Dynamic modulation of an orientation preference map by GABA responsible for age-related cognitive performance

Abstract

Accumulating evidence suggests that cognitive declines in old (healthy) animals could arise from depression of intracortical inhibition, for which a decreased ability to produce GABA during senescence might be responsible. By simulating a neural network model of a primary visual cortical (V1) area, we investigated whether and how a lack of GABA affects cognitive performance of the network: detection of the orientation of a visual bar-stimulus. The network was composed of pyramidal (P) cells and GABAergic interneurons such as small (S) and large (L) basket cells. Intrasynaptic GABA-release from presynaptic S or L cells contributed to reducing ongoing-spontaneous (background) neuronal activity in a different manner. Namely, the former exerted feedback (S-to-P) inhibition and reduced the frequency (firing rate) of action potentials evoked in P cells. The latter reduced the number of saliently firing P cells through lateral (L-to-P) inhibition. Non-vesicular GABA-release, presumably from glia and/or neurons, into the extracellular space reduced the both, activating extrasynaptic GABAa receptors and providing P cells with tonic inhibitory currents. By this combinatorial, spatiotemporal inhibitory mechanism, the background activity as noise was significantly reduced, compared to the stimulus-evoked activity as signal, thereby improving signal-to-noise (S/N) ratio. Interestingly, GABA-spillover from the intrasynaptic cleft into the extracellular space was effective for improving orientation selectivity (orientation bias), especially when distractors interfered with detecting the bar-stimulus. These simulation results may provide some insight into how the depression of intracortical inhibition due to a reduction in GABA content in the brain leads to age-related cognitive decline.

Appendix

The neural network model

Dynamic evolution of the membrane potential of the ith pyramidal (P) cell that belongs to orientation column θ is defined by

$$ \begin{aligned} c_m^{P} \frac{du_{i}^{P}(\theta;t)}{dt} &= -g_m^{P}(u_{i}^{P}(\theta;t)-u_{\rm rest}^{P}) + I_{i,{\rm rec}}^{\rm ex}(\theta;t) + I_{i,{\rm fed}}^{ih}(\theta;t) + I_{i,{\rm lat}}^{ih}(\theta;t) + I_{\rm ext}^{ih}(t) \\ & + I_{\rm LGN}(\theta), \\ \end{aligned} $$

(1)

where I ^ex _i,rec (θ; t) is a recurrent excitatory postsynaptic current within orientation columns, I ^ih _i,fed (θ; t) a feedback inhibitory postsynaptic current, I ^ih _i,lat (θ; t) a lateral inhibitory postsynaptic current, I ^ih_ext (t) an inhibitory non-postsynaptic current caused by GABA-spillover from synaptic clefts and non-vesicular GABA-release into the extracellular space, and I _LGN(θ) an excitatory input current triggered by an oriented bar-stimulus (θ_inp). These currents are defined by

$$ I_{i,{\rm rec}}^{\rm ex}(\theta;t) = -\hat{g}_{\rm AMPA}(u_i^{P}(\theta;t) - u_{rev}^{\rm AMPA}) \sum_{j=1}^{N_\theta}w_{ij,{\rm rec}}^{\rm ex}(\theta)r_{j}^{P}(\theta;t), $$

(2)

$$ I_{i,{\rm fed}}^{ih}(\theta;t) = -\hat{g}_{\rm GABA}(u_i^{P}(\theta;t) - u_{\rm rev}^{\rm GABA})w_{i,{\rm fed}}^{ih}(\theta)r_{i}^{S}(\theta;t), $$

(3)

$$ I_{i,{\rm lat}}^{ih}(\theta;t) = -\hat{g}_{\rm GABA}(u_i^{P}(\theta;t) - u_{\rm rev}^{\rm GABA}) \sum_{\theta'=0(\theta' \ne \theta)}^{7\pi/8}\sum_{j=1}^{N_\theta}w_{ij,{\rm lat}}^{ih}(\theta,\theta') r_{j}^{L}(\theta';t), $$

(4)

$$ I_{\rm ext}^{ih}(t) = -\hat{g}_{\rm GABA}(u_i^{P}(\theta;t) - u_{rev}^{\rm GABA}) \delta r_{\rm ext}^{\rm GABA}(t), $$

(5)

$$ I_{\rm LGN}(\theta) = c_0 \times \{c_1 + cos [2(\theta-\theta_{\rm inp})]\}. $$

(6)

Dynamic evolution of the membrane potentials of small basket (S) cells and large basket (L) cells is defined by

$$ c_m^{S} \frac{du_{i}^{S}(\theta;t)}{dt} = -g_m^{S}(u_{i}^{S}(\theta;t)-u_{\rm rest}^{S}) + I_i^{S}(\theta;t), $$

(7)

$$ c_m^{L} \frac{du_{i}^{L}(\theta;t)}{dt} = -g_m^{L}(u_{i}^{L}(\theta;t)-u_{\rm rest}^{L}) + I_i^{L}(\theta;t), $$

(8)

where I ^S _i (θ; t) and I ^L _i (θ; t) are excitatory postsynaptic currents and defined by

$$ I_i^{S}(\theta;t) = -\hat{g}_{\rm AMPA}(u_i^{S}(\theta;t) - u_{rev}^{\rm AMPA})w_i^{S}(\theta)r_{i}^{P}(\theta;t), $$

(9)

$$ I_i^{L}(\theta;t) = -\hat{g}_{\rm AMPA}(u_i^{L}(\theta;t) - u_{\rm rev}^{\rm AMPA})w_i^{L}(\theta)r_{i}^{P}(\theta;t). $$

(10)

In these equations, c ^Y _m is the membrane capacitance of Y (Y = P, S, L) cell, u ^Y _i (θ; t) the membrane potential of the ith Y cell of θ column at time t, g ^Y _m the membrane conductance of Y cell, and u ^Y_rest the resting potential. $\hat{g}_{Z}$ and u ^Z_rev (Z = AMPA or GABA) are, respectively, the maximal conductance and the reversal potential for the current mediated through Z-type receptor. N _θ is the number of cell units constituting each orientation column. w ^ex _ij,rec (θ) and w ^ih _i,fed (θ) are, respectively, the excitatory synaptic strength from the jth to the ith P cell and the inhibitory synaptic strength from S-to-P cell of unit i within columns. w ^ih _ij,lat (θ, θ′) is the inhibitory synaptic strength from the jth L cell of θ′ column to the ith P cell of θ column (θ′ ≠ θ). w ^S _i (θ) and w ^L _i (θ) are, respectively, the excitatory synaptic strengths from P to S cell and to L cell within unit i. θ_inp in Eq. 6 denotes the orientation (angle) of an input stimulus (a bar).

r ^P _j (θ; t) is the fraction of AMPA-receptors in the open state induced by a presynaptic action potential of the jth P cell belonging to θ column, and r ^Y _j (θ; t) is that of GABAa receptors induced by the jth presynaptic S cell (Y = S) or by the jth presynaptic L cell (Y = L). r ^GABA_ext (t) is the fraction of GABAa receptors in the open state, which are located on extrasynaptic membrane regions of P cells. δ denotes a relative amount of extrasynaptic GABAa receptors. Dynamics of these receptors are described by Destexhe et al. (1998)

$$ \frac{dr_j^{P}(\theta;t)}{dt} = \alpha_{\rm AMPA}[{\rm Glut}]_j^{P}(\theta;t)(1-r_j^{P}(\theta;t)) - \beta_{\rm AMPA} r_j^{P}(\theta;t), $$

(11)

$$ \frac{dr_j^K(\theta;t)}{dt} = \alpha_{\rm GABA}[{\rm GABA}]_j^K(\theta;t)(1-r_j^K(\theta;t)) - \beta_{\rm GABA} r_j^K(\theta;t),\quad (K = S, L) $$

(12)

$$ \frac{dr_{ext}^{\rm GABA}(t)}{dt} = \alpha_{\rm GABA}[{\rm GABA}]_{\rm ext}(t)(1-r_{\rm ext}^{\rm GABA}(t)) - \beta_{\rm GABA} r_{\rm ext}^{\rm GABA}(t), $$

(13)

where α _z and β _z (z = AMPA or GABA) are positive constants. [T] ^Y _j (θ; t) (T = Glut or GABA) is the concentration of glutamate or GABA in the synaptic cleft. [T] ^Y _j (θ; t) = T _Y for 1 ms when the jth presynaptic Y cell fires, and 0 otherwise. [GABA]_ext(t) is ambient (extrasynaptic) GABA concentration and defined by

$$ \begin{aligned} \frac{d[{\rm GABA}]_{\rm ext}(t)}{dt} &= \frac{1}{\tau_{\rm ext}}([{\rm GABA}]_{\rm ext}(t)- [{\rm GABA}]_0) \\ & + \sum_{\theta^{\prime}=0}^{7\pi/8}\sum_{j=1}^{N_\theta} \int_{-\infty}^tC_{\rm ext}e^{\frac{-(t-t^{\prime})}{\tau_{\rm dec}}}\{[{\rm GABA}]_j^{S} (\theta^{\prime};t^{\prime})+ [{\rm GABA}]_j^{L}(\theta^{\prime};t^{\prime})\}dt^{\prime}, \\ \end{aligned} $$

(14)

where τ_ext is a time constant for ambient GABA concentration, and [GABA]₀ is a basal (resting GABA) concentration determined by non-vesicular GABA-release. The second term (on the right-hand side of Eq. 14) describes a relative amount of GABA-spillover from the synaptic clefts of presynaptic S and L cells. C _ext is a positive constant, and τ_dec determines a degree of contribution of previously released 1 ms pulses of GABA _K (K = S, L). We assume that GABA molecules diffuse rapidly across the network.

Probability of firing of the jth Y cell belonging to θ column is defied by

$$ Prob[Y_j(\theta;t); {\rm firing}] = { \frac{1} {1+e^{-\eta_Y(u_j^Y(\theta;t)-\zeta_Y)}}}, $$

(15)

where η _Y and $\zeta_Y$ are, respectively, the steepness and the threshold of the sigmoid function. After firing, the membrane potential is reset to the resting potential.

Unless otherwise stated, c ^P _m = 0.5 nF, c ^S _m = 0.2 nF, c ^L _m = 0.5 nF, g ^P _m = 25 nS, g ^S _m = 20 nS, g ^L _m = 25 nS, u ^P_rest = −65 mV, and u ^S_rest = u ^L_rest = −70 mV (Koch 1999; McCormick et al. 1985; Kawaguchi and Shindou 1998). $\hat{g}_{\rm AMPA}$ = 0.5 nS, $\hat{g}_{\rm GABA}$ = 0.7 nS, u ^AMPA_rev = 0 mV, and u ^GABA_rev = −80 mV. Each orientation column consists of ten cell units: N _θ = 10. w ^ex _ij,rec (θ) = 5.0, w ^ih _i,fed (θ) = w ^ih _ij,lat (θ, θ′) = 1.0, w ^S _i (θ) = w ^L _i (θ) = 10.0. δ = 1000.0, c ₀ = 5.0 × 10⁻¹⁰, c ₁ = 1.0. α_AMPA = 1.1 × 10⁶, α_GABA = 5.0 × 10⁵, β_AMPA = 190.0, β_GABA = 180.0, Glut _P = GABA _S = GABA _L = 1.0 mM, τ_ext = 1.0, [GABA]₀ = 1 μM, C _ext = 0.2, τ_dec = 10.0, η _P = η _S = η _L = 350.0, and $\zeta_{P}$ = $\zeta_{S}$ = $\zeta_{L}$ = −50  mV. For these values, see our previous studies (Hoshino 2006, 2008a, b, 2009, 2010, 2011a, b).