Roe, A.W. (2019). Columnar connectome: towards a mathematics of brain function. Network Neuroscience. Advance publication. https://doi.org/10.1162/netn_a_00088 1 Columnar connectome: towards a mathematics of brain function 2 1,2 3 Anna Wang Roe 4 1 5 Institute of Interdisciplinary Neuroscience & Technology, 6 Zhejiang University, Hangzhou, China 2 7 Oregon National Primate Research Center, OHSU, Portland, OR, USA 8 9 Keywords: primate, cerebral cortex, functional networks, functional tract tracing, matrix 10 mapping, brain theory, artificial intelligence 11 Correspondence: Anna Wang Roe ([email protected]) 12 Pages: 9 13 Words: 3880 14 Figures: 5 15 References: 83 16 17 Acknowledgments 18 This research was conducted at Zhejiang University, and was supported by National Natural 19 Science Foundation Grants 81430010 and 31627802 (A.W.R.), National Hi-Tech Research 20 and Development Program Grant 2015AA020515 (to A.W.R.), and NIH NS093998 (A.W.R). 21 Thanks to Charles Gilbert and Akshay Edathodathil for useful discussions. 22 23 Competing Interests: The author declares she has no competing interests. 24 25 Abstract 26 27 Understanding brain networks is important for many fields, including neuroscience, 28 psychology, medicine, and artificial intelligence. To address this fundamental need, there are 29 multiple ongoing connectome projects in the US, Europe, and Asia producing brain 30 connection maps with resolutions at macro-, meso-, and micro-scales. This viewpoint focuses 31 on the mesoscale connectome (the columnar connectome). Here, I summarize the need for 32 such a connectome, a method for achieving such data rapidly on a largescale, and a proposal 33 about how one might use such data to achieve a mathematics of brain function. 34 35 36 2 37 Understanding brain networks is important for many fields, including neuroscience, 38 psychology, medicine, and artificial intelligence. To address this fundamental need, there are 39 multiple ongoing connectome projects in the US, Europe, and Asia producing brain 40 connection maps with resolutions at macro-scale (e.g. Human Connectome Project) and 41 micro-scales (e.g. Brainsmatics, Gong et al 2016). However, still lacking is a meso-scale 42 connectome. This viewpoint (1) explains the need for a mesoscale connectome in the primate 43 brain, (2) presents a new method for studying mesoscale connectivity, and (3) proposes a 44 mathematical approach to representing the mesoscale connectome. 45 46 The cortical column is a modular processing unit. In humans and nonhuman primates 47 (NHPs), the cerebral cortex occupies a large proportion of the brain volume. This remarkable 48 structure is highly organized. Anatomically, it is a two-dimensional (2D) sheet, roughly two 49 millimeters in thickness, and divided into different cortical areas, each specializing in some 50 aspect of sensory, motor, cognitive, and limbic function. There is a large literature, especially 51 from studies of NHP visual cortex, to support the view that the cerebral cortex is composed 52 of submillimeter modular functional units, termed ‘columns’ (Mountcastle 1997). Columns 53 span the 2-mm thickness of cortex and are characterized by 6 input/output layers (laminae) 54 linked together via inter-laminar circuits (Figure 1). The tens of thousands of neurons within 55 a single column are not functionally identical but share common functional preference such 56 that single stimuli maximally activate the population and produce a coherent columnar 57 response. These coherent responses can be visualized using multiple methods, including 58 electrophysiology (e.g. Hubel and Wiesel 1977, Mountcastle 1997, Katzner et al 2009), 2- 59 deoxyglucose (e.g. Tootell et al 1988), optical imaging (e.g. Blasdel and Salama 1986, 60 Grinvald et al 1986), and high spatial resolution fMRI methods (e.g. Cheng 2012, Nasr et al 61 2016, Li et al 2019). More in depth and scholarly articles about the definition and existence 3 62 of the column are available (e.g Horton and Adams 2005, Rakic 2008, Ts’o et al 2009, da 63 Costa and Martin 2010, Rockland 2010). 64 In non-visual cortical areas, data on columnar organization is more limited (DeFelipe et 65 al 1986, Lund et al 1993, Krizter and Goldman-Rakic 1995, Friedman et al 2004, Gharbawie 66 et al 2014). However, there is accumulating evidence, as well as compelling genetic and 67 developmental (Rakic 1988, Torii 2009, Li et al 2012), and computational reasons (Swindale 68 2004, Schwalger et al 2017, Berkowitz and Sharpee 2018) to believe that columnar 69 organization may be a fundamental feature throughout cortex. Borrowing from Pasko Rakic 70 (2008): “The neurons within a given column are stereotypically interconnected in the vertical 71 dimension, share extrinsic connectivity, and hence act as basic functional units subserving a 72 set of common static and dynamic cortical operations that include not only sensory and motor 73 areas but also association areas subserving the highest cognitive functions.” For the 74 purposes of this viewpoint, the term ‘column’ refers to a unit of information integration and 75 functional specificity. 76 77 Why a columnar connectome is needed. Columns come in different flavors and have very 78 specific connections with other columns. For example (Figure 2), in primary visual cortex (V1, 79 dotted lines divide V1, V2, and V4), different functional columns focus on visual features such 80 as eye specificity (ocular dominance columns, Fig 2B), color (blobs; Fig 1C: dark dots in V1 81 are color ‘blobs’, red dot overlies a blob), and orientation (orientation columns; Fig 1D dark 82 and light domains in V1, yellow dot overlies a horizontal orientation domain). In the second 83 visual area (V2), columns within the thin stripe (green dots) and thick/pale stripe (blue dots) 84 types integrate columnar information from V1, to generate higher order parameters of color 85 (thin stripes: hue), form (thick/pale stripes: cue-independent orientation response), and depth 86 (thick stripes: near to far binocular disparity) (for review, Roe et al 2009). Columns in V4 are 4 87 hypothesized to perform further abstractions such as color constancy (Kusunoki et al 2006), 88 invariance of shape position and size (Rust & DiCarlo 2010, Sharpee et al 2012), and relative 89 (vs absolute) depth (Shiozaki et al 2012, Fang et al 2018) (for review, Roe et al 2012). 90 A key aspect of cortical columns is their highly specific connections with other columns 91 (Figure 2CD, red and yellow arrows). This has been demonstrated from studies using focal 92 injections of tracer targeted to single columns. Such studies have revealed sets of patchy 93 connections, both intra-areal (Figure 1, inset) and inter-areal (Figure 2, arrows) (e.g. 94 Livingstone and Hubel 1984, Sincich and Horton 2005, Shmuel et al 2005, Federer et al 2013). 95 Column-specific connection patterns thus embody a functionally specific (e.g. orientation or 96 color) network. However, to date, due to the demanding nature of these experiments, there 97 are only a small number of such studies. Thus far, there has not been a method that permits 98 systematic largescale study of columnar connectivity. In fact, over 40 years after Hubel and 99 Wiesel’s (1977) description of the organization of functional columns in V1, little is known 100 about the organization of cortical connectivity at the columnar level. I propose that we extend 101 the concept of the hypercolumn (all the machinery required to represent a single point in 102 space) to the connectional hypercolumn (all the connections of that unit of representation). 103 104 The primary limitation of current methods is (1) lack of spatial resolution. Most anatomical 105 mapping methods employ tracer injections 2-5 mm in size. Human connectomes are based 106 on resting state or diffusion methods which typically are mapped at 2-3 mm voxel resolution. 107 These volumes (white rectangle in Figure 2E) encompass multiple columns and therefore 108 reveal connections of a population of multiple functionally distinct columns. Since individual 109 nearby columns can exhibit quite distinct connectivity patterns (e.g. Fig 2CD: color blobs to 110 thin stripes vs orientation columns to pale/thick stripes), connections arising from such 111 averages are inaccurate and misleading (Figure 2E). (2) Slow and expensive. Traditional 5 112 anatomical tract tracing typically requires 2-3 weeks for tracer transport, animal sacrifice to 113 acquire tissue, and time-consuming weeks to map label locations and 3D reconstruction. (3) 114 Not largescale. Anatomical studies are limited to several tracers and therefore the 115 connections of only a handful of nodes can be studied in any single brain. Other methods 116 such as electrophysiological stimulation with fMRI mapping has elegantly revealed networks 117 underlying specific behaviors (e.g. Tolias et al 2005); but electrical methods can suffer from 118 current spread, leading to lack of spatial specificity, as well as inability to map local 119 connections due to signal dropout near the electrode. Optogenetic stimulation with fMRI 120 mapping is a powerful cell type specific approach (e.g. Gerits et al 2012); however, in 121 primates, it takes weeks for viral expression and has thus far been limited by the small 122 number of transfected nodes, making largescale mapping of connections in the primate brain 123 challenging. (4) Correlation based functional connectivity. fMRI BOLD signal correlation 124 (resting state studies) non-invasively probes networks in human and animal brains, but are 125 limited to inference about correlation rather than connectivity. Such limitations also exist with 126 neurophysiological cross correlation studies of spike timing coincidence. 127 128 A new mapping method. To overcome some of these limitations, we have developed a new 129 rapid in vivo mapping technique. This method combines an optical stimulation method, 130 termed pulsed infrared neural stimulation (INS), with high field fMRI (Xu et al 2019a).