Brain organization


{Stiso and Bassett, 2018, Neuro}

Evidence from genetics suggests that neurons with similar functions as operationalized by similar gene expression tend to have more similar connection profiles than neurons with less similar functions [7, 9, 10]. Of course, it is important to note that some spatial similarity of expression profiles is expected due to the influence of small scale spatial gradients in growth factors over periods of development [7]. However, evidence from the Allen Brain Atlas suggests that interareal connectivity profiles in rodent brains are even more correlated with gene co-expression than expected simply based on such spatial relationships [9]. This heightened correlation could be partially explained by observations in mathematical modeling studies that neurons with similar inputs (and therefore potentially performing similar functions) tend to have more similar connection profiles than neurons with dissimilar inputs [11].

Yet, while genetic coding and functional utility each play important roles, a key challenge lies in summarizing the various constraints on connection formation in a simple and intuitive theory that can guide future predictions. One particularly acclaimed candidate mechanism for such a theory is that of physical constraints on the development, maintenance, and use of connections. Metabolism related to neural architecture and function is costly, utilizing 20% of the body’s energy, despite comprising only 2% of its volume [12, 13]. Even the development of axons alone, comprising only a small portion of cortical tissue, extorts a large material cost [7]. The existence of these pervasive costs motivated early work to postulate that wiring minimization is a fundamental driver of connection formation. Consistent with this hypothesis, the connectomes of multiple species are predominantly comprised of wires extending over markedly short distances [13–19], and this observation holds across different methods of data collection [16, 18, 19].

However, mounting evidence suggests that pressures for wiring minimization may compete against pressures for efficient communication [20–22]. Early evidence supporting the role of efficient communication came from the observation that one can fix the network architecture of inter-areal projections in the macaque cortex and then rearrange the location of areas in space to obtain a configuration with significantly (32%) lower wiring cost than that present in the real system [21]. A similar method can be used to obtain a configuration of the C. elegans neuronal connectome with 48% lower wiring cost than that present in the real system [21]. Interestingly, the connections whose length is decreased most also tend to be those that shorten the characteristic path length – one of many ways to quantify how efficiently a network can communicate [21, 23]. Consistent observations have been made in human white matter tractography [20], the mouse inter-areal connectome [10], and dendritic arbors [7, 14]. Notably, computational models that instantiate both constraints on wiring and efficient communication produce topologies more similar to the true topologies than models that instantiate a constraint on wiring minimization alone [11, 24]. Moreover, models that allow for changes in this trade-off over developmental time periods better fit observed connectome growth patterns than prior models [25]. It is precisely this balance between wiring minimization and communication efficiency that is thought to produce the complex network topologies observed in neural systems, along with markedly precise spatial embedding [24, 26].

To better understand this spatially embedded topology, it is useful to consider methods that can simultaneously (rather than independently) assess topology and geometry.

One such method that has proven particularly useful in the study of neural systems from mice to humans is Rentian scaling, which assesses the efficiency of a network’s spatial embedding [20, 27–30]. Originally developed in the context of computer circuits, Rentian scaling describes a power-law scaling relation- ship between the number of nodes in a volume and the number of connections crossing the boundary of the volume [7, 20]. The existence of such a power law relationship with an exponent known as Rent’s exponent is consistent with an efficient spatial embedding of a complex topology [31, 32]. In turn that efficient spatial embedding is thought to support a broad repertoire of functional dynamics. For example, tracts that bridge disparate areas of cortex to increase communication efficiency despite greater wiring cost, also critically add to the functional diversity of the brain in a manner that is distinct from that predicted by path length alone [33].

see refs on small world topology, e.g.

Sporns, Olaf. “The Non-Random Brain: Efficiency, Economy, and Complex Dynamics.” Frontiers in Computational Neuroscience 5 (2011): 5.


  • Kozloski, James, and Guillermo A Cecchi. “A Theory of Loop Formation and Elimination By Spike Timing-Dependent Plasticity.” Frontiers in Neural Circuits 4 (2010)
  • Maass, Wolfgang, Prashant Joshi, and Eduardo Sontag. “Principles of Real-Time Computing With Feedback Applied to Cortical Microcircuit Models.” Advances in Neural Information Processing Systems, Volume 18. MIT Press, 2006.

Last edited Aug 26, 2019