Modelling the formation of neural circuits
Final Report Abstract
Anatomical relationships in neural circuits have long been linked to the function that these circuits implement. In particular, notions of optimality have been instrumental in better understanding the brain since the brain requires a significant amount of resources that demand strict housekeeping. Geometric ratios, scaling relationships as well as the nature of neural activity itself can therefore often be understood from the starting principle that Nature uses underlying resources carefully. In preliminary work, we had developed a simple computational model that describes the morphology of dendrites if the location of the inputs is known. This graph theoretical model is based on optimising material and signal conduction times and is useful to study the structure function relationship in single neurons. However, this simplified approach does not take into account dendrite growth, consequences of the model on the circuit and consequences of the circuit on the single cell and does not allow for modelling larger-scale neural network morphologies. In particular, the spatial distribution of the inputs is assumed but should rather be considered a consequence of optimisation principles. The present work explores a more comprehensive usage of optimisation principles for generative models at the network level. These complement and extend the simple single cell models described above exquisitely. The original plan was an ambitious sweep to redefine generative models across levels and their dynamics. In accordance with a rededication proposal of this project, however, this work focused specifically on modelling the impact of optimisation principles on neuroanatomical structures. In order to expand generative models for synthetic dendritic trees based on optimal wiring constraints to link them to more macroscopic scales at the circuit level, we established here an entirely new modelling approach for the optimal placement of neurons and synaptic targets in a circuit according to the optimisation of their connectivity and the features that neurons encode. Briefly, our new model is based on the simple idea that neurons that are connected to each other should also be located near each other. Using dimension reduction methods as well as other optimisation tools, we were able to thereby predict entire neuronal layouts for any given connectivity matrix. The resulting neuronal placements exhibit shorter spatial distances between neurons, which are more strongly connected. Overall, the resulting neuronal placement significantly reduces the material required and the signal conduction times between neurons compared to a random positioning. An obvious test case scenario for the resulting model was the emergence of neural maps in the visual system of cortex. Based on the idea that neurons with similar preferred responses are preferentially connected to one another, we found that neurons with different orientation preference with respect to visual stimuli organise in characteristic structures that resemble pinwheels as observed in the visual cortex of mammals. These pinwheel-like structures repeat across the entire surface of the primary visual cortex. Surprisingly, we found when decreasing the neuron numbers that neurons are optimally dispersed without forming a coherent structure, an arrangement commonly referred to as salt-and-pepper that is observed in many rodents. We therefore showed in various examples that macroscopic structures in the brain can be linked to microscopic structures through optimisation principles. Most interestingly, predicted details of resulting anatomical phenotypes may vary dramatically without assuming differences in their underlying connection principles.
Publications
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(2017) Universal transition from unstructured to structured neural maps. PNAS 114(20):E4057-E4064
Weigand M, Sartori F, Cuntz H
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(2018) A regularity index for dendrites – local statistics of a neuron’s input space. PLoS Computational Biology, 14(11):e1006593
Anton-Sanchez L, Effenberger F, Bielza C, Larrañaga P, Cuntz H
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(2019) Transient localization of the Arp2/3 complex initiates neuronal dendrite branching in vivo. Development, dev.171397
Stürner T, Tatarnikova A, Mueller J, Schaffran B, Cuntz H, Zhang Y, Nemethova M, Bogdan S, Small V, Tavosanis G
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(2020) A model of brain folding based on strong local and weak long-range connectivity requirements. Cerebral Cortex, 30(4):2434- 2451
Groden M, Weigand M, Triesch J, Jedlicka P, Cuntz H
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A developmental stretch-and-fill process that optimises dendritic space filling (bioRxiv, 2020)
Baltruschat L, Tavosanis G, Cuntz H
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The branching code: a model of actin-driven dendrite arborisation (bioRxiv, 2020)
Stürner T, Ferreira Castro A, Philipps M, Cuntz H , Tavosanis G
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(2021) Excess neuronal branching allows for innervation of specific dendritic compartments in cortex. Cerebral Cortex, bhaa271
Bird AD, Deters LH, Cuntz H
