Context-aware modeling of neuronal morphologies

Abstract

physical overlap between dendrites and axons constrain the circuit topology, and the precise shape and composition of dendrites determine the integration of inputs to produce an output signal. At the same time, morphologies are highly diverse and variant. The variance, presumably, originates from neurons developing in a densely packed brain substrate where they interact (e.g., repulsion or attraction) with other actors in this substrate. However, when studying neurons their context is never part of the analysis and they are treated as if they existed in isolation. Here we argue that to fully understand neuronal morphology and its variance it is important to consider neurons in relation to each other and to other actors in the surrounding brain substrate, i.e., their context. We propose a context-aware computational framework, NeuroMaC, in which large numbers of neurons can be grown simultaneously according to growth rules expressed in terms of interactions between the developing neuron and the surrounding brain substrate. As a proof of principle, we demonstrate that by using NeuroMaC we can generate accurate virtual morphologies of distinct classes both in isolation and as part of neuronal forests. Accuracy is validated against population statistics of experimentally reconstructed morphologies. We show that context-aware generation of neurons can explain characteristics of variation. Indeed, plausible variation is an inherent property of the morphologies generated by context-aware rules. We speculate about the applicability of this framework to investigate morphologies and circuits, to classify healthy and pathological morphologies, and to generate large quantities of morphologies for large-scale modeling.

Keywords: computational modeling; dendrite; extracellular space; growth cone; morphology.

FIGURE 1

Schematic of the proposed context-aware framework, NeuroMaC, to generate virtual morphologies. (A) The simulated brain substrate is decomposed into small sub volumes (SVs). Sub volumes keep track of all neurites and other relevant actors inside their spanning volume. (B) Algorithm performed by each sub volume during one simulated, centrally controlled time step. (C) Fronts are implemented as cellular automaton-like machines and conceptually related to growth cones in that they update their location based on the local context. Full lines: neurites (black and gray: existing; green: newly added). Circles represent active (filled) or inactive (open) fronts. Dashed lines represent the contextual cues influencing the direction of growth of an active front to be extended (indicated by a red circle). Here the contextual cues are defined by an inertial forward-directed influence, another neurite, and a gradient in the substrate.

FIGURE 2

Validation of generated alpha motor neurons. (A–C) Exemplar experimentally reconstructed spinal cord alpha motor neurons [A,B from the Fyffe archive (Alvarez et al., 1998), C from the Burke archive (Cullheim et al., 1987)]. (D–F) Virtual morphologies generated by NeuroMaC. (G–I) Quantitative comparison. Population morphometrics are shown for the Burke (“Burke”) and Fyffe (“Fyffe”) archives and for the generated morphologies (“Syn”). (G) Euclidean distance between the soma and each terminal point in all morphologies. (H) Topological order of each branching point in all morphologies. (I) Occurrence of branching points in each morphology as a function of Euclidean distance (i.e., Sholl-intersections, see main text). See Table 3 for detailed statistics of these (and other) morphometrics.

FIGURE 3

Validation of generated hippocampal granule cells. (A–C) Experimentally reconstructed granule cells (from the Lee archive; Carim-Todd et al., 2009). (D–F) Virtual morphologies generated by NeuroMaC. (G) Forest of 100 simultaneously generated, non-overlapping granule cells. (H–K) Quantitative comparison. Population morphometrics are shown for the Lee archive (“Lee”), synthetic neurons generated in isolation (“Syn”) and as part of a forest (“Forest”). (H) Euclidean distance between all terminal tips and the soma. (I) Maximum topological order in the individual morphologies. (J) Topological order of each branching point in all morphologies. (K) Occurrence of branching points in each morphology as a function of Euclidean distance (i.e., Sholl-intersections). See Table 4 for a detailed quantification of these (and other) morphometrics.

FIGURE 4

Validation of generated layer 5 pyramidal neurons. (A) Experimentally reconstructed layer 5 pyramidal neurons (from the Kawaguchi archive). (B) Virtual morphologies generated by NeuroMaC. Simulated laminar structure (L1–L5, from top to bottom) indicated by dashed lines; blue line represents the pia. (C) Forest of 100 simultaneously generated, non-overlapping pyramidal neurons. (D–F) Quantitative comparison. Population morphometrics are shown for the Kawaguchi archive, synthetic neurons generated in isolation (“Syn”) and as part of a forest (“Forest”). Statistics are given for basal (left panels) and apical (right panels) trees separately. Shown are total number of branching points (D), Euclidean distance between terminal tips and the soma (E) and the total length of the dendrites (F). Detailed statistics of these (and other) morphometrics in Table 6.