This page describes how the common input model can be used
to infer the bandwidth of a model neurone under large scale synaptic input.

**Definition and measurement of neural bandwidth**

- Neural bandwidth is the range of frequencies (in the Fourier sense) over which the firing characteristics of the pre-synaptic inputs under consideration can modulate the output discharges of the two neurones.
- A Correlation analysis of the output discharges can be used to indirectly infer the neural bandwidth for the subset of the total synaptic input which is common to both cells.

**Bandwidth for Uncorrelated Synaptic Input**

Correlation analysis of the output discharge of the two cell model with
50 % common synaptic inputs. Each cell has 1000 inputs firing randomly at
32 spikes/sec, they share 16,000 EPSPs/sec.
(a) The two cells demonstrate a tendency for synchronous discharges - due to the common input. (b) The range of frequencies involved is up to 50 Hz. Thus the bandwidth for this configuration, which reflects the ability
of 50% of the total synaptic input to modulate the output discharge, is 50
Hz. |

- Despite the fact that the two cells share 50% of their total synaptic input, the output discharges are only weakly correlated at frequencies up to 50 Hz. The coherence indicates that the output discharge of one cell can predict at most 8% of the variability in the output discharge of the second cell.

- The bandwidth for 80% of the total synaptic inputs is in excess of 200 Hz.
- With 80% shared synaptic input (25,600 EPSPs/sec) the output discharge of one cell can predict at most 16% of the variability in the output discharge of the second cell.

Altering the correlation structure, without altering the firing rates, or numbers of inputs, has a dramatic impact on neural bandwidth.

Coherence between the output discharges of the two cell model with 10
% common synaptic inputs (3200 EPSPs/sec), provided by: (a) One hundred broad band inputs (32 spikes/sec; c.o.v = 1.0) which are weakly correlated over a broad range of frequencies. (b) Two sets of periodically firing weakly correlated inputs (160 inputs at 10 spikes/sec; 64 inputs at 25 spikes/sec) which are correlated at their mean firing rate. Inputs are distributed uniformly over the dendritic tree. |

**Dynamic Modulation of Neural Bandwidth.**

- The correlation between the outputs accurately reflects the correlation structure in the common inputs - The bandwidth of the neurones is determined by the correlation structure present in the pre-synaptic inputs. In other words the bandwidth of the neurone is determined by the firing characteristics of the pre-synaptic inputs.
- A small change in the temporal correlation structure of a sub set of the total synaptic input, without any alteration in mean firing rate, can alter the bandwidth of the cells.
- The strength of correlation amongst the input spike train required to achieve this is sufficiently weak, that a correlation analysis of pairs of sample inputs may fail to reveal the presence of any correlation. The peak coherence between sample inputs is typically around 0.01.

**Further details**

For further details see the following article

Halliday, D.M. (2000). Temporal correlation of large scale synaptic input is a major determinant of neuronal bandwidth,If you require further details please contact David Halliday.Neural Computation,12, 693-707. PDF is available in the publications page. Abstract is available here.

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Last Modified 09 July 2002