The governing learning rule in cultured neural networks.

<p>The rule was determined from (A) learning efficacies, (B) the Bayesian information criterion (BIC), and (C) model predictions of connectivity changes, and summarized in (D). <b>(A)</b> The expectation of learning efficacy estimated from connection strengths under the assumption that synaptic plasticity in cultured neural networks obeys either a Hebbian (<i>μ</i>^<i>α</i>; left) or state-dependent Hebbian (<i>μ</i>^<i>β</i>1, <i>μ</i>^<i>β</i>2; right) rule. <i>μ</i>^<i>β</i>2 was correlated with <i>μ</i>^<i>β</i>1 (*, <i>p</i> = 0.037; <i>n</i> = 23 cultures, Spearman test) and their ratio was 27.1%. <b>(B)</b> The BIC of the <i>α</i>- and <i>β</i>-models. BIC of the <i>β</i>-model was significantly smaller than that of the <i>α</i>-model (****, <i>p</i> < 10⁻⁶; <i>n</i> = 23 cultures). <b>(C)</b> Measured changes in connection strengths and those estimated from Hebbian and state-dependent Hebbian plasticity rules. Black bars are the mean ± S.E.M of the change (trial 100 –trial 1) in <i>W</i>₁₁ and <i>W</i>₂₂ (<i>n</i> = 46 from 23 cultures), which increased in all cases (****, <i>p</i> < 10⁻⁵). White bars are the mean ± S.E.M of the change in <i>W</i>₁₂ and <i>W</i>₂₁ (<i>n</i> = 46 from 23 cultures). <i>W</i>₁₂ and <i>W</i>₂₁ tended to decrease after training when calculated from response data (left; <i>p</i> = 0.069). <i>W</i>₁₂ and <i>W</i>₂₁ estimated from the <i>α</i>-model significantly increased (center; ****, <i>p</i> < 10⁻⁴). <i>W</i>₁₂ and <i>W</i>₂₁ estimated from the <i>β</i>-model significantly decreased (right; *, <i>p</i> = 0.023), in agreement with the experimentally determined results. <b>(D)</b> Suggested learning rule, which is based on state-dependent Hebbian plasticity, and leads to blind source separation. Synaptic plasticity in cultured neural networks almost followed a strict Hebbian rule. However, experimental data indicate that learning efficacy was not the same for each input state. Substantial Hebbian plasticity occurred when <b>u</b> = (1,0) or <b>u</b> = (0,1), while limited or anti-Hebbian plasticity occurred when <b>u</b> = (1,1). From the estimated efficacies <i>μ</i>^<i>β</i>1 and <i>μ</i>^<i>β</i>2, the efficacy of <b>u</b> = (1,1) was apparently only 27% of that of <b>u</b> = (1,0) or (0,1).