Investigating large-amplitude protein loop motions as extreme events using recurrence interval analysis

We investigate large amplitude motions of the two key residues ASP49 and PHE142 in β-lactamase inhibitor protein BLIP as extreme events, using recurrence interval analysis. The recurrence intervals for distance returns between the centers of mass of these two residues over a period of 300 ns are calculated. We find that the probability distribution functions for these recurrence intervals above a range of positive threshold q>0, Pq(τ), show limited scaling with the mean recurrence interval τavgat each respective threshold as Pq(τ)=1τavgf(τ∕τavg). Half of the scaled distributions are fitted by a power law t−γ at the significance level of 1%, with γ’s ranging from 1.72 to 1.79 for the corresponding thresholds. A stretched exponential fit exp−(ττavg)γ, fails at the 1% significance level for all of the scaled distributions. The scaled distributions also show short term and long term memory behavior, which is removed by shuffling the distance return time series.