Local intracortical circuitry not only for feature binding but also for rapid neuronal responses

Abstract

Neurons of primary sensory cortices are known to have specific responsiveness to elemental features. To express more complex sensory attributes that are embedded in objects or events, the brain must integrate them. This is referred to as feature binding and is reflected in correlated neuronal activity. We investigated how local intracortical circuitry modulates ongoing-spontaneous neuronal activity, which would have a great impact on the processing of subsequent combinatorial input, namely, on the correlating (binding) of relevant features. We simulated a functional, minimal neural network model of primary visual cortex, in which lateral excitatory connections were made in a diffusive manner between cell assemblies that function as orientation columns. A pair of bars oriented at specific angles, expressing a visual corner, was applied to the network. The local intracortical circuitry contributed not only to inducing correlated neuronal activation and thus to binding the paired features but also to making membrane potentials oscillate at firing-subthreshold during an ongoing-spontaneous time period. This led to accelerating the reaction speed of principal cells to the input. If the lateral excitatory connections were selectively (instead of “diffusively”) made, hyperpolarization in ongoing membrane potential occurred and thus the reaction speed was decelerated. We suggest that the local intracortical circuitry with diffusive connections between cell assemblies might endow the network with an ongoing subthreshold neuronal state, by which it can send the information about combinations of elemental features rapidly to higher cortical stages for their full and precise analyses.

Appendix

Description of the network

Dynamic evolution of the membrane potential of the ith P cell that belongs to cell assembly θ _n is defined by

$$ \begin{aligned} c_m^{P} {\frac{du_{i}^{P}(\theta_n;t)}{dt}} &= -g_m^{P}(u_{i}^{P}(\theta_n;t)-u_{rest}^{P}) + I_{i,rec}^P(\theta_n;t) + I_{i,fed}^P(\theta_n;t) + I_{i,lat}^P(\theta_n;t)\\ &\quad+ \tilde{I}_{i,lat}^P(\theta_n;t) + I_{LGN}(\theta_n;\theta_{inp}), &(1) \cr \end{aligned} $$

(1)

where $I_{i,rec}^P(\theta_n;t)$ is a recurrent excitatory current, $I_{i,fed}^P(\theta_n;t)$ a feedback inhibitory current, $I_{i,lat}^P(\theta_n;t)$ a lateral inhibitory current, $\tilde{I}_{i,lat}^P(\theta_n;t)$ a lateral excitatory current, and I _LGN (θ _n ;θ _inp ) an excitatory input current triggered by a feature stimulus (θ _inp ), where θ _inp  ∈ {θ₀, θ₁, θ₂, θ₃, θ₄, θ₅, θ₆, θ₇}. These currents are defined by

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

(2)

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

(3)

$$ I_{i,lat}^P(\theta_n;t) = -\hat{g}_{GABA}(u_i^{P}(\theta_n;t) - u_{rev}^{GABA}) \sum_{j=1}^{N}w_{ij,lat}^P(\theta_n)r_{j}^{L}(\theta_n;t), $$

(4)

$$ \tilde{I}_{i,lat}^P(\theta_n;t) = -\hat{g}_{AMPA}(u_i^P(\theta_n;t) - u_{rev}^{AMPA}) \times\sum_{n'=0 (n' \ne n)}^{7} \sum_{j=1}^{N} \tilde{w}_{ij,lat}^P(\theta_n, \theta_{n'})r_j^{P}(\theta_{n'};t), $$

(5)

$$ I_{LGN}(\theta_n;\theta_{inp}) = \alpha_P e^{-({\frac{n-inp} {\tau_P}})^2}. $$

(6)

Dynamic evolution of the membrane potentials of the ith F cell is defined by

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

(7)

where $I_i^F(\theta_n;t)$ is an excitatory current, and defined by

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

(8)

Dynamic evolution of the membrane potential of the ith L cell is defined by

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

(9)

where $I_i^L(\theta_n;t)$ is an excitatory current and defined by

$$ I_i^L(\theta_n;t) = -\hat{g}_{AMPA}(u_i^L(\theta_n;t) - u_{rev}^{AMPA}) \times\sum_{n'=0 (n' \ne n)}^7 w_i^L(\theta_n, \theta_{n'})r_i^{P}(\theta_{n'};t), $$

(10)

$$ w_i^L(\theta_n,\theta_{n'}) = w_L e^{-({\frac{n-n'} {\tau_{lat}}})^2}. $$

(11)

In these equations, $c_m^Y$ is the membrane capacitance of Y (Y = P, F, L) cell, $u_i^{Y}(\theta_n;t)$ the membrane potential of the ith Y cell at time $t, g_m^Y$ the membrane conductance of Y cell, and $u_{rest}^{Y}$ the resting potential. $\hat{g}_{Z}$ and $u_{rev}^{Z}$ (Z = AMPA or GABA) are, respectively, the maximal conductance and the reversal potential for the current regulated by Z-type receptor. N is the number of cell units constituting each cell assembly. $w_{ij,rec}^{P}(\theta_n)$ is the recurrent excitatory synaptic strength from the jth to ith P cell within cell assembly θ _n . w ^P_i,fed (θ _n ) is the feedback inhibitory synaptic strength from F to P cell within cell unit i. $w_{ij,lat}^P(\theta_n)$ is the inhibitory synaptic strength from the jth L to ith P cell. $\tilde{w}_{ij,lat}^P(\theta_n, \theta_{n'})$ is the excitatory synaptic strength between different cell assemblies θ _n , and θ _n (n′≠n). $w_i^F(\theta_n)$ is the excitatory synaptic strength from P to F cell within cell unit i. $w_i^L(\theta_n, \theta_{n'})$ is the excitatory synaptic strength from the ith P cell belonging to a different cell assembly (θ _n ), to the ith L cell belonging to the cell assembly θ _n , which weakens as the functional distance between cell assemblies increases (see Eq. 11; n and n′). Note that a periodic boundary condition was given,...,θ₋₂ = θ₆, θ₋₁ = θ₇, θ₀ = θ₈, θ₁ = θ₉, θ₂ = θ₁₀,....

Receptor dynamics and parameter settings

We employed the receptor dynamics proposed by Destexhe et al. (1998). $r_j^P (\theta_n;t)$ (see Eq. 2) is the fraction of AMPA-receptors in the open state induced by presynaptic action potentials of the jth P cell belonging to cell assembly θ _n at time t. $r_j^F(\theta_n;t)$ and $r_j^L(\theta_n;t)$ (see Eqs. 3 and 4) are the fractions of GABAa-receptors in the open state induced by presynaptic action potentials of the jth F cell and L cell, respectively. The dynamics is described as

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

(12)

$$ \begin{aligned} {\frac{dr_j^Y(\theta_n;t)}{dt}} &= \alpha_{GABA}[GABA]_j^Y(\theta_n;t)(1-r_j^Y(\theta_n;t))\\ &\quad- \beta_{GABA} r_j^Y(\theta_n;t), (Y = F, L) \end{aligned} $$

(13)

where α _z and β _z (z = AMPA or GABA) are positive constants. $[Glut]_j^P(\theta_n;t)$ and $[GABA]_j^Y(\theta_n;t)$ are the concentrations of glutamate and GABA in the synaptic cleft, respectively. $[Glut]_j^P(\theta_n;t)$ = $Glut_{max}^P$ and $[GABA]_j^Y(\theta_n;t)$ = $GABA_{max}^Y$ for 1 ms when the presynaptic jth P cell and Y cell fire, respectively. Otherwise, $[Glut]_j^P(\theta_n;t)$ = 0 and $[GABA]_j^Y(\theta_n;t)$ = 0.

Probability of firing of the jth Y cell belonging to cell assembly θ _n is defined by

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

(14)

where η _Y and ζ _Y are, respectively, the steepness and the threshold of the sigmoid function. When a cell fires, its membrane potential is depolarized to −10 mV, which is kept for 1 ms, and then reset to the resting potential.

Unless stated otherwise, $c_m^P =0.5\,\hbox{nF}, c_m^F =0.2\,\hbox{nF}, c_m^L =0.6\,\hbox{nF}, g_m^P =25\,\hbox{nS}, g_m^F =20\,\hbox{nS}, g_m^L =15\,\hbox{nS}, u_{rest}^P =-65\,\hbox{mV}, u_{rest}^F =u_{rest}^L =-70\,\hbox{mV}, \hat{g}_{AMPA} =0.5\,\hbox{nS}, \hat{g}_{GABA} =0.7\,\hbox{nS}, u_{rev}^{AMPA} =0\,\hbox{mV}, u_{rev}^{GABA} =-80\,\hbox{mV, N} =20, w_{ij,rec}^P(\theta_n) =6.0, w_{i,fed}^P(\theta_n) =20.0, w_{ij,lat}^P(\theta_n) =10.0, \tilde{w}_{ij,lat}^P(\theta_n , \theta_{n'}) =0.2 (n {\ne}n'), w_i^F(\theta_n) =30.0, w_L =0.5, {\alpha_P}=1.0 {\times}10^{-10}, {\tau_P}=1.0, \tau_{lat} =5.0, \alpha_{AMPA} =1.1 {\times}10^6, \alpha_{GABA} =5.0 {\times}10^5, \beta_{AMPA} =190.0, \beta_{GABA} =180.0, Glut_{max}^P = GABA_{max}^F =GABA_{max}^L =1.0\,\hbox{mM}, {\eta_P}=220, {\eta_F}= {\eta_L}=180.0, {\zeta_P}=-36\,\hbox{mV}$ and ζ _F = ζ _L = −38 mV. For these parameter values, see references (Hoshino 2008a, b).