Today I shared a PRL paper considering the Heterogeneity in integrate-and-fire neurons' threshold.

http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.108.228102

They consider a all-to-all excitatory integrate-and-fire network and varied the deviation of their thresholds. What they found is that a proper level of heterogeneity will introduce low-threshold neurons that enhance the activity and sensitivity of the all-to-all network. This kind of enhancement leads to a proper level for the efficiency of rate coding and spike-time coding. 

      Also, in their more recent efforts, they found that the heterogeneity effect in inhibitory population is different from the one in excitatory population in their previous consideration.

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4162374/

      As CKC have comment, this kind of proper heterogeneity level may be quite specific to the all-to-all network case. For other network topology, this might not be true. Also, the threshold is actually a time variable associated with time in the network with synapitc plasticity.