  An important idea in neural information processing is the
communication-through-coherence hypothesis, according to which communication
between two brain regions is effective only if they are phase-locked. Also of
importance is neuronal variability, a phenomenon in which a single neuron's
inter-firing times may be highly variable. In this work, we aim to connect
these two ideas by studying the effects of that variability on the capability
of neurons to reach phase synchronization. We simulate a network of
modified-Hodgkin-Huxley-bursting neurons possessing a small-world topology.
First, variability is shown to be correlated with the average degree of phase
synchronization of the network. Next, restricting to spatial variability -
which measures the deviation of firing times between all neurons in the network
- we show that it is positively correlated to a behavior we call promiscuity,
which is the tendency of neurons to to have their relative phases change with
time. This relation is observed in all cases we tested, regardless of the
degree of synchronization or the strength of the inter-neuronal coupling: high
variability implies high promiscuity (low duration of phase-locking), even if
the network as a whole is synchronized and the coupling is strong. We argue
that spatial variability actually generates promiscuity. Therefore, we conclude
that variability has a strong influence on both the degree and the manner in
which neurons phase synchronize, which is another reason for its relevance in
neural communication.
