Representative results are depicted in Figure 6c, indicating the average radius of curvature of the molecular loop during simulation. For stable conditions, the average radius is approximately constant (with thermal fluctuations). In contrast, temperature-induced unfolding results in a corresponding increase in radius (from 3.7 to 8.3 Å for n = 72 and 9.0 to 15.6 Å

for n = 144 loops, respectively). From this global perspective, the loop is homogeneously unfolding, which would lead to a constant decrease in potential energy. The average radius of curvature, however, is insufficient to describe the more complex dynamics of unfolding. The linked and continuous looped structure impedes homogeneous relaxation of GF120918 nmr curvature; indeed, GDC-0449 nmr for sections of the structure to unfold, instantaneous increase in local curvature is observed. In effect, the relaxation of one or two loops results in the local bending increase of adjacent carbon bonds. Figure 6 Curvature definition and global unfolding. (a) Defining local radius of curvature, r(ŝ), in the carbyne loop (ŝ = 0 to L), averaged to calculate the global radius of curvature and κ. (b) Schematic of coordinates used for the numerical solution

to Equation 2, where each point represents adjacent carbon atoms. (c) Averaging the local curvatures across the molecule (here, n = 72 and n = 144) and calculating the associated radius of curvature, stable loop configurations have little change in radius at low temperatures (dashed arrows), while unfolding induced by high temperature results

in a global increase in radius with respect to time (solid arrows) as anticipated (by definition, Ibrutinib the unfolded structure will have a lower curvature). To confirm, the local curvature is plotted as a function of time across the length of the carbyne molecule (Figure 7). Due to thermal fluctuations, the unfolding trajectory is highly stochastic, and the curvature plots are representative only. Both n = 72 and n = 144 are plotted as examples and are the same trajectories as the average curvatures plotted in Figure 6. For n = 72, a CH5183284 supplier relatively low temperature is required for a stable three-loop structure (T = 50 K). Curvature is approximately constant (κ ≈ 0.27 Å-1, for a radius of approximately 3.7 Å) with slight variation along the molecular length due to temperature-induced oscillations. The two  peaks’ (κ ≈ 0.3 to 0.04 Å-1) occur approximately at the crossover of the carbon chains (see Figure 1c), necessitating a slight increase in local curvature. At a higher temperature (T = 200 K), there is enough energy to initiate unfolding. While globally the average radius increases, local unfolding induces increases in curvature in adjacent sections of the loop. Large peaks in the local curvature exceed 0.5 Å-1 before the structure  relaxes’ to a homogeneous, unfolded state (κ ≈ 0.12 Å-1).