Impact of intrinsic biophysical diversity on the activity of spiking neurons

We study the effect of intrinsic heterogeneity on the activity of a population of leaky integrate-and-fire neurons. By rescaling the dynamical equation, we derive mathematical relations between multiple neuronal parameters and a fluctuating input noise. To this end, common input to heterogeneous neurons is conceived as an identical noise with neuron-specific mean and variance. As a consequence, the neuronal output rates can differ considerably, and their relative spike timing becomes desynchronized. This theory can quantitatively explain some recent experimental findings.Comment: 4 pages, 5 figure

Significance of Input Correlations in Striatal Function

The striatum is the main input station of the basal ganglia and is strongly associated with motor and cognitive functions. Anatomical evidence suggests that individual striatal neurons are unlikely to share their inputs from the cortex. Using a biologically realistic large-scale network model of striatum and cortico-striatal projections, we provide a functional interpretation of the special anatomical structure of these projections. Specifically, we show that weak pairwise correlation within the pool of inputs to individual striatal neurons enhances the saliency of signal representation in the striatum. By contrast, correlations among the input pools of different striatal neurons render the signal representation less distinct from background activity. We suggest that for the network architecture of the striatum, there is a preferred cortico-striatal input configuration for optimal signal representation. It is further enhanced by the low-rate asynchronous background activity in striatum, supported by the balance between feedforward and feedback inhibitions in the striatal network. Thus, an appropriate combination of rates and correlations in the striatal input sets the stage for action selection presumably implemented in the basal ganglia

Place-cell capacity and volatility with grid-like inputs

What factors constrain the arrangement of the multiple fields of a place cell? By modeling place cells as perceptrons that act on multiscale periodic grid-cell inputs, we analytically enumerate a place cell’s repertoire – how many field arrangements it can realize without external cues while its grid inputs are unique – and derive its capacity – the spatial range over which it can achieve any field arrangement. We show that the repertoire is very large and relatively noise-robust. However, the repertoire is a vanishing fraction of all arrangements, while capacity scales only as the sum of the grid periods so field arrangements are constrained over larger distances. Thus, grid-driven place field arrangements define a large response scaffold that is strongly constrained by its structured inputs. Finally, we show that altering grid-place weights to generate an arbitrary new place field strongly affects existing arrangements, which could explain the volatility of the place code.</jats:p

Place-cell capacity and volatility with grid-like inputs

What factors constrain the arrangement of the multiple fields of a place cell? By modeling place cells as perceptrons that act on multiscale periodic grid-cell inputs, we analytically enumerate a place cell’s repertoire – how many field arrangements it can realize without external cues while its grid inputs are unique – and derive its capacity – the spatial range over which it can achieve any field arrangement. We show that the repertoire is very large and relatively noise-robust. However, the repertoire is a vanishing fraction of all arrangements, while capacity scales only as the sum of the grid periods so field arrangements are constrained over larger distances. Thus, grid-driven place field arrangements define a large response scaffold that is strongly constrained by its structured inputs. Finally, we show that altering grid-place weights to generate an arbitrary new place field strongly affects existing arrangements, which could explain the volatility of the place code

Signal representation in the striatum network when stimulus input to individual stimulated neurons was correlated.

<p>(A) Scheme of stimulus configuration-I ( = 0; 0) presented to a fraction of striatum neurons, on top of the background excitatory input from the cortex and background inhibitory input from other striatal neurons. (B,C) Examples of MSNs spiking responses when 30% of striatal neurons were stimulated for 100 ms (starting at 600 ms) with excitatory input with an ensemble firing rate  = 400 Hz and low ( = 0.001; B) or high ( = 0.02; C) input correlations, respectively. (D,E) Firing rate of the stimulated MSNs (D) and the unstimulated MSNs (E), averaged over the stimulation epoch, as a function of input correlation , for two different input firing rates. Observe that the response rate in both subpopulation varied in a non-monotonic fashion with increasing input correlation . The dashed line indicates the level of baseline activity. (F,G) Synchrony index of the stimulated MSNs (F) and the unstimulated MSNs (G) as a function of input correlation . The synchrony index of the stimulated MSNs is close to 1 so there is no significant synchrony. (H) Signal-to-noise ratio (SNR) of the striatum network, quantified by the ratio of the average firing rates of the stimulated and unstimulated MSNs, as a function of input correlation . Observe that SNR varied in a non-monotonic fashion with increasing input correlation . By contrast, SNR increased monotonically with input firing rate (). (I) Peak SNR of the striatum network as a function of input correlation for different strengths of feedback and feedforward inhibition . The blue trace shows peak SNR for different values of and a fixed  = 1 nS. The red trace shows peak SNR for different values of and a fixed  = 0.3 nS. Observe that increasing either type of inhibition increased the peak SNR, because stronger inhibition is more effective in suppressing the background activity.</p

Network dynamics and signal representation in the striatum network when the spiking of FSIs is correlated.

<p>(A) Spiking activity in the striatum for  = 0. Blue and black rasters show the spiking activity of MSNs and FSIs, respectively. PSTHs of the corresponding rasters are shown at the bottom. (B) Spiking activity in the striatum for  = 1. Red and black rasters show the spiking activity of MSNs and FSIs, respectively. PSTHs of the corresponding rasters are shown at the bottom. (C) Firing rate of the stimulated MSNs, averaged over the stimulation epoch, as a function of input correlation , for four different values of . (D) Firing rate of the unstimulated MSNs, averaged over the stimulation epoch, as a function of input correlation , for four different values of . (E) Signal-to-noise ratio (SNR) of the striatum network as a function of input correlation , for four different values of FSIs' output correlation . Observe that inhibitory input correlation decreased the SNR, which maintained its non-monotonicity and shifted its peak to a slightly lower value of .</p