Monocular deprivation during the critical period shifts cortical ocular dominance toward the open eye, but the two classic deprivation protocols differ dramatically: eyelid suture causes a rapid loss of deprived-eye cortical responses, whereas retinal inactivation with tetrodotoxin (TTX) produces a much smaller shift. Linden et al. (2009) showed that this difference cannot be explained by changes in thalamic drive, because monocular inactivation leaves the mean firing rates of lateral geniculate nucleus (LGN) relay neurons unchanged while increasing correlations between them. Blais, Cooper and Shouval (2009) then showed, using linearized analysis of the Bienenstock-Cooper-Munro (BCM) rule, random-matrix constructions and simulations, that high rate-based correlations among deprived-eye LGN inputs slow the loss of deprived-eye responses under BCM-type (homosynaptic-depression) rules, with time constant [ϵ⟨n2⟩(1−q)]−1[\epsilon\langle n^2\rangle(1-q)]^{-1} governed by the eigenvalue 1−q1-q of the input correlation matrix, whereas principal-component-analysis/Oja-type (heterosynaptic) rules are nearly independent of the correlation qq and respond oppositely to noise variance. This reconciliation requires rate-based correlations near q≈0.8q\approx0.8, yet spike-based cross-correlations measured in mouse LGN are only around 0.1, and the quantitative correspondence between the two correlation measures was analyzed only for one simple doubly stochastic case. The open problem is to establish, in vivo and in theory, how deprived-eye LGN correlations at unchanged mean rates gate ocular-dominance plasticity: measure the deprived-eye LGN rate-covariance structure during retinal inactivation, develop and validate the quantitative mapping between rate-based and spike-based correlation measures, and test the correlation dependence of the rate of fall-off of response from the deprived eye in MI, which would check the opposing predictions of homosynaptic (BCM-like) and heterosynaptic (Hebbian/PCA-like) plasticity mechanisms.

Background

Ocular dominance plasticity is the canonical paradigm for experience-dependent synaptic plasticity in the visual cortex: during a postnatal critical period (a window of heightened sensitivity of cortical circuits to altered visual experience), closing or otherwise depriving one eye (monocular deprivation, MD) causes cortical neurons to lose their responsiveness to the deprived eye. The lateral geniculate nucleus (LGN) is the thalamic relay station that carries retinal input to primary visual cortex. Two variants of monocular deprivation have qualitatively different outcomes. Monocular lid closure (called MC or MD in the source paper) produces a rapid loss of deprived-eye cortical responses, whereas monocular retinal inactivation (MI), produced by injecting tetrodotoxin (TTX, a sodium-channel blocker that silences retinal spiking) into the eye, produces a much smaller ocular-dominance shift (Rittenhouse et al., 1999; Frenkel and Bear, 2004).

Two classes of synaptic plasticity rules make different predictions about such deprivation experiments. BCM (Bienenstock-Cooper-Munro) rules modify each synapse according to a modification function of the postsynaptic output that has a sliding threshold, so that the loss of deprived-eye weights during deprivation is homosynaptic: it depends on the deprived input itself, through the covariance of deprived-eye inputs. Hebbian rules related to principal component analysis (for example the Oja rule, which normalizes Hebbian growth and converges to the leading eigenvector of the input covariance) redistribute weight between synapses heterosynaptically, so deprived-eye weight loss is driven by competition with the open eye rather than by the deprived-eye input statistics alone.

The classical BCM account of MC-versus-MI assumed that retinal inactivation reduces the LGN 'noise' that reaches cortex, slowing the homosynaptic decay. Linden et al. (2009) tested this premise by recording from the dorsal LGN of awake mice during normal vision, eyelid suture, and TTX inactivation: mean firing rates were not reduced by either deprivation protocol, but lid suture decorrelated adjacent relay neurons whereas retinal inactivation made them more correlated. Earlier work in developing ferret LGN (Weliky and Katz, 1999; Ohshiro and Weliky, 2006) had likewise found that spontaneous correlations between nearby LGN neurons persist without retinal input and fall off with receptive-field separation.

Blais, Cooper and Shouval (2009) incorporated these findings. Writing the deprived-eye rate vector as having variance ⟨n2⟩\langle n^2\rangle per input and correlation matrix Q\mathbf{Q} (an N×NN\times N matrix, for NN deprived-eye inputs, with diagonal 1 and off-diagonal structure set by a rate-based correlation parameter qq), the linearized BCM dynamics for the deprived-eye synaptic weights w\mathbf{w} are w˙=−ϵ⟨n2⟩Qw\dot{\mathbf{w}}=-\epsilon\langle n^2\rangle \mathbf{Q}\mathbf{w}, with ϵ\epsilon a small learning-rate parameter, so weight components decay with time constants (ϵ⟨n2⟩λi)−1(\epsilon\langle n^2\rangle\lambda_i)^{-1} where λi\lambda_i are the eigenvalues of Q\mathbf{Q}. For a constant partial correlation Q=(1−q)I+qJ\mathbf{Q}=(1-q)\mathbf{I}+q\mathbf{J} (with J\mathbf{J} the all-ones matrix), the dc (uniform) eigenvector, the component carrying equal weight on every deprived-eye input, has eigenvalue 1+(N−1)q1+(N-1)q, but the response-relevant, selective weight components (those orthogonal to the uniform component, which encode the neuron's input selectivity) decay with time constant [ϵ⟨n2⟩(1−q)]−1[\epsilon\langle n^2\rangle(1-q)]^{-1}: high correlations (the paper uses q≈0.8q\approx0.8 to reproduce the observed MI time course) slow the deprivation-induced loss by roughly a factor of five relative to uncorrelated noise, and total correlation produces no loss at all. In contrast, for PCA/Oja-type rules the deprivation time course is governed by the difference between the open-eye (natural-image) leading eigenvalue and the deprived-eye noise eigenvalue, is nearly independent of qq, and depends on noise variance in the opposite direction to BCM. The paper also analyzed random perturbations of Q\mathbf{Q} using random-matrix constructions: Wigner matrices (large random symmetric matrices whose eigenvalues follow the semicircle law) and Wishart matrices (covariance matrices of Gaussian samples), for which the eigenvalue distribution is cut off at λ<2−2q\lambda<2-2q before the matrix loses positive semidefiniteness; the results were insensitive to such perturbations.

A quantitative gap remains at the center of this account. The correlations it requires are rate-based: qq measures the correlation of the firing rates of LGN neurons, the quantities that enter rate-based plasticity models. The correlations that Linden et al. measured are spike-based cross-correlations between spike trains, which came out near 0.1. The two measures are not the same: the paper's appendix analyzes one simple doubly stochastic case (memoryless switching of correlated rates) in which a rate-based q=0.8q=0.8 with 20 Hz mean and 10 Hz standard deviation yields a spike-based correlation of only about 0.018. Whether real deprived-eye LGN correlations during retinal inactivation are large enough in the rate-based sense to produce the BCM stabilization, how the two correlation measures quantitatively correspond across firing regimes and measurement timescales, and how the rate of fall-off of response from the deprived eye in MI depends on the correlation level, discriminating the two rule classes in vivo — all of these remain to be established.

Problem Statement

Establish how deprived-eye lateral geniculate nucleus (LGN) firing-rate correlations at unchanged mean rates gate ocular-dominance plasticity, and thereby determine which class of synaptic plasticity rule operates in vivo during monocular deprivation. The problem is distilled from the distinct open issues posed by Blais, Cooper and Shouval (2009): the paper explicitly poses the experimental determination of the magnitude of deprived-eye LGN rate-based correlations during monocular inactivation ('It remains to be determined experimentally how great this correlation is'), the quantitative correspondence between rate-based and spike-based correlation measures ('this comparison requires more research'), and the test of the correlation dependence of the rate of fall-off of response from the deprived eye in MI, framed as 'a more detailed check of theoretical predictions':

  1. Measurement. Quantitatively establish, in awake animals during monocular retinal inactivation (MI), the magnitude and spectral structure of rate-based correlations among deprived-eye LGN relay neurons — specifically, measure rate-covariance matrices Q\mathbf{Q} (not only short-timescale spike cross-correlations), whose normalized off-diagonal entries are the rate-based pairwise correlations between relay neurons (the source's uniform model uses a single parameter qq) — and determine whether the rate-based correlation strengths required for the BCM spectral stabilization, near q≈0.8q\approx0.8 in the rate model, actually occur in vivo.

  2. Correspondence. Develop and experimentally validate the quantitative mapping between the rate-based correlation parameters used in plasticity models and the spike-based cross-correlation metrics commonly reported in neurophysiology, beyond the single doubly stochastic case (spikes drawn from stochastically switching correlated firing rates) analyzed in the source's appendix, across realistic LGN firing regimes and measurement timescales (binning choices).

  3. Correlation-dependence test. Test the correlation dependence of the rate of fall-off of response from the deprived eye in MI, as suggested by the source as a more detailed check of its theoretical predictions, with the rate-based correlation parameter qq distinguished from the noise variance ⟨n2⟩\langle n^2\rangle as separately controlled quantities, as in the source's own parametrization. BCM-like homosynaptic rules predict a correlation-dependent slowing of the deprived-eye loss (time constant scaling as (1−q)−1(1-q)^{-1}, with no loss at total correlation), whereas PCA/Oja-like heterosynaptic rules predict near-independence from qq with the opposite dependence on noise variance; the measured dependence discriminates the rule classes.

The common objective uniting these open issues is a mechanistic decision: whether deprivation-induced loss of deprived-eye cortical responses is gated by the correlation structure of thalamic input (homosynaptic, BCM-like) or by competition with open-eye input (heterosynaptic, Hebbian/PCA-like).

The three sub-questions are jointly posed. The correspondence mapping of (2) quantifies how the rate-based correlations the theory requires relate to the spike-based quantities that are measured, and the mechanistic decision that defines the objective is addressed by the in-vivo determination of the deprived-eye rate-covariance structure (1) together with the correlation-dependence test of the deprived-eye response fall-off (3).

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