Computational model of excitatory/inhibitory ratio imbalance role in attention deficit disorders

Abstract

Impairments in attentional behaviors, including over-selectivity, under-selectivity, distractibility and difficulty in shift of attention, are widely reported in several developmental disorders, including autism. Uncharacteristic inhibitory to excitatory neuronal number ratio (IER) and abnormal synaptic strength levels in the brain are two broadly accepted neurobiological disorders observed in autistic individuals. These neurobiological findings are contrasting and their relation to the atypical attentional behaviors is not clear yet. In this paper, we take a computational approach to investigate the relation of imbalanced IER and abnormal synaptic strength to some well-documented spectrum of attentional impairments. The computational model is based on a modified version of a biologically plausible neural model of two competing minicolumns in IT cortex augmented with a simple model of top-down attention. Top-down attention is assumed to amplify (attenuates) attended (unattended) stimulus. The inhibitory synaptic strength parameter in the model is set such that typical attentional behavior is emerged. Then, according to related findings, the parameter is changed and the model’s attentional behavior is considered. The simulation results show that, without any change in top-down attention, the abnormal inhibitory synaptic strength values – and IER imbalance- result in over-selectivity, under-selectivity, distractibility and difficulty in shift of attention in the model. It suggests that the modeled neurobiological abnormalities can be accounted for the attentional deficits. In addition, the atypical attentional behaviors do not necessarily point to impairments in top-down attention. Our simulations suggest that limited changes in the inhibitory synaptic strength and variations in top-down attention signal affect the model’s attentional behaviors in the same way. So, limited deficits in the inhibitory strength may be alleviated by appropriate change in top-down attention biasing. Nevertheless, our model proposes that this compensation is not possible for very high and very low values of the inhibitory strength.

Appendix

In this section, detailed equations and the parameters’ values in the simulations are given. For more information, refer to (Moldakarimov et al. 2005). In Eqs. (1) and (2), ${I_{{mem}}}\left( {V,n,h} \right)$ is the membrane current and is modeled by:

$$ {I_{{mem}}}\left( {V,n,h} \right) = {g_{_L}}.\left( {V - {V_L}} \right) + {g_{_K}}.{n^4}.\left( {V - {V_K}} \right) + {g_{{Na}}}.m_{\infty }^3.h.\left( {V - {V_{{Na}}}} \right) $$

where

$$ \begin{array}{*{20}{c}} {{m_{\infty }}(V) = {\alpha_m}(V)/\left[ {{\alpha_m}(V) + {\beta_m}(V)} \right]} \hfill \\ {{\alpha_m}(V) = 0.1.\left( {V + 30} \right)/\left( {1 - \exp \left[ { - 0.1.\left( {V + 30} \right)} \right]} \right),{\beta_m}(V) = 4.\exp \left. {\left[ { - \left( {V + 55} \right)/18} \right]} \right)} \hfill \\ {\frac{{{\text{d}}n}}{{{\text{d}}t}} = \psi .\left[ {{\alpha_n}(V).\left( {1 - n} \right) - {\beta_n}(V).n} \right]} \hfill \\ {{\alpha_n}(V) = 0.01.\left( {V + 34} \right)/\left( {1 - \exp \left[ { - 0.1.\left( {V + 34} \right)} \right]} \right),\left. {{\beta_n}(V) = 0.125.\exp \left[ { - \left( {V + 44} \right)/80} \right]} \right)} \hfill \\ {\frac{{{\text{d}}h}}{{{\text{d}}t}} = \psi \left[ {{\alpha_h}(V).\left( {1 - h} \right) - {\beta_h}(V).h} \right]} \hfill \\ {\left. {{\alpha_h}(V) = 0.07.\exp \left[ { - \left( {V + 44} \right)/20} \right]} \right),{\beta_h}(V) = 1/\left( {1 + \exp \left[ { - 0.01.\left( {V + 14} \right)} \right]} \right)} \hfill \\ \end{array} $$

With V _L  = −65, V _Na  = 55, V _K  = −80, V _Ca  = 120, g _L  = 0.05, g _Na  = 100, g _K  = 40, ψ = 3.

${I_{{AHP}}}\left( {{V_e},\left[ {Ca} \right]} \right)$, the calcium-dependent potassium adaptation current, obeys

$$ {I_{{AHP}}}\left( {{V_e},\left[ {Ca} \right]} \right) = {g_{{AHP}}}.\left[ {Ca} \right]/\left( {\left[ {Ca} \right] + 1} \right).\left( {{V_e} - {V_K}} \right) $$

where

$$ \frac{{{\text{d}}[Ca]}}{{{\text{d}}t}} = - 0.002.{g_{{Ca}}}({V_e} - {V_{{Ca}}})/(1 + \exp ( - ({V_e} + 25)/2.5)) - [Ca]/{\tau_{{AHP}}} $$

With g _Ca  = 0.975, τ _AHP  = 100, and g _AHP  = 0.25.

In Eqs. (3) and (4), the synaptic gating variables, s _e [k] and s _i [k], and the depression factors, ϕ _e [k] and ϕ _i [k], are given by:

$$ \matrix{{*{20}{c}} {\frac{{{\text{d}}{s_e}\left[ k \right]}}{{{\text{d}}t}} = \left( {A.\sigma \left( {{V_e}} \right).\left( {1 - {s_e}\left[ k \right]} \right) - {s_e}\left[ k \right]} \right)/{\tau_e}} \\ {\frac{{{\text{d}}{s_i}\left[ k \right]}}{{{\text{d}}t}} = \left( {A.\sigma \left( {{V_i}} \right).\left( {1 - {s_i}\left[ k \right]} \right) - {s_i}\left[ k \right]} \right)/{\tau_i}} \\ {\frac{{{\text{d}}{\phi_e}\left[ k \right]}}{{{\text{d}}t}} = \left( { - {f_e}.\sigma \left( {{V_e}} \right).{\phi_e}\left[ k \right] + \left( {1 - {\phi_e}\left[ k \right]} \right)} \right)/{\tau_{{ge}}}} \\ {\frac{{{\text{d}}{\phi_i}\left[ k \right]}}{{{\text{d}}t}} = \left( { - {f_i}.\sigma \left( {{V_i}} \right).{\phi_i}\left[ k \right] + \left( {1 - {\phi_i}\left[ k \right]} \right)} \right)/{\tau_{{gi}}}} \\ {\sigma (V) = 1/\left( {1 + \exp \left( { - \left( {V + 20} \right)/4} \right)} \right)} \\ } $$

where V _ei  = −80, V _ee  = 0, A = 20, τ _e  = 8, τ _i  = 10, τ _ge  = 1,000, τ _gi  = 800, J _ie  = 0.55, J _ee  = 0.01, f _e =0.02, and f _i =0.015. J _ei varies from 0 to 1. The exact value of J _ei is mentioned in the caption of each figure.