, and the vertical lines are the first and third quantiles containing 50% of the data. Stars denote significance with unpaired t-test (two-tailed) with Bonferroni’s correction. The simulations and analysis code related to the above figure can be executed in any browser by following this link: https://github.com/Poirazi-Lab/dendrify/blob/main/paper_figures/Fig5_notebook.ipynb.
Fig. 6
Fig. 6. Estimating Dendrify’s performance for increasing network complexity and size.
a Schematic illustration of the three model cases used for the scalability analysis. In all cases, the neuronal model was an adapted version of the four-compartment model shown in Fig. 2a. Note that the number of Poisson input generators scaled with N. Left: a group of N neurons with passive dendrites and no recurrent synapses. Middle: a group of N neurons with active dendrites (i.e., furnished with Na+ dSpikes) and no recurrent synapses. Right: a recurrent network of N neurons with active dendrites and ~50 synapses/neuron. b Scalability plots, showing how the combined build and simulation time scales when increasing N. The times plotted here represent the average of 10 runs. Simulations were performed on a laptop (blue, orange, and green) or an iPad (black). For more information, refer to Supplementary Table 4. All scalability codes and the raw results are available on GitHub.
Fig. 7
Fig. 7. From biological neurons to reduced compartmental neuron models.
a A morphologically detailed reconstruction of a human CA1 PC (adopted from NeuroMorpho.Org). Red arrow: EC layer III input, orange arrows: CA3 input. Horizontal dotted lines: borders of the four CA1 layers (slm: stratum lacunosum-moleculare, sr: stratum radiatum, sp: stratum pyramidale, so: stratum oriens). b Schematic illustration of a basic five-compartment CA1 model consisting of a somatic and four dendritic segments (1× basal, 1× proximal trunk, 1× distal trunk, 1× tuft). Grey numbers: distance of the indicated points from the soma. Red axon: EC layer III input, orange axons: CA3 inputs. Horizontal dotted lines: borders of the four CA1 layers as in panel (a).
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