Assumptions  Parameter Adaptation   Firing Rate Information

Information in the Spike Times

Using techniques that have now become standard in quantitative neurophysiology Bialek et al. (1991), Rieke et al. (1997), Gabbiani and Koch (1996),one can estimate the information in the spike times by asking how well one can reconstruct the signal from the spikes. In essence, one replaces each spike by a band-limited function in time, such that the summed overlap of these functions (also known as linear reconstruction kernels) optimally approximates the synaptic conductance signal. Fig. 3 displays these reconstruction kernels for the case where the model neuron ``learned'' to produce a uniform distribution of spike counts.
 
   

Figure 3: Linear reconstruction kernels corresponding to model neuron in Figs. 2a and 2b of the text.

 

Adaptation of the modulatory conductances leads to reconstruction kernels that are not only smaller in amplitude, but also more tightly centered about the time axis. As a consequence, after learning to maximize the information in the firing rate, the model neuron's spike train is better able to signal rapid changes in the input, as shown in Fig. 4. The information in the spike times increases accordingly from 22.1 bits/second to 35.6 bits/second, or 0.52 bits/spike to 0.88 bits/spike.

 

 

Figure 4: Linear stimulus reconstruction from the spike times. Each spike  was replaced by the optimal reconstruction kernel in Fig. 3.

 Given the simple, yet fundamental nature of the encoding problem, i.e., the representation of a continuous input variable in a one-to-one fashion in the neuron's output, it is hardly surprising that  the information in the firing rate and the spike times both increase.  Moreover, the information in the spike times of adapted neurons is more robust to the addition of noise (not shown).
 

When an additional goal becomes energy conservation, the overall information rate in the neuron's spike times can, in fact, decrease due to adaptation because the number of spikes decreases . Yet the information per spike increases, since the model neuron becomes more ``efficient'' in transmitting information. In the case shown in Fig. 2c of the text, the information rate in the spike times is 17.5 bits/second after adaptation, which translates to 0.88 bits/spike.

1998-08-17