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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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Firing rate propagation through networks of gain-scaling and nongain-scaling neurons.A,B. Top: The – curves (green) for GS neurons ( pS/µm2 and  pS/µm2) at two levels of noise,  pA (low noise) and  pA (high noise). The linear input-output relationships from the mean field (black) predict how the mean output firing rate of a given network layer can be derived from the mean input current into the first layer with the standard deviation of the prediction shown in gray. Dashed arrows show the iterated map dynamics transforming different mean input currents into a single output firing rate determined by the stable fixed point (green star). Bottom: The network mean firing rates for a range of mean input currents (to layer 1) as a function of layer number, with a clear convergence to the fixed point by layer 5. The results from numerical simulations over 10 second-long trials are shown as full lines (mean  from 2000 neurons in each layer) and mean field predictions are shown in dashed lines with a shaded background in the same color (for each different input) illustrating the standard deviation of the prediction. Other network parameters: connection probability , synaptic strength  and range of mean input currents 0–22 pA. C,D. Same as A,B but for NGS neurons ( pS/µm2 and  pS/µm2) with stronger synaptic strength  and range of mean input currents 0–70 pA. The network dynamics show a region of stable firing rate propagation (green box) where the – curve behaves like it is tangent to the input-output line for a large range of mean input currents (to layer 1). The size of the region increases with noise (until  pA). Bottom panels show the transmission of a range of input firing rates across different layers in the network. The arrow denotes a case where the firing rate first decreases towards 0 and then stabilizes. E,F. Same synaptic strength as C,D but for GS neurons ( pS/µm2 and  pS/µm2). Bottom panels show the convergence of firing rates to a single fixed point similar to the weakly connected GS network in A,B. As for the NGS networks in C,D, the mean field analysis predicts convergence to a slightly higher firing rate than the numerical simulations.
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pcbi-1003962-g006: Firing rate propagation through networks of gain-scaling and nongain-scaling neurons.A,B. Top: The – curves (green) for GS neurons ( pS/µm2 and pS/µm2) at two levels of noise, pA (low noise) and pA (high noise). The linear input-output relationships from the mean field (black) predict how the mean output firing rate of a given network layer can be derived from the mean input current into the first layer with the standard deviation of the prediction shown in gray. Dashed arrows show the iterated map dynamics transforming different mean input currents into a single output firing rate determined by the stable fixed point (green star). Bottom: The network mean firing rates for a range of mean input currents (to layer 1) as a function of layer number, with a clear convergence to the fixed point by layer 5. The results from numerical simulations over 10 second-long trials are shown as full lines (mean from 2000 neurons in each layer) and mean field predictions are shown in dashed lines with a shaded background in the same color (for each different input) illustrating the standard deviation of the prediction. Other network parameters: connection probability , synaptic strength and range of mean input currents 0–22 pA. C,D. Same as A,B but for NGS neurons ( pS/µm2 and pS/µm2) with stronger synaptic strength and range of mean input currents 0–70 pA. The network dynamics show a region of stable firing rate propagation (green box) where the – curve behaves like it is tangent to the input-output line for a large range of mean input currents (to layer 1). The size of the region increases with noise (until pA). Bottom panels show the transmission of a range of input firing rates across different layers in the network. The arrow denotes a case where the firing rate first decreases towards 0 and then stabilizes. E,F. Same synaptic strength as C,D but for GS neurons ( pS/µm2 and pS/µm2). Bottom panels show the convergence of firing rates to a single fixed point similar to the weakly connected GS network in A,B. As for the NGS networks in C,D, the mean field analysis predicts convergence to a slightly higher firing rate than the numerical simulations.

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)

Firing rate propagation through networks of gain-scaling and nongain-scaling neurons.A,B. Top: The – curves (green) for GS neurons ( pS/µm2 and  pS/µm2) at two levels of noise,  pA (low noise) and  pA (high noise). The linear input-output relationships from the mean field (black) predict how the mean output firing rate of a given network layer can be derived from the mean input current into the first layer with the standard deviation of the prediction shown in gray. Dashed arrows show the iterated map dynamics transforming different mean input currents into a single output firing rate determined by the stable fixed point (green star). Bottom: The network mean firing rates for a range of mean input currents (to layer 1) as a function of layer number, with a clear convergence to the fixed point by layer 5. The results from numerical simulations over 10 second-long trials are shown as full lines (mean  from 2000 neurons in each layer) and mean field predictions are shown in dashed lines with a shaded background in the same color (for each different input) illustrating the standard deviation of the prediction. Other network parameters: connection probability , synaptic strength  and range of mean input currents 0–22 pA. C,D. Same as A,B but for NGS neurons ( pS/µm2 and  pS/µm2) with stronger synaptic strength  and range of mean input currents 0–70 pA. The network dynamics show a region of stable firing rate propagation (green box) where the – curve behaves like it is tangent to the input-output line for a large range of mean input currents (to layer 1). The size of the region increases with noise (until  pA). Bottom panels show the transmission of a range of input firing rates across different layers in the network. The arrow denotes a case where the firing rate first decreases towards 0 and then stabilizes. E,F. Same synaptic strength as C,D but for GS neurons ( pS/µm2 and  pS/µm2). Bottom panels show the convergence of firing rates to a single fixed point similar to the weakly connected GS network in A,B. As for the NGS networks in C,D, the mean field analysis predicts convergence to a slightly higher firing rate than the numerical simulations.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1003962-g006: Firing rate propagation through networks of gain-scaling and nongain-scaling neurons.A,B. Top: The – curves (green) for GS neurons ( pS/µm2 and pS/µm2) at two levels of noise, pA (low noise) and pA (high noise). The linear input-output relationships from the mean field (black) predict how the mean output firing rate of a given network layer can be derived from the mean input current into the first layer with the standard deviation of the prediction shown in gray. Dashed arrows show the iterated map dynamics transforming different mean input currents into a single output firing rate determined by the stable fixed point (green star). Bottom: The network mean firing rates for a range of mean input currents (to layer 1) as a function of layer number, with a clear convergence to the fixed point by layer 5. The results from numerical simulations over 10 second-long trials are shown as full lines (mean from 2000 neurons in each layer) and mean field predictions are shown in dashed lines with a shaded background in the same color (for each different input) illustrating the standard deviation of the prediction. Other network parameters: connection probability , synaptic strength and range of mean input currents 0–22 pA. C,D. Same as A,B but for NGS neurons ( pS/µm2 and pS/µm2) with stronger synaptic strength and range of mean input currents 0–70 pA. The network dynamics show a region of stable firing rate propagation (green box) where the – curve behaves like it is tangent to the input-output line for a large range of mean input currents (to layer 1). The size of the region increases with noise (until pA). Bottom panels show the transmission of a range of input firing rates across different layers in the network. The arrow denotes a case where the firing rate first decreases towards 0 and then stabilizes. E,F. Same synaptic strength as C,D but for GS neurons ( pS/µm2 and pS/µm2). Bottom panels show the convergence of firing rates to a single fixed point similar to the weakly connected GS network in A,B. As for the NGS networks in C,D, the mean field analysis predicts convergence to a slightly higher firing rate than the numerical simulations.
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