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Power-law input-output transfer functions explain the contrast-response and tuning properties of neurons in visual cortex.

Persi E, Hansel D, Nowak L, Barone P, van Vreeswijk C - PLoS Comput. Biol. (2011)

Bottom Line: We test these results with numerical simulations of a network of conductance-based model (CBM) neurons and we demonstrate that they are valid and more robust here than in the rate model.The results indicate that because of the acceleration in the transfer function, described here by a power-law, the orientation tuning curves of V1 neurons are more tuned, and their CRF is steeper than those of their inputs.Comparison with experimental data suggests that both sources contribute nearly equally to the diversity of CRF shapes observed in V1 neurons.

View Article: PubMed Central - PubMed

Affiliation: Laboratoire de Neurophysique et Physiologie, Université Paris Descartes, Paris, France.

ABSTRACT
We develop a unified model accounting simultaneously for the contrast invariance of the width of the orientation tuning curves (OT) and for the sigmoidal shape of the contrast response function (CRF) of neurons in the primary visual cortex (V1). We determine analytically the conditions for the structure of the afferent LGN and recurrent V1 inputs that lead to these properties for a hypercolumn composed of rate based neurons with a power-law transfer function. We investigate what are the relative contributions of single neuron and network properties in shaping the OT and the CRF. We test these results with numerical simulations of a network of conductance-based model (CBM) neurons and we demonstrate that they are valid and more robust here than in the rate model. The results indicate that because of the acceleration in the transfer function, described here by a power-law, the orientation tuning curves of V1 neurons are more tuned, and their CRF is steeper than those of their inputs. Last, we show that it is possible to account for the diversity in the measured CRFs by introducing heterogeneities either in single neuron properties or in the input to the neurons. We show how correlations among the parameters that characterize the CRF depend on these sources of heterogeneities. Comparison with experimental data suggests that both sources contribute nearly equally to the diversity of CRF shapes observed in V1 neurons.

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Distribution of CRFs induced by heterogeneous neuron properties.Examples of CRFs for (A) excitatory and (B) inhibitory neurons. Dotted lines: Population averaged CRF. Distribution histograms of the the H-ratio parameters ,  and  are shown for excitatory neurons in C, D and E respectively (all the neurons are included). Bottom: pair-wise scatter plot of these parameters,  vs.  (F),  vs.  (G) and  vs.  (H). Dots in the scatter plot show all neurons, and circles show neurons with a good fit (N = 368). The correlation coefficient between  and  is . The other two correlations are not statistically significant.
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pcbi-1001078-g010: Distribution of CRFs induced by heterogeneous neuron properties.Examples of CRFs for (A) excitatory and (B) inhibitory neurons. Dotted lines: Population averaged CRF. Distribution histograms of the the H-ratio parameters , and are shown for excitatory neurons in C, D and E respectively (all the neurons are included). Bottom: pair-wise scatter plot of these parameters, vs. (F), vs. (G) and vs. (H). Dots in the scatter plot show all neurons, and circles show neurons with a good fit (N = 368). The correlation coefficient between and is . The other two correlations are not statistically significant.

Mentions: Examples of CRFs obtained under these conditions are given in Fig. 10A,B. As in the case of LGN input heterogeneities, the excitatory CRFs are steeper ( is higher) and saturate earlier ( is lower) than in the LGN inputs. Here also, most of the CRFs are well fitted to the H-ratio function (92%). However, none of the cells exhibit super-saturation. This is because and are the same for all the neurons. The heterogeneity in and can only shift and scale the CRF.


Power-law input-output transfer functions explain the contrast-response and tuning properties of neurons in visual cortex.

Persi E, Hansel D, Nowak L, Barone P, van Vreeswijk C - PLoS Comput. Biol. (2011)

Distribution of CRFs induced by heterogeneous neuron properties.Examples of CRFs for (A) excitatory and (B) inhibitory neurons. Dotted lines: Population averaged CRF. Distribution histograms of the the H-ratio parameters ,  and  are shown for excitatory neurons in C, D and E respectively (all the neurons are included). Bottom: pair-wise scatter plot of these parameters,  vs.  (F),  vs.  (G) and  vs.  (H). Dots in the scatter plot show all neurons, and circles show neurons with a good fit (N = 368). The correlation coefficient between  and  is . The other two correlations are not statistically significant.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3044767&req=5

pcbi-1001078-g010: Distribution of CRFs induced by heterogeneous neuron properties.Examples of CRFs for (A) excitatory and (B) inhibitory neurons. Dotted lines: Population averaged CRF. Distribution histograms of the the H-ratio parameters , and are shown for excitatory neurons in C, D and E respectively (all the neurons are included). Bottom: pair-wise scatter plot of these parameters, vs. (F), vs. (G) and vs. (H). Dots in the scatter plot show all neurons, and circles show neurons with a good fit (N = 368). The correlation coefficient between and is . The other two correlations are not statistically significant.
Mentions: Examples of CRFs obtained under these conditions are given in Fig. 10A,B. As in the case of LGN input heterogeneities, the excitatory CRFs are steeper ( is higher) and saturate earlier ( is lower) than in the LGN inputs. Here also, most of the CRFs are well fitted to the H-ratio function (92%). However, none of the cells exhibit super-saturation. This is because and are the same for all the neurons. The heterogeneity in and can only shift and scale the CRF.

Bottom Line: We test these results with numerical simulations of a network of conductance-based model (CBM) neurons and we demonstrate that they are valid and more robust here than in the rate model.The results indicate that because of the acceleration in the transfer function, described here by a power-law, the orientation tuning curves of V1 neurons are more tuned, and their CRF is steeper than those of their inputs.Comparison with experimental data suggests that both sources contribute nearly equally to the diversity of CRF shapes observed in V1 neurons.

View Article: PubMed Central - PubMed

Affiliation: Laboratoire de Neurophysique et Physiologie, Université Paris Descartes, Paris, France.

ABSTRACT
We develop a unified model accounting simultaneously for the contrast invariance of the width of the orientation tuning curves (OT) and for the sigmoidal shape of the contrast response function (CRF) of neurons in the primary visual cortex (V1). We determine analytically the conditions for the structure of the afferent LGN and recurrent V1 inputs that lead to these properties for a hypercolumn composed of rate based neurons with a power-law transfer function. We investigate what are the relative contributions of single neuron and network properties in shaping the OT and the CRF. We test these results with numerical simulations of a network of conductance-based model (CBM) neurons and we demonstrate that they are valid and more robust here than in the rate model. The results indicate that because of the acceleration in the transfer function, described here by a power-law, the orientation tuning curves of V1 neurons are more tuned, and their CRF is steeper than those of their inputs. Last, we show that it is possible to account for the diversity in the measured CRFs by introducing heterogeneities either in single neuron properties or in the input to the neurons. We show how correlations among the parameters that characterize the CRF depend on these sources of heterogeneities. Comparison with experimental data suggests that both sources contribute nearly equally to the diversity of CRF shapes observed in V1 neurons.

Show MeSH