Simulations were performed using three methods: Metropolis. Monte. Carlo with .... of residues connected by non-covalent bonds, which form a sterically rigid ...
I S S N 0 2 3 3 - 7 6 5 7 . Біополімери і клітина. 2 0 0 4 . Т. 20. № З
МОЛЕКУЛЯРНА БІОФІЗИКА
Clustering Monte Carlo simulations of the hierarchical protein folding on a simple lattice model 1
1
S. O. Yesylevskyy , A. P. Demchenko '
2
і Palladin Institute of Biochemistry of the National Academy of Sciences of Ukraine Leontovycha str. 9, Kyiv 0 1 0 3 0 , Ukraine 1, 2 Research Institute for Genetic Engineering and Biotechnology TUBITAK, Gebze-Kocaeli, 4 1 4 7 0 , Turkey
A role of specific collective motions and clustering behavior In protein folding was investigated using simple 2D lattice models. Two model peptides, which have the sequences of hierarchical and non-hierarchical design, were studied comparatively. Simulations were performed using three methods: Metropolis Monte Carlo with the local move set, Metropolis Monte Carlo with unspeclflc rigid rotations, and the Clustering Monte Carlo (CMC) algorithm that has been recently described by the authors. The latter was developed with particular aim to provide a realistic description of cluster dynamics. We present convincing evidence that the folding pathways and kinetics of hierarchically folding sequence are not adequately described in conventional MC simulations. In this case the account for cluster dynamics provided by CMC algorithm reveals important features of folding of hierarchically organized sequences. Our data suggest that the methods, which enable specific cluster motions, should be used for realistic description of hierarchical folding.
Introduction. T h e ideas t h a t proteins fold hierar chically, by sequential formation a n d association of clusters of residues with increasing their size and complexity, are in t h e minds of m a n y researchers [ 1 — 1 1 ] . Definitely, t h e process of folding is not a one-step event, a n d the acquisition of native structure occurs via formation a n d ordering its less organized elements. T h e sequential acquisition of structure can explain the observation of equilibrium a n d kinetic intermediates [3—6, 10, 11] including those with non-native structural elements [ 1 2 — 1 5 ] . T h i s mecha nism explains the observed very fast kinetics of the folding process [16] a n d provides a clear solution of Levinthal paradox [ 1 7 ] . Instead of global unfoldingfolding equilibrium, a spectrum of available protein conformations is observed in h y d r o g e n exchange experiments [ 1 8 — 2 0 ] . T h e hierarchical n a t u r e of fluctuations in the native state at equilibrium h a s b e e n established based on these d a t a , a n d t h e possibility that they may represent folding intermediates of variable complexity has been suggested. During t h e process of folding the appearance of stable structures of larger a n d larger ©
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YESYLEVSKYY,
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DEMCHENKO,
2004
dimension should change the whole broad spectrum of collective motions [20 ]. When some group of residues forms a cluster stabilized by non-covalent inter actions, then t h e r e a p p e a r new degrees of freedom, which are the rotations a n d translations of the cluster, with dramatic reduction of conformational space avai lable for individual residues forming the cluster [21 ]. Since such mechanism seems reasonable a n d sup ported by n u m e r o u s experimental observations, have been many attempts for its modeling a n d simulation with different objectives a n d on different level of complexity [7—9, 22, 2 3 ] . T h e extreme complexity of t h e folding process justifies t h e development of highly simplified models [ 2 4 — 2 7 ] . Lacking t h e details, these models should be able to observe t h e role of basic physical principles otherwise h i d d e n by atomic description a n d capture essential elementary events of t h e folding. T h e most popular examples of simplified models a r e the lattice models, in which t h e residues a r e represented by beads connected by rigid «sticks». In these models the motion of a chain is restricted to a lattice, a n d the only allowed interactions are the interactions with the nearest neighbors. T h e folding of lattice proteins is
CLUSTERING
usually simulated by different Monte Carlo
