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Intrinsic neuronal properties switch the mode of information transmission in networks.

Gjorgjieva J, Mease RA, Moody WJ, Fairhall AL - PLoS Comput. Biol. (2014)

Bottom Line: Depending on the neurons' intrinsic properties, noise plays different roles in modulating neuronal input-output curves, which can dramatically impact network transmission.The developmental change in intrinsic properties supports a transformation of a networks function from the propagation of network-wide information to one in which computations are scaled to local activity.This work underscores the significance of simple changes in conductance parameters in governing how neurons represent and propagate information, and suggests a role for background synaptic noise in switching the mode of information transmission.

View Article: PubMed Central - PubMed

Affiliation: Center for Brain Science, Harvard University, Cambridge, Massachusetts, United States of America.

ABSTRACT
Diverse ion channels and their dynamics endow single neurons with complex biophysical properties. These properties determine the heterogeneity of cell types that make up the brain, as constituents of neural circuits tuned to perform highly specific computations. How do biophysical properties of single neurons impact network function? We study a set of biophysical properties that emerge in cortical neurons during the first week of development, eventually allowing these neurons to adaptively scale the gain of their response to the amplitude of the fluctuations they encounter. During the same time period, these same neurons participate in large-scale waves of spontaneously generated electrical activity. We investigate the potential role of experimentally observed changes in intrinsic neuronal properties in determining the ability of cortical networks to propagate waves of activity. We show that such changes can strongly affect the ability of multi-layered feedforward networks to represent and transmit information on multiple timescales. With properties modeled on those observed at early stages of development, neurons are relatively insensitive to rapid fluctuations and tend to fire synchronously in response to wave-like events of large amplitude. Following developmental changes in voltage-dependent conductances, these same neurons become efficient encoders of fast input fluctuations over few layers, but lose the ability to transmit slower, population-wide input variations across many layers. Depending on the neurons' intrinsic properties, noise plays different roles in modulating neuronal input-output curves, which can dramatically impact network transmission. The developmental change in intrinsic properties supports a transformation of a networks function from the propagation of network-wide information to one in which computations are scaled to local activity. This work underscores the significance of simple changes in conductance parameters in governing how neurons represent and propagate information, and suggests a role for background synaptic noise in switching the mode of information transmission.

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Related in: MedlinePlus

Fixed points of the iterated map dynamics.Top: An illustration of three – curves (colors) and the corresponding linear input-output relation (black dashed) with slope  derived from the mean field. Bottom left: The dynamics has a single stable fixed point and all input currents are attracted to it (indicated by small arrows converging to the fixed point). This corresponds to – curves of GS neurons at all values of . Middle: The dynamics has a line of stable fixed points that allow robust transmission of a large range of input currents in the network. NGS neurons with high values of  have such dynamics. Right: The stable line of fixed points is smaller for – curves that are more "thresholding,'' corresponding to NGS neurons with low .
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pcbi-1003962-g005: Fixed points of the iterated map dynamics.Top: An illustration of three – curves (colors) and the corresponding linear input-output relation (black dashed) with slope derived from the mean field. Bottom left: The dynamics has a single stable fixed point and all input currents are attracted to it (indicated by small arrows converging to the fixed point). This corresponds to – curves of GS neurons at all values of . Middle: The dynamics has a line of stable fixed points that allow robust transmission of a large range of input currents in the network. NGS neurons with high values of have such dynamics. Right: The stable line of fixed points is smaller for – curves that are more "thresholding,'' corresponding to NGS neurons with low .

Mentions: Thus, these two curves serve as an iterated map whereby an estimate of the firing rate in the Lth layer, , is converted into a mean input current to the next layer, , which can be further converted into , propagating mean activity across multiple layers in the network (Figures 5, 6). While for neurons in the first layer, the selected – curve is the one corresponding to the level of intrinsic noise injected into the first layer, , for neurons in deeper layers, the choice of – curve depends not only on the magnitude of the independent noise fluctuations injected into each neuron, but also on the fluctuations arising from the input from the previous layer (see Eq. 16 in Methods). The behavior of this iterated map is shaped by its fixed points, the points of intersection of the – curve with the input-output line , which organize the way in which signals are propagated from layer to layer. The number, location and stability of these fixed points depend on the curvature of and on (Figure 5). When the slope of at the fixed point is less than , the fixed point is stable. This implies that the entire range of initial DC inputs (into layer 1) will tend to iterate toward the value at the fixed point as the mean current is propagated through downstream layers in the network (Figure 5, left). Therefore, all downstream layers will converge to the same population firing rate that corresponds to the fixed point. In the interesting case that becomes tangent to the linear input-output relation, i.e. the – curve has a slope equal to , the map exhibits a line attractor: there appears an entire line of stable fixed points (Figure 5, middle). This ensures the robust propagation of many input currents and population rates across the network. Interestingly, the – curves of the GS and NGS neurons for different values of fall into one of the regimes illustrated in Figure 5: GS neurons with their -invariant – curves have a single stable fixed point (Figure 5, left), while the NGS neurons have line attractors with exact details depending on (Figure 5, middle and right). The mechanics of generating a line attractor have been most extensively explored in the context of oculomotor control (where persistent activity has been interpreted as a short-term memory of eye position that keeps the eyes still between saccades) and decision making in primates (where persistent neural activity has been interpreted as the basis of working memory) [30].


Intrinsic neuronal properties switch the mode of information transmission in networks.

Gjorgjieva J, Mease RA, Moody WJ, Fairhall AL - PLoS Comput. Biol. (2014)

Fixed points of the iterated map dynamics.Top: An illustration of three – curves (colors) and the corresponding linear input-output relation (black dashed) with slope  derived from the mean field. Bottom left: The dynamics has a single stable fixed point and all input currents are attracted to it (indicated by small arrows converging to the fixed point). This corresponds to – curves of GS neurons at all values of . Middle: The dynamics has a line of stable fixed points that allow robust transmission of a large range of input currents in the network. NGS neurons with high values of  have such dynamics. Right: The stable line of fixed points is smaller for – curves that are more "thresholding,'' corresponding to NGS neurons with low .
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4256072&req=5

pcbi-1003962-g005: Fixed points of the iterated map dynamics.Top: An illustration of three – curves (colors) and the corresponding linear input-output relation (black dashed) with slope derived from the mean field. Bottom left: The dynamics has a single stable fixed point and all input currents are attracted to it (indicated by small arrows converging to the fixed point). This corresponds to – curves of GS neurons at all values of . Middle: The dynamics has a line of stable fixed points that allow robust transmission of a large range of input currents in the network. NGS neurons with high values of have such dynamics. Right: The stable line of fixed points is smaller for – curves that are more "thresholding,'' corresponding to NGS neurons with low .
Mentions: Thus, these two curves serve as an iterated map whereby an estimate of the firing rate in the Lth layer, , is converted into a mean input current to the next layer, , which can be further converted into , propagating mean activity across multiple layers in the network (Figures 5, 6). While for neurons in the first layer, the selected – curve is the one corresponding to the level of intrinsic noise injected into the first layer, , for neurons in deeper layers, the choice of – curve depends not only on the magnitude of the independent noise fluctuations injected into each neuron, but also on the fluctuations arising from the input from the previous layer (see Eq. 16 in Methods). The behavior of this iterated map is shaped by its fixed points, the points of intersection of the – curve with the input-output line , which organize the way in which signals are propagated from layer to layer. The number, location and stability of these fixed points depend on the curvature of and on (Figure 5). When the slope of at the fixed point is less than , the fixed point is stable. This implies that the entire range of initial DC inputs (into layer 1) will tend to iterate toward the value at the fixed point as the mean current is propagated through downstream layers in the network (Figure 5, left). Therefore, all downstream layers will converge to the same population firing rate that corresponds to the fixed point. In the interesting case that becomes tangent to the linear input-output relation, i.e. the – curve has a slope equal to , the map exhibits a line attractor: there appears an entire line of stable fixed points (Figure 5, middle). This ensures the robust propagation of many input currents and population rates across the network. Interestingly, the – curves of the GS and NGS neurons for different values of fall into one of the regimes illustrated in Figure 5: GS neurons with their -invariant – curves have a single stable fixed point (Figure 5, left), while the NGS neurons have line attractors with exact details depending on (Figure 5, middle and right). The mechanics of generating a line attractor have been most extensively explored in the context of oculomotor control (where persistent activity has been interpreted as a short-term memory of eye position that keeps the eyes still between saccades) and decision making in primates (where persistent neural activity has been interpreted as the basis of working memory) [30].

Bottom Line: Depending on the neurons' intrinsic properties, noise plays different roles in modulating neuronal input-output curves, which can dramatically impact network transmission.The developmental change in intrinsic properties supports a transformation of a networks function from the propagation of network-wide information to one in which computations are scaled to local activity.This work underscores the significance of simple changes in conductance parameters in governing how neurons represent and propagate information, and suggests a role for background synaptic noise in switching the mode of information transmission.

View Article: PubMed Central - PubMed

Affiliation: Center for Brain Science, Harvard University, Cambridge, Massachusetts, United States of America.

ABSTRACT
Diverse ion channels and their dynamics endow single neurons with complex biophysical properties. These properties determine the heterogeneity of cell types that make up the brain, as constituents of neural circuits tuned to perform highly specific computations. How do biophysical properties of single neurons impact network function? We study a set of biophysical properties that emerge in cortical neurons during the first week of development, eventually allowing these neurons to adaptively scale the gain of their response to the amplitude of the fluctuations they encounter. During the same time period, these same neurons participate in large-scale waves of spontaneously generated electrical activity. We investigate the potential role of experimentally observed changes in intrinsic neuronal properties in determining the ability of cortical networks to propagate waves of activity. We show that such changes can strongly affect the ability of multi-layered feedforward networks to represent and transmit information on multiple timescales. With properties modeled on those observed at early stages of development, neurons are relatively insensitive to rapid fluctuations and tend to fire synchronously in response to wave-like events of large amplitude. Following developmental changes in voltage-dependent conductances, these same neurons become efficient encoders of fast input fluctuations over few layers, but lose the ability to transmit slower, population-wide input variations across many layers. Depending on the neurons' intrinsic properties, noise plays different roles in modulating neuronal input-output curves, which can dramatically impact network transmission. The developmental change in intrinsic properties supports a transformation of a networks function from the propagation of network-wide information to one in which computations are scaled to local activity. This work underscores the significance of simple changes in conductance parameters in governing how neurons represent and propagate information, and suggests a role for background synaptic noise in switching the mode of information transmission.

Show MeSH
Related in: MedlinePlus