. . . . "In the hierarchical Bell model applied to alpha-helices, 3–4 parallel hydrogen bonds per turn are optimal for the protein's combined mechanical and thermodynamic stability, matching the 3.6 hydrogen bonds per turn of real alpha-helices." . "prediction" . . "Notation basis: The optimum and the observed value are stated in the abstract; the objective being optimised is in the full text." . "Three to four parallel hydrogen bonds per turn is the mechanically and thermodynamically favoured number" . "b^{*} \\in \\{3, 4\\} \\quad (\\text{observed } b = 3.6 \\text{ H-bonds per turn})" . "Theodor Ackbarow et al., “Hierarchies, multiple energy barriers, and robustness govern the fracture mechanics of α-helical and β-sheet protein domains”, Proceedings of the National Academy of Sciences 104, 16410-16415 (2007), doi:10.1073/pnas.0705759104; Abstract. Scope: Alpha-helical protein domains" . "Theodor Ackbarow, Xuefeng Chen, Sinan Keten, Markus J. Buehler. Hierarchies, multiple energy barriers, and robustness govern the fracture mechanics of α-helical and β-sheet protein domains. Proceedings of the National Academy of Sciences 104, 16410-16415 (2007). doi:10.1073/pnas.0705759104" . "Theodor Ackbarow, Xuefeng Chen, Sinan Keten, Markus J. Buehler" . "2007"^^ . "PMC2034213" . "doi:10.1073/pnas.0705759104" . "pmid:17925444" . "Hierarchies, multiple energy barriers, and robustness govern the fracture mechanics of α-helical and β-sheet protein domains" . . . "delphisci buehler-protein-materials claim extractor" . . . . "Claude Fable 5.1" . . . . . . . . . . . . "Quoted from the published abstract as returned by Europe PMC (2007-hierarchies.abstract.txt, sha256 4f052f4a8a9ddc7dfecc384493c31e0f00fcd9873ded36486b8618493fdf4e18); the full text was not read (not in Europe PMC open-access subset). Checked by build/check.py." . . . "We exemplify our model in a study of AHs, and show that 3-4 parallel HBs per turn are favorable in light of the protein's mechanical and thermodynamical stability, in agreement with experimental findings that AHs feature 3.6 HBs per turn." . . "4f052f4a8a9ddc7dfecc384493c31e0f00fcd9873ded36486b8618493fdf4e18" . "Checksum of the vendored text file inputs/2007-hierarchies.abstract.txt, not of the publisher's copy." . . . "Abstract of Hierarchies, multiple energy barriers, and robustness govern the fracture mechanics of α-helical and β-sheet protein domains, as read" . . "buehler-protein-materials" . "2026-11-08T04:38:11.893Z"^^ . . . . . "Theodor Ackbarow et al. 2007 claim: Three to four parallel hydrogen bonds per turn is the mechanically and thermodynamically favoured number" . . "RSA" . "MIIBIjANBgkqhkiG9w0BAQEFAAOCAQ8AMIIBCgKCAQEAyFHtPB6p0mCjDozxlOY9CmO3nBm7Te3jFbXyLmM+G1tGe47Da0jYIbhkl9Oo1ZjxmCa3LCwlEqK8gj6hEIcL4ahW30JXh9HycfKVk1bugkzMEV15tJdTzAU3sGMFnbNsn43xY2LFLy45tApkRm5byEiM7oRRrooIdwoQKnP4Wzq/bfAoJ9qvW+MGkelyOTd1jbSt+KfmT7xKmDfWzAHddUlWwMX2QJOLxDaffOteTop6ZRgPiNmPJKA/S62Gac9XtSYT3oDkZ6/nr5cxxNLpOyxTf5FPISiCe11xYO/unYjY+mwnOfA8yhJIyx1l0O9I0vpOpn+E5TvyHJV+oSTrvwIDAQAB" . "cOD+kt5F+fIj92K3/uLPBb76PGCD3fqo5sy05xiQ7QB5I69Buk+cgvt6IIUKjYmx72PPHhsvw5bV7h9dR1i6RNjXa9acfqQjnNWS6ITba49YEpnbSzf9890X0GP2q5S9l+8Hur5t3iSoJvyccrx+ENRLA9aettNyZBWy+zrkaWdngf3mFryiFL1i7t7r/tD7eAZfDx9B+za0YHcPuSzFby/SnKPSLowmHXLIFx7D7qlqlzr+SadqAO/Lx+zS5OnENQLgF7SYuVwjNDAo+qg7JflFmzAnTdsPA1K3JFRCTIFt+usWURvDN0TjcAtnvBOH0eC0IqAh0+FjfYF3XHJ0sQ==" . . .