Figure 2. Snapshots of the histone H3.1 at t = 107 time step at the temperatures T = 0.016 using MJ potential2. doi:10.1371/journal.pone.0049352.g002 Regardless of appreciable fluctuations, the radius of gyration seems to reach steady-state values at most temperatures (inset figure 5). It should be pointed out that MC step (t) is not the real time but provides a mean to test stochastic dynamics. We also know that the asymptotic dynamics of a chain are diffusive at high temperature as for a gas molecule in a dilute gas. The approach to diffusive motion of the protein chain at high temperature is clearly seen (the inset in figure 5 for Rc). Reducing the temperature leads Random Coil to Globular Thermal Response (H3.1) to slow dynamics; a systematic slowing down of the protein dynamics as observed here (figure 5 inset) is thus consistent with the expectation. These trends support the reliability of such a coarse-grained approach in gaining the global insight into the structural evolution of the protein at large scales. It should be pointed out that not every sequence of 136 amino acids can lead to such transition from a random coil to a globular conformation. As mentioned above, a similar histone (H2AX) of comparable size exhibits [33] very different thermal response, i.e., a non- monotonic dependence of its gyration radius with the temperature with the same MJ potential. The thermal response of the radius of gyration of the protein with all three potentials, i.e., MJ, BT, and BFKV, is presented in figure 6 for comparison. We see both similarity and differences. The protein expands on raising the temperature within a range (DT), a general cooperative characteristics of the histone H3.1 results from all potentials. The range over which a systematic (monotonic) response occurs, however, depends on the potential matrix. The range of temperatures is DTMJ<0.013–0.020 with the MJ potential. The range shifts towards higher temperatures DTBT<0.018–0.026 with the BT potential and towards lower temperatures DTBFKV<0.006–0.013 with the BFKV potential. At the high temperature regime, the magnitudes of Rg converge to a steady-state value with a random coil structure (see below) with all potentials. There is an anomaly, however, with the BFKV potential where the magnitude of Rg decreases on raising the temperature in a range DTA<0.015–0.018 before reaching its saturation. It is difficult to know which potential is better than another over the entire range of temperatures due to lack of explicit experimental data on the variation of the Rg of the histone H3.1 with the temperature. The potential matrices BT and BFKV proposed by Betancourt and Thirumalai [7] and Bastolla et al. [8], respectively, seem to be an improvement over the classical MJ potential [2]. Results from both potentials, BT and BFKV, show opposite shift with respect to MJ potential. Despite similar statistics regarding the sampling, the data for Rg in figure 6 with BFKV appear smoother than that with MJ and BT which is primarily due to differences in its contact matrices. The reduced unit of temperature (with Boltzmann constant and interaction energy) used here appears somewhat arbitrary but it is kept the same for all potential matrices in our coarse-grained MC approach as are the potentials which are phenomenological as described above. Therefore, some guidance will be welcome from clean experiments to identify the thermal response of histone H3.1. Such a calibration may help identify the range of validity or reliability of different potentials. The common features (e.g., random coil to globular transition) in thermal response resulting from all potentials may also help with understanding and interpreting the universal characteristics of the histone H3.1 in future experiments. In order to examine the spatial distribution of residues, i.e., the shape of the protein, we have analyzed the structure factor S(q) (Figure 7): S(q)~S 1 D XN e{i~q:~r 2 D TD~qD N j~1 where rj is the position of each residue and |q| = 2p/l is the wave vector of wavelength, l. From the power-law scaling of the structure factor with the wave vector, S(q)/q21/n, one can estimate n the spatial distribution of residues in the protein (Rg / N ). Of particular interest is the range of the wave vector, q < 0.35–0.75 corresponding to the average size of the protein, Rg<10–26 (see PLOS ONE | www.plosone.org 4 November 2012 | Volume 7 | Issue 11 | e49352