Pyramidal arborizations and activity spread in neocortex

Neurocomputing 26}27 (1999) 483}490

Pyramidal arborizations and activity spread inneocortex

Adrian Robert*Department of Cognitive Science, 0515 University of California, San Diego, La Jolla, CA 92093-0515, USA

Abstract

A model of a patch of neocortex was constructed by reference to the details of pyramidal andinhibitory arbors in rat somatosensory cortex, and its behavior was compared to slice experi-ments measuring activity spread following point-stimulation. Two features of pyramidal arborsplayed a prominent role in the results and may a!ect cortical information transmission: (1) dualhorizontal structure, in which connections are made densely within 0.5mm and sparsely over2}3mm } a!ected characteristic length and rate of propagation; and, (2) signi"cant restrictionof projections to the vertical compartment (super"cial, middle, deep) of origin } resulted inlaminar di!erences in activity levels. ( 1999 Elsevier Science B.V. All rights reserved.

Keywords: Neocortex; Lamination; Propagation; Arbor

1. Introduction

Each hemisphere of the neocortex consists of a relatively #at, laminated sheet inwhich several anatomically distinguishable layers (six, by convention) of cells arejuxtaposed. In addition to local connections, cells within one localized region, or area,project to and receive from a limited set of other areas. These projections originatefrom and terminate in subsets of the layers, often following particular patterns[3] (Fig. 1, left). During sensory processing, they convey stimulus-related activityfrom essentially one starting point (the `primary areaa) through a network of areas(about 30 in the visual system of macaque monkeys and higher primates). Usually,connections from areas synaptically closer to the primary area to those further awayfollow the FF pattern, while those in the opposite direction follow the FB pattern

*Corresponding author. E-mail address: [email protected] (A. Robert)

0925-2312/99/$ } see front matter ( 1999 Elsevier Science B.V. All rights reserved.PII: S 0 9 2 5 - 2 3 1 2 ( 9 9 ) 0 0 0 3 8 - 7

Fig. 1. As noted in [3], connections between areas fall largely into one of the two forms on the left; FF andFB stand for `feedforwarda and `feedbacka, respectively. The right "gure illustrates typical within-areacortical cell arborization patterns. Black, white, and grey indicate dendritic, axonal, and overlappingarborizations, respectively.

(Fig. 1, left). Presumably, these patterns re#ect a computational need to treat stimu-lus-driven activity di!erently from the internal state-driven activity in each area [10];however it is di$cult to make this more precise simply based on the anatomy, becausemost cortical cell types possess dendritic and axonal arborizations extending overmultiple layers [6] (Fig. 1, right). On the other hand, technical constraints render itdi$cult to physiologically determine the quantitative impacts that di!erent inputshave on areas.

We have therefore taken an approach via modeling, constructing a series of threemodels incorporating di!ering levels of anatomical detail. The most complex modelcontained six layers and could be compared directly with simple physiologicalexperiments for purposes of veri"cation and calibration. The simplest containeda single layer, and was best suited for theoretical analysis and comparison witha number of previous cortical models. The third model was intermediate in complex-ity, containing three layers, and represented a compromise a!ording both comparisonwith physiology and investigation of computational properties. In this note wedescribe the construction of the models and the comparison of the three- andone-layer versions with experimental results on spread of activity in rat somatosen-sory neocortical slices. The results highlight and quantitatively characterize importantbasic aspects of the horizontal and vertical connections underlying cortical informa-tion transfer.

2. Model construction

All the three models shared the same basic structure: a stack of square grids of cellunits interconnected with strengths decaying exponentially over horizontal distance.The whole represented a 2]4mm patch of neocortex, simulating one in 30 cells.The main goal guiding construction was accurate representation of aspects ofthe biology most likely to a!ect interlayer information transmission. Because theamount of time for transfer between layers can determine dynamical structure such aslocal feedback circuits that could magnify or shrink in#uences, a single cell modelcapable of representing this temporal element was chosen. Because the arborization

484 A. Robert / Neurocomputing 26}27 (1999) 483}490

characteristics of the di!erent cell types determine routes of interlayer communica-tion, the distribution and arborization of the di!erent cell types (Fig. 1) was used todetermine connectivity.

2.1. Cell unit

Cortical cells were modeled by single-compartment conductance-based units ana-logous to those described in [13]. Membrane potential is updated every 10~4 saccording to synaptic and leak current across a capacitive membrane. If the mem-brane potential reaches threshold in a unit, it is reset to the resting potential anda spike is propagated with a delay to synapses on other cells, the e!ects of which aremodeled by alpha-function conductance changes. The time constants and peakconductances for synapses were determined according to what portion of the cell theparticular class of input involved is known from anatomical data to contact. Corticalcells fall into three classes based on intrinsic response properties [9]. Additionalconducting channels were included in the cell models to mimic the e!ects of currentsdi!erentiating these classes. See [12] for further details.

2.2. Six-layer model

The six-layer model was an attempt to be maximally faithful to what is knownabout the structure of rat sensory cortex and served as a basis for simpli"cation tobuild the other models. It was constructed in three stages } "rst, anatomical data oncells and their interconnections was gathered by surveying the literature. This result-ed, after some initial simpli"cation, in 51 separate cell populations, consisting of 14pyramidal populations (75% of the total cells) plus 11 subtypes of inhibitory cells splitinto several populations each. The relative numbers of each population and theirinterconnections are not fully speci"ed by the literature; however the values that areknown constrain the others. We therefore made educated estimates of unknownqualities and then adjusted all values by means of a relaxation network.

In this network, each cell population was represented by a single node witha density value and a set of values representing outputs to other nodes. On eachoptimization step, these latter values were propagated to their targets scaled byrelative densities to set input values, which were then compared with known orestimated values to compute error. This error was applied to adjust the outputs anddensities based on the relative con"dences in estimated values. Simulated annealingwas employed to relax the network, and, while di!erent runs led to di!erent sets of"nal values, any particular value would vary no more than 10%, suggesting that thebaseline estimated value set was situated within a broad, #at minimum in the space ofarchitectures.

2.3. Three-layer model

We constructed the three-layer model based on insights from building the six-layerone. Regarding pyramidal cells, axon tracing studies in rat SI and elsewhere

A. Robert / Neurocomputing 26}27 (1999) 483}490 485

Fig. 2. Left: Typical pyramidal in#uence via axonal arbor on same compartment (left) and both othercompartments combined (right); to scale, arbitrary units (the within-compartment shape results fromsuperposition of 3 arbor widths with di!erent frequencies of occurrence } typically 0.5, 1, and 2mm in therat). Right: Schematic of the experimental setup.

[5,8] show that their arborizations possess three general characteristics (seeFig. 2, left):

f In a given layer, some cells give rise to wide arbors stretching over distances of morethan a millimeter, while other cells have narrower arbors of much less thana millimeter range.

f Terminal distribution remains largely (usually &70%) within the compartment ofthe cell soma } either super"cial (layers I}III), middle (layer IV), or deep (layersV}VI).

f The widest portions of arbors from cells in a layer remain within the samecompartment.

Based on this, the three layers in the simpler model represented these three compart-ments, with a single pyramidal population in each arborizing as described. Regardinginhibitory cells, a reduction in number of types from 11 to 3 was achieved bycollapsing highly similar ones. The "rst class consists of small inhibitory cells withaxons and dendrites localized within a compartment (e.g., neurogliaform, chandelier),the second consists of wide inhibitory cells also largely localized within a compart-ment (e.g., large basket), while the third consists of narrow inhibitory cells with arborsspanning compartments (e.g., bipolar). In the model, the middle layer contained onlythe "rst type, while the other two contained all three, leading to a total of just 10 cellpopulations including three pyramidals.

2.4. Single-layer model

The one-layer model contained two cell populations (excitatory and inhibitory) andwas constructed by computing average horizontal arborizations for cell classes in thesix-layer model. To investigate the composite structure of pyramidal arbors horizon-tally (Fig. 2, left), four versions of this model were constructed. In the `baselineacondition, these arbors were directly modeled by a weighted sum-of-exponentials. Inthe `short conditiona, only the shortest exponential, renormalized, was used. In the`averagea condition, a single exponential out to the weighted average maximumradius of the arbors was used, while in the `"ta condition, a single exponential arborwas least-squares "t to the weighted average. Each of these lateral connectivityconditions led to di!erences in activity propagation, to be described.


3. Experimental comparison

All three models were compared to two sets of experiments on cortical slicesmeasuring activity spread following point stimulation at the layer VI-white matterboundary [1,7]. Previously [11], we reported comparisons involving the one-layerand six-layer models, showing that they, like the slices, displayed three regimes ofquiescence, wave propagation, and explosion depending on the relative strengths ofinhibitory synapses. Additionally, the six-layer model captured certain aspects of the"rst experiment that the single-layer model did not. Here, we discuss these aspects andothers in greater detail for the three-layer model, whose behavior was qualitativelysimilar to that of the six-layer one, focusing on the e!ects of the characteristics ofpyramidal arborizations discussed above.

3.1. Horizontal activity spread

Fig. 2 (right) depicts the experimental setup in both [1] (henceforth, CC) and [7](LS). The pharmacological conditions and methods of measurement were slightlydi!erent in the two cases, but they both observed propagation of waves of activity ata certain rate and width, reproduced in all three models [11].

LS also observed that activity appeared to propagate in discrete steps: the "rst waveof synaptically-stimulated activity following stimulation was observable only out toabout 200}300lm on either side; the time to earliest activity further out was greaterby an amount consistent with (increasingly) multisynaptic transmission. LS inter-preted this as indicating that pyramidal}pyramidal connections are su$ciently strongto support large-scale activity transmission only within a range of (400 lm. Fig. 3shows similar results from three versions of the one-layer model illustrating the e!ectsof pyramidal horizontal arbor structure.

Note that, in addition to variation in transmission distance, di!erences inwavelength and speed are also visible. The `shorta condition, not shown, was similarto the baseline except that, due to the lack of longer-distance arbors, propagation wasfrom 20 to 50% slower depending on disinhibition level.

Fig. 3. Variation in monosynaptic transmission distance with model connectivity. Each of the three plotsdisplays membrane potential over 40ms for cells at successively further points from the origin (top trace).The vertical lines indicate the "rst peaks of the traces; in each case, there is a jump from peaks being within(5 ms of each other (a shorter time than required for charging and synaptic transmission) to being muchfurther apart. For the baseline case, this occurs between 300 and 600lm, for the average and "t cases,between 600 and 1200lm.


3.2. Vertical transfer

CC and LS recorded from both deep and super"cial cortex, "nding indication thatactivity spread preferentially through the deep layers. CC found while recordingintracellularly from super"cial pyramidals that during extracellular "eld potentialevents accompanying wave passage, the cells often did not "re, and in fact evendisplayed depressed membrane potentials relative to rest. On the other hand, theyfound that deep pyramidals, particularly burst cells, almost always "red. LS foundactivity appeared to travel faster in the deep layers } in particular, a delay of almost9ms between the earliest deep and earliest super"cial activities occurred at 1.5mmlateral distance.

The three-layer model showed similar behavior (Fig. 4). Intuitively, activity isinitially strongest in the deep layers owing to the proximity of the stimulation site and,aided by partial isolation, continues to propagate there more strongly. Comparison(not shown) with noncompartmentalized versions of the model, in which pyramidalconnections were made equally throughout all layers, supported this explanation,because the latter versions did not display any interlayer di!erences in activity afterthe "rst few milliseconds.

4. Computational implications

Many models have investigated Hebbian development of connection weightsto single, laterally connected cortical layers exposed to input with correlation

Fig. 4. Wave propagation activity in super"cial and deep layers in three-layer model. Left: membranepotential traces as in Fig. 3 for four locations over 30ms. Right: spiking activity of all the pyramidals in eachlayer for three successive times (msec) } each point is the "ring rate averaged locally over 4]4 cells and2msec (lighter"more active). Deep activity propagates further, faster, and with greater amplitude. (Themiddle layer was intermediate.)


structure [2], but these generally only take into account the shortest excitatory lateralinteractions } corresponding to the `shorta condition here. The prominence of thelonger connections in determining propagation rate and other characteristicsof activity waves in our anatomically based models suggests that they should beincluded as well; theoretical analyses [4] emphasize that lateral length constants areimportant.

Comparatively few cortical models have incorporated laminar structure, largelybecause the relevant architectural details are not clear from the biology. The presentwork suggests based on convergent evidence that processing with di!erent compart-ments is partially independent, and it lays foundations for investigating this quantitat-ively. The three-layer model is currently being employed to study Hebbian learningunder the in#uence of feedforward and feedback inputs. Although this model wasbased on rat primary sensory cortex, a preliminary survey of data on areas in otherregions and species suggests that at its level of detail, the situation is fairly similaracross other areas and other species.

References

[1] Y. Chagnac-Amitai, B.W. Connors, Horizontal spread of synchronized activity in neocortex and itscontrol by GABA-mediated inhibition, J. Neurophysiol. 61 (1989) 747}58.

[2] E. Erwin, K. Obermayer, K. Schulten, Models of orientation and ocular dominance columns in thevisual cortex: a critical comparison, Neural Comput. 7 (1995) 425}68.

[3] D.J. Felleman, D.C. Van Essen. Distributed hierarchical processing in the primate cerebral cortex,Cerebral Cortex 1 (1991) 1}47.

[4] G.J. Goodhill, The in#uence of neural activity and intracortical connections on the periodicity ofocular dominance stripes, Network 9 (1998) 419}32.

[5] J.P. Gottlieb, A. Keller, Intrinsic circuitry and physiological properties of pyramidal neurons in ratbarrel cortex, Exp. Brain Res. 115 (1997) 47}60.

[6] E.G. Jones, A. Peters (Eds.), Cerebral Cortex, vol. I. Cellular Components of the Cerebral Cortex,Plenum Press, New York, 1984.

[7] R.B. Langdon, M. Sur, Components of "eld potentials evoked by white matter stimulation in isolatedslices of primary visual cortex: spatial distributions and synaptic order, J. Neurophysiol. 64 (1990)1484}1501.

[8] J.B. Levitt, D.A. Lewis, T. Yoshioka, J.S. Lund, Topography of pyramidal neuron intrinsicconnections in macaque monkey prefrontal cortex (areas 9 and 46), J. Comp. Neurol. 338360}76.

[9] D.A. Prince, J.R. Huguenard, Functional properties of neocortical neurons, in: W. Singer, P. Rakic(Eds.), Neurobiology of Neocortex, Wiley, New York, 1988.

[10] R.P.N. Rao, D.H. Ballard, Dynamic model of visual recognition predicts neural response properties inthe visual cortex, Neural Comput. 9 (1997) 805}47.

[11] A. Robert, A model of the e!ects of lamination and celltype specialization in the neocortex,in: J.M. Bower (Ed.), Computational Neuroscience: Trends in Research, 1998, Plenum Press, NewYork, 1998.

[12] A. Robert, Lamination and activity spread in mammalian neocortex: a model, J. Neurosci. (1998),submitted.

[13] M.A. Wilson, J.M. Bower, The simulation of large-scale neural networks, in: C. Koch, I. Segev (Eds.),Methods in Neuronal Modeling, MIT Press, Cambridge, MA, 1989.


Adrian Robert received Bachelor's degrees in computer science and mathematicsfrom Cornell University in 1992. He went on to study in the cognitive sciencedepartment at the University of California in San Diego, where he is now "nishinghis doctoral thesis on computational aspects of the medium-scale anatomicalstructure of the mammalian cerebral cortex.


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Pyramidal arborizations and activity spread in neocortex