We demonstrate that the recently proposed pruned-enriched Rosenbluth method PERM (P. Grassberger, Phys. Rev. E 56 (1997) 3682) leads to very efficient algorithms for the folding of simple model proteins. We test it on several models for lattice heteropolymers, and compare to published Monte Carlo studies of the properties of particular sequences. In all cases our method is faster than the previous ones, and in several cases we find new minimal energy states. In addition to producing more reliable candidates for ground states, our method gives detailed information about the thermal spectrum and, thus, allows to analyze static aspects of the folding behavior of arbitrary sequences.

In the two-dimensional HAP Model we analyze the thermodynamic folding behavior of sequences that have n-helix and n-member beta-sheet ground state structures.

We demonstrate that the recently proposed pruned-enriched Rosenbluth method (PERM) (Grassberger, Phys. Rev. E 56:3682, 1997) leads to extremely efficient algorithms for the folding of simple model proteins. We test it on several models for lattice heteropolymers, and compare it to published Monte Carlo studies of the properties of particular sequences. In all cases our method is faster than the previous ones, and in several cases we find new minimal energy states. In addition to producing more reliable candidates for ground states, our method gives detailed information about the thermal spectrum and thus allows one to analyze thermodynamic aspects of the folding behavior of arbitrary sequences.

Electrophilic Additions to the Bicyclo[1.1.0]butane System of Tricyclo[4.1.0.02,7]heptane Derivatives: Halogen ElectrophilesThe known reactions of 8,8‐dibromotetracyclo[5.1.0.02,4.03,5]octane (3a) and homobenzvalene (7) with pyridinium bromide perbromide and iodine, respectively, were carried out in the presence of tetra‐n‐butylammonium chloride. The formation of the chloro‐substituted norpinane derivatives 6a and 9 is evidence for cationic intermediates. The same mechanism is operative in the reaction of pyridinium bromide perbromide with the dichlorotetracyclooctane 3b, which was prepared from 7 and dichlorocarbene. On exposure of tricyclo[4.1.0.02,7]heptane (1) to N‐bromosuccinimide in acetone/water/triethylamine, the bromonorpinanol 22, the bromonorcaranols 23, and cyclohex‐1‐ene‐1‐carboxaldehyde (24) were obtained. On the basis of the steric course and thermodynamic considerations, the cationic intermediates generated in the above reactions by attack of the electrophiles at the bicyclobutane systems are assigned the halonium ion structure 38 and the nonclassical structures 34 and 35, respectively. Elemental bromine and iodine converted the phenyltricycloheptane 10 into the respective diastereomeric norpinanes 11 and 12, which were transformed smoothly into the diastereomeric methyl ethers 13 and 14 by treatment with sodium methoxide in methanol. The reactions of 10 with pyridinium bromide perbromide in pyridine, cyanogen bromide in the presence of aluminium trichloride, and N‐bromosuccinimide in acetone/water gave rise to norpinane derivatives, i.e. the pyridinium salt 15, the nitrile 16, and the alcohol 18, respectively. In the case of cyanogen iodide in acetonitrile, the solvent participated in the process to yield the 2‐(norpinylimino)propionitriles 17. Corresponding to the configurations of the products, the attack of a halogen electrophile at 10 leads to classical 6‐phenyl‐6‐norpinyl cations 41, which may be approached by nucleophiles from the two possible faces. As origin for the low tendency of the cations 33–35 and 41 to rearrange to norcaryl cations, the electronegativity of the halogen atoms is suggested. The reduced migratory aptitude of a CHHal relative to a CH2 group results from its electron deficiency and from the decreased stability of 7‐halo‐2‐norcaryl relative to the parent 2‐norcaryl cations. The chlorophenyltricycloheptane 25 was prepared from 10 and treated with aqueous sulfuric acid to give the norpinanol 27. Formed by protonation of the bicyclobutane system of 25, the cationic precursor of 27 shows a behaviour similar to that of cations 41.

Electrophilic Additions to the Bicyclo[1.1.0]butane System of 1‐Phenyl‐ and 1‐(4‐Anisyl)tricyclo[4.1.0.02,7]heptane: Acid‐Catalyzed Reactions with Water and Methanol, Addition of Acetic Acid, and Oxymerucuration1‐(4‐Anisyl)tricyclo[4.1.0.02,7]heptane (37) was prepared from 1‐(4‐anisyl)cyclohexene, tetrabromomethane, and methyllithium in a one‐pot reaction. Starting from 37 and the analogous phenyl compound 19, the oxymercuration/demercuration sequence provided the exo‐6‐aryl‐endo‐6‐norpinanols 30a and 20a, respectively. By reaction with triphenyl‐stannane, the bromo compound 27a was converted into endo‐6‐phenyl‐exo‐6‐norpinanol 28a. Treatment of 19 with aqueous sulfuric acid led to a mixture of the alcohols 20a–25a. Mixtures of a very similar composition were obtained on hydrolysis of the 3,5‐dinitrobenzoates 20b and 28b of 20a and 28a in 80% aqueous acetone. Kinetic measurements revealed the same rate for the hydrolysis of 20b and 28b. The proof of the presence of 20a among the products of the reactions of 19, 20b, and 28b showed the intermediacy of an unrearranged cation, to which the classical structure 16 is ascribed. That acetic acid is too weak a nucleophile to intercept 16 follows from the structure of the adducts to 19. All of them (21b, 22b, 25b, 26b) have rearranged skeletons. In contrast, the stronger nucleophile methanol trapped 16 more efficiently than water to give the diastereomeric 6‐norpinyl methyl ethers 20d and 28d. The reaction of 37 with acetic acid and 10−4 M hydrochloric acid as well as the hydrolysis the 3,5‐dinitrobenzoate 30c of 30a produced mainly the diastereomeric 6‐norpinyl acetates 30b and 31b and 6‐norpinanols 30a and 31a, respectively. Whereas the protonation of 19 and 37 gives the classical cations 16 and 17, respectively, the oxymercuration of these substrates results in the generation of the nonclassical cations 44 and 46. This was concluded from the configuration of the demercuration products 20a and 30a and the absence of the diastereomers 28a and 31a.

Solvolyses of cis-tricyclo[3.1.0.0(2,6)]hex-3,4-diyl ditosylate (12) and cis-bicyclo[2.1.1]hex-2,3-diyl ditosylate (27) have been carried out in 80% aqueous ethanol in the presence of ethyldiisopropylamine. In the former case, endo,endo-tricyclo[2.2.0.0(2,6)]hexane-3,5-diol (13a), its monoether 13b and diether 13c were products whereas in the latter the monoethers 28b, d, e, g and the diethers 28a, c, f of bicyclo[3.1.0]hexane were formed. In pure ethanol, 12 was converted into pure 13c in good yield. In the presence of the weaker base 2,6-lutidine, the solvolysis of 12 in aqueous ethanol gave different products, i.e. exo,exo-4,6-diethoxybicyclo[3.1.0]hex-2-ene (14a) and several aldehydes, inter alia cyclopentadiene-1-carboxaldehyde (15). In control experiments, the tricyclic compounds 13b, c were converted into 14a, 15 and further aldehydes as well as into the bicyclo[2.1.1]hexene derivatives 19a, b. Sulfonates of tricyclo[3.1.0.0(2,6)]hexan-3-ol (21a) could not be isolated but its mesylate 21c was characterized by NMR spectroscopy and hydrolysed in aqueous acetone to give tricyclo[2.2.0.0(2,6)]hexanendo-3-ol (22a). It is concluded from these results that the dissociations of the above sulfonates do not lead to unrearranged carbocations. Rather, they proceed with participation of the beta-carbon in trans position relative to the leaving group resulting in the immediate generation of rearranged cations. - Kinetic studies show that the tricyclic mesylate 21c solvolyses in 80% ethanol/water 1.4 . 10(5) times as fast as bicyclo[2.1.1]hex-2-yl tosylate (25), and the tricyclic ditosylate 12 solvolyses 6 . 10(5) as fast as the corresponding bicyclic ditosylate 27. These rate enhancements are similar to those previously observed for less strained cyclopropylcarbinyl substrates.