Competition for neurotrophic factors: ocular dominance columns

Abstract

Activity-dependent competition between afferents in the primary visual cortex of many mammals is a quintessential feature of neuronal development. From both experimental and theoretical perspectives, understanding the mechanisms underlying competition is a significant challenge. Recent experimental work suggests that geniculocortical afferents might compete for retrograde neurotrophic factors. We show that a mathematically well-characterized model of retrograde neurotrophic interactions, in which the afferent uptake of neurotrophic factors is activity-dependent and in which the average level of uptake determines the complexity of the axonal arbors of afferents, permits the anatomical segregation of geniculocortical afferents into ocular dominance columns. The model induces segregation provided that the levels of neurotrophic factors available either by activity-independent release from cortical cells or by exogenous cortical infusion are not too high; otherwise segregation breaks down. We show that the model exhibits changes in ocular dominance column periodicity in response to changes in interocular image correlations and that the model predicts that changes in intraocular image correlations should also affect columnar periodicity.

Fig. 1.

The final pattern of OD as a function of the NTF diffusion parameter ς_c. Eachsquare in each map represents one cortical cell. The shade of gray assigned to each square represents the percentage control by the left LGN sheet; white squares are entirely controlled by the right LGN sheet (R), and black squares are entirely controlled by the left LGN sheet (L). Three cortical maps are shown, each with a value of ς_c as indicated. The other parameters are c = 19,l = 9, N = 5,T₀ = 0, T₁ = 20,a = 1, ς_l = 0.75, andp = 0.0 (C = −1.0).

Fig. 2.

The power spectra corresponding to the threemaps in Figure 1. The solid linerepresents ς_c = 0.50, thelong-dashed line represents ς_c = 0.75, and theshort-dashed line represents ς_c = 1.00.

Fig. 3.

The final pattern of OD as a function of the intraocular image correlation parameter ς_l. Three cortical maps are shown, each with a value of ς_l as indicated. The other parameters arec = 19, l = 9,N = 5, T₀ = 0,T₁ = 20, a = 1, ς_c = 0.75, and p = 0.0 (C = −1.0).

Fig. 4.

The power spectra corresponding to the threemaps in Figure 3. The solid linerepresents ς_l = 0.50, thelong-dashed line represents ς_l = 0.75, and theshort-dashed line represents ς_l = 1.00.

Fig. 5.

The final pattern of OD as a function of the interocular image correlation parameter C. Three cortical maps are shown, each with a value ofC = 2p − 1 as indicated. The other parameters are c = 19,l = 9, N = 5,T₀ = 0, T₁ = 20,a = 1, ς_c = 0.75, and ς_l = 0.75.

Fig. 6.

The power spectra corresponding to the threemaps in Figure 5. The solid linerepresents C = −0.4, thelong-dashed line representsC = 0.0, and the short-dashed line represents C = +0.4.

Fig. 7.

The simulated infusion of NTF into the visual cortex in which geniculocortical afferents have partially but not completely segregated. Left, Map that is the result of 20,000 presentations of LGN activity patterns and hasT₀ = 0. Right,Map generated by setting T₀ = 100 and running the simulation for a further 30,000 presentations of LGN activity patterns. The other parameters are c = 19, l = 9, N = 5,T₁ = 20, a = 1, ς_c = 0.75, ς_l = 0.75, and p = 0.0 (C = −1.0).