A developmental stretch-and-fill process that optimises dendritic wiring

Abstract

<jats:title>Abstract</jats:title><jats:p>The way in which dendrites spread within neural tissue determines the resulting circuit connectivity and computation. However, a general theory describing the dynamics of this growth process does not exist. Here we obtain the first time-lapse reconstructions of neurons in living fly larvae over the entirety of their developmental stages. We show that these neurons expand in a remarkably regular stretching process that conserves their shape. Newly available space is filled optimally, a direct consequence of constraining the total amount of dendritic cable. We derive a mathematical model that predicts one time point from the previous and use this model to predict dendrite morphology of other cell types and species. In summary, we formulate a novel theory of dendrite growth based on detailed developmental experimental data that optimises wiring and space filling and serves as a basis to better understand aspects of coverage and connectivity for neural circuit formation.</jats:p><jats:sec><jats:title>In brief</jats:title><jats:p>We derive a detailed mathematical model that describes long-term time-lapse data of growing dendrites; it optimises total wiring and space-filling.</jats:p></jats:sec><jats:sec><jats:title>Highlights</jats:title><jats:p><jats:list list-type="bullet"><jats:list-item><jats:p>Dendrite growth iterations guarantee optimal wiring at each iteration.</jats:p></jats:list-item><jats:list-item><jats:p>Optimal wiring guarantees optimal space filling.</jats:p></jats:list-item><jats:list-item><jats:p>The growth rule from fly predicts dendrites of other cell types and species.</jats:p></jats:list-item><jats:list-item><jats:p>Fly neurons stretch-and-fill target area with precise scaling relations.</jats:p></jats:list-item><jats:list-item><jats:p>Phase transition of growth process between fly embryo and larval stages.</jats:p></jats:list-item></jats:list></jats:p></jats:sec>

Achieving functional neuronal dendrite structure through sequential stochastic growth and retraction

“…Taken together, our results demonstrate that a specialised dendritic tree pattern that minimises wire can be obtained by the precise temporal arrangement of stochastic developmental programs. Interestingly, evidence can be found that similar stages and strategies may be preserved across different cell types (Richardson and Shen, 2019;Gao et al, 2000;Sugimura et al, 2003Sugimura et al, , 2007Baltruschat et al, 2020) and species (Yoong et al, 2019). The flexible usage of such self-organisational programs provides developmental resilience and robustness to perturbations in the growth medium (Hiesinger and Hassan, 2018).…”

“…C, Time courses of the total length of dendrite cable (left) and square root of the surface area (right) during development (see also Figure 6C). D, Scaling behaviour of the square root of the surface area against total length (left) and total length against number of branch points (right) showing the relationships expected from the optimal wire equations (Cuntz et al, 2012;Baltruschat et al, 2020). The dashed line shows the average scaling behaviour of simulated synthetic trees (n = 1, 000 simulations; see Methods).…”

“…Comparing the relationships between basic geometric features of tree structures has previously allowed linking dendritic architecture with wire saving algorithms (Cuntz et al, 2012;Baltruschat et al, 2020). For planar dendrites that minimise wire, a scaling law relating branch points (N ), total length (L) and surface area of the spanning field (S) was formerly derived (Cuntz et al, 2012):…”

“…The model was based on previous morphological models that satisfy optimal wire considerations through minimising total dendritic cable and conduction times from dendrite tips to the soma (Cuntz et al, 2007(Cuntz et al, , 2008(Cuntz et al, , 2010. In particular, it relied on a recent model designed for class IV da (c4da) neurons that satisfies wire constraints while reproducing the iterations of dendrite growth during development (Baltruschat et al, 2020). A, Synthetic dendrite morphologies of a sample c1vpda during the entire embryonic development until the stabilisation phase.…”

“…However, some of these growth models rely on large number of parameters that are not available from experimental data, and they tend to provide phenomenological insights rather than a mechanistic understanding of a given system (Goodhill, 2018). Most notably, none of those approaches have specifically modelled development quantitatively (but see Yalgin et al, 2015;Sugimura et al, 2007;Baltruschat et al, 2020). Also none of those approaches have focused on a quantitative understanding of retraction in the developmental process even though the importance has been emphasised widely (van Pelt, 1997;Beining et al, 2017;Luczak, 2006; Torben-Nielsen and De Schutter, 2014; Williams and Truman, 2004).…”