Temperature dependence of s 2 and density for five archetypal systems. Panel (b) quantifies the temperature dependence of chain density (in units of gm-cm−3), which is calculated as , where MW denotes the molecular weight in gm mol−1.
Temperature dependence of fluctuations in density and energy for five archetypal systems. Panel (a) shows the temperature dependence of the density fluctuations quantified as the variance of the density distribution for a given temperature, i.e., . Panel (b) shows the temperature dependence of the specific heat capacity. The specific, constant volume heat capacities were calculated as , where MW is the molecular weight and ⟨E⟩ is the ensemble-averaged potential energy for simulated ensembles at a given temperature. Typically, one expects sharp transitions for well-defined order-to-disorder transitions and yet, interestingly, the Q56 system shows the sharpest transition. The relatively broad transitions for NTL9 and GB1 highlight the joint contributions of gradual melting and different degrees of residual local structure in their unfolded states.
Sample distributions P( ) for two systems at different temperatures. The panel on the left shows P( ) distributions for NTL9 at three different temperatures and the panel on the right shows these distributions for the Q56 system at three different simulation temperatures. In both panels, the solid curves represent intra-ensemble P( ) distributions whereas the dashed curves are for comparisons between conformations within an ensemble at temperature T and conformations drawn from the FRC ensemble.
Temperature dependence of ⟨ ⟩ and Φ for the five archetypal systems. Panel (b) includes error bars from a bootstrap analysis whereby 100 distinct bootstrap trials were performed to estimate Φ and the error bars therefore represent standard deviations for the estimate of the mean Φ values.
(a)–(d) Plots to quantify the assessments of conformational properties that derive from the joint analysis s 2 (ordinates) and Φ (abscissae). In each panel, the symbol colors progress from cool to hot as temperature increases.
Assessments conformational heterogeneity in ensembles with different degrees of helical structure. Panel (a) plots Φ against for T = 298 K. The results are shown for 17 naturally occurring and designed sequences. Panel (b) plots Φ against σ2(R g) and panel (c) plots Φ against σ2( ) for each of the 17 bZIP-bRs.
Analysis of conformational heterogeneity in terms of the distribution of helical segment lengths for three of the bZIP-bRs. The figure shows three panels one each for the bZIP-bR of fra1, the chimeric cys3-fos, and gcn4. Each panel shows a histogram of helical segment lengths within the simulated ensembles. A helical segment corresponds to a consecutive stretch of residues in a conformation with a DSSP “H” designation. The value of Φ is dictated by the width of a segment length distribution as opposed to the ensemble-averaged helicity.
Temperature dependence of the variance of calculated from the distributions of values for each of the five archetypal systems. All inferences regarding conformational heterogeneity that are drawn from analysis of the variance are consistent with those drawn from analysis of Φ.
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