A computational model of rapid task-related plasticity of auditory cortical receptive fields

Abstract

Receptive field properties of neurons in A1 can rapidly adapt their shapes during task performance in accord with specific task demands and salient sensory cues (Fritz et al., Hearing Research, 206:159–176, 2005a, Nature Neuroscience, 6: 1216–1223, 2003). Such modulatory changes selectively enhance overall cortical responsiveness to target (foreground) sounds and thus increase the likelihood of detection against the background of reference sounds. In this study, we develop a mathematical model to describe how enhancing discrimination between two arbitrary classes of sounds can lead to the observed receptive field changes in a variety of spectral and temporal discrimination tasks. Cortical receptive fields are modeled as filters that change their spectro-temporal tuning properties so as to respond best to the discriminatory acoustic features between foreground and background stimuli. We also illustrate how biologically plausible constraints on the spectro-temporal tuning of the receptive fields can be used to optimize the plasticity. Results of the model simulations are compared to published data from a variety of experimental paradigms.

Appendix I

Derivation of Eq. (1)

$$ d = \int\limits_{t_1}^{t_2} {\left( {{r_1}(t) - {r_2}(t)} \right)\,} dt = \int\limits_{t_1}^{t_2} {\left( {{r_1}{{(t)}^2} + {r_2}{{(t)}^2} - 2{r_1}(t){r_2}(t)} \right)} \,dt $$

(4)

Expanding the first term:

$$ \begin{array}{*{20}{c}} {\int\limits_{t_1}^{t_2} {{r_1}{{(t)}^2} = \int\limits_{t_1}^{t_2} {\sum\limits_f {\sum\limits_k {\int\limits_\tau {\int\limits_\alpha {h\left( {\tau, f} \right){s_1}\left( {t - \tau, f} \right)h\left( {\alpha, k} \right){s_1}\left( {t - \alpha, k} \right)\,\,d\tau \,\,} } d\alpha \,\,} } dt} } } \\ { = \sum\limits_f {\sum\limits_k {\int\limits_\tau {\int\limits_\alpha {h\left( {\tau, f} \right)h\left( {\alpha, k} \right)\,d\tau \,d\alpha \,\int\limits_t {{s_1}\left( {t - \tau, f} \right){s_1}\left( {t - \alpha, k} \right)} \,dt} } } } } \\ { = \sum\limits_f {\sum\limits_k {\int\limits_\tau {\int\limits_\alpha {h\left( {\tau, f} \right)h\left( {\alpha, k} \right){c_{1,1}}\left( {\tau - \alpha, f,k} \right)\,d\tau \,d\alpha } } } } } \\ { = \sum\limits_f {\sum\limits_k {H(f){C_1}\left( {f,k} \right)H(k)} } } \\ \end{array} $$

(5)

Where H and C ₁ are defined as:

$$ \begin{gathered} H(f) = \left[ {h\left( {0,f} \right)h\left( {1,f} \right)...h\left( {n,f} \right)} \right] \hfill \\ {C_{1,1}}(f,k) = \left[ {\begin{array}{*{20}{c}} {{c_{1,1}}(0,f,k)} & {{c_{1,1}}(1,f,k)} & \cdots & {{c_{1,1}}(n,f,k)} \\ {{c_{1,1}}( - 1,f,k)} & {{c_{1,1}}(0,f,k)} & \cdots & {{c_{1,1}}(n - 1,f,k)} \\ \vdots & \vdots & {} & \vdots \\ {{c_{1,1}}( - n,f,k)} & {{c_{1,1}}( - n + 1,f,k)} & \cdots & {{c_{1,1}}(0,f,k)} \\ \end{array} } \right] \hfill \\ \end{gathered} $$

But the Eq. (5) is a quadratic form itself:

$$ \sum\limits_f {\sum\limits_k {H(f){C_{1,1}}\left( {f,k} \right)H(k)} } = \Pi \,{\Omega_{1,1}}\,{\Pi^T} $$

Expanding the other two terms of Eq. (4) in the same way, d can be written as:

$$ \begin{array}{*{20}{c}} {d = \Pi \,\,\left( {{\Omega_{1,1}} + {\Omega_{2,2}} - 2{\Omega_{1,2}}} \right)\,\,{\Pi^T}} \\ { = \Pi \,\Omega \,{\Pi^T}} \\ \end{array} $$