Dependence of folding rates on protein length

Using three-dimensional Go lattice models with side chains for proteins, we investigate the dependence of folding times on protein length. In agreement with previous theoretical predictions, we find that the folding time grows as a power law with the chain length N with exponent $\lambda \approx 3.6$ for the Go model, in which all native interactions (i.e., between all side chains and backbone atoms) are uniform. If the interactions between side chains are given by pairwise statistical potentials, which introduce heterogeneity in the contact energies, then the power law fits yield large $\lambda$ values that typically signifies a crossover to an underlying activated process. Accordingly, the dependence of folding time is best described by the stretched exponential \exp(\sqrt{N}). The study also shows that the incorporation of side chains considerably slows down folding by introducing energetic and topological frustration.Comment: 6 pages, 5 eps figure

ABSENCE OF REENTRANCE IN THE TWO-DIMENSIONAL XY-MODEL WITH RANDOM PHASE SHIFT

We show, that the 2D XY-model with random phase shifts exhibits for low temperature and small disorder a phase with quasi-long-range order, and that the transition to the disordered phase is {\it not} reentrant. These results are obtained by heuristic arguments, an analytical renormalization group calculation, and a numerical Migdal-Kadanoff renormalization group treatment. Previous predictions of reentrance are found to fail due to an overestimation of the vortex pair density as a consequence of independent dipole approximations. At positions, where vortex pairs are energetically favored by disorder, their statistics becomes effectively fermionic. The results may have implications for a large number of related models.Comment: 5 pages, latex, with 2 figures, one author added, minor text changes, to be published in J. de Physique

MECHANISM OF OLIGOMERIZATION OF SHORT PEPTIDES

Nonˇbrillar soluble oligomers, which are likely to be transient intermediates in the transitions from monomers to amyloidˇbrils, may be the toxic species in Alzheimer's disease. For this reason it is very important to understand early events that direct assembly of amyloidogenic peptides. Using all-atom simulations with the GROMOS96 forceˇeld 43a1 in explicit water we have recently shown that the oligomerization of Aβ16−22 peptides obeys the dock-lock mechanism. We have also proposed a toy lattice model which allows us to ascertain this conclusion using a much larger number of monomers. In this contribution we review our all-atom as well as lattice simulation results on the dock-lock mechanism of short peptides which is probably a generic mechanism forˇbril elongation of proteins and long peptides. ¥Ë¨¡·¨²²Ö·´Ò¥ · ¸É¢μ·¨³Ò¥ 첨£μ³¥·Ò, ±μÉμ·Ò¥, ¢¥·μÖÉ´μ, Ö¢²ÖÕÉ¸Ö ±μ·μÉ±μ¦¨¢ÊШ³É ¥·³¥¤¨ É ³¨, ³μ£ÊÉ ¡ÒÉÓ Éμ±¸¨Î´Ò³¨¢Ò¤¥²¥´¨Ö³¨ ¶·¨¡μ²¥ §´¨²ÓÍ£¥°³¥· . μ ÔÉμ° ¶·¨-Ψ´¥ μÎ¥´Ó ¢ ¦´μ¨¸¸²¥¤μ¢ ÉÓ ¶¥·¢¨Î´Ò¥ Ö¢²¥´¨Ö, ±μÉμ·Ò¥ Ê ¶· ¢²ÖÕÉ ¶·μÍ¥¸¸μ³ μ¡· §μ¢ ´¨Ö ˨¡·¨²²Ö·´μ£μ¸μ¸ÉμÖ´¨Ö ¤²Ö ¶¥ ¶É¨¤μ¢ ³¨²μ¨¤ .ˆ¸ ¶μ²Ó §ÊÖ ¶μ²´μ Éμ³´Ò¥¸¨³Ê²Öͨ¨¢ ¶ ±¥É¥ GROMOS96¸¸¨²μ¢Ò³ ¶μ²¥³ 43 1 ¢ ¢μ¤¥, ³Ò´¥¤ ¢´μ ¶μ± § ²¨, ÎÉμ ¶·μÍ¥¸¸μ²¨£μ³¥·¨ § ͨ ¶ ¥ ¶É¨¤μ¢ Aβ16−22 ¶μ¤Î¨´Ö¥É¸Ö ¤μ±-²μ±-³¥Ì ´¨ §³Ê. ' ±¦¥ ³Ò ¶·¥¤²μ¦¨²¨¨£·ÊϥδÊÕ ·¥Ï¥-ÉμδÊÕ ³μ¤¥²Ó, ¶μ §¢μ²ÖÕÐÊÕ¨ §ÊÎ ÉÓ £μ· §¤μ ¡μ²ÓÏ¥¥ Ψ¸²μ ³μ´μ³¥·μ¢¨¤ ÕÐÊÕ Ê¢¥·¥´´μ¸ÉÓ ¢´ ¤¥¦´μ¸É¨ÔÉμ£μ ³¥Ì ´¨ §³ . ‚ · ¡μÉ¥ ¶·¥¤¸É ¢²¥´Ò ·¥ §Ê²ÓÉ ÉÒ, ¶μ²ÊÎ¥´´Ò¥¸ ¶μ³μÐÓÕ ± ± ¶μ²´μ Éμ³´ÒÌ, É ±¨·¥Ï¥ÉμδÒÌ ³μ¤¥²¥°. ´¨ ¶μ¤É¢¥·¦¤ ÕÉ ³¥Ì ´¨ §³ ¤μ±-²μ± ¤²Ö ±μ·μɱ¨Ì ¶¥ ¶É¨¤μ¢,¨, ¢¥·μÖÉ´μ, ÔÉμÉ ³¥Ì ´¨ §³ É ±¦¥ ¶·¨³¥´¨³ ± μ¡· §μ¢ ´¨Õ ˨¡·¨²²μ¢¨ § ¡¥²±μ¢¤ ²¨´´ÒÌ ¶¥ ¶É¨¤μ¢

Probing the Mechanisms of Fibril Formation Using Lattice Models

Using exhaustive Monte Carlo simulations we study the kinetics and mechanism of fibril formation using lattice models as a function of temperature and the number of chains. While these models are, at best, caricatures of peptides, we show that a number of generic features thought to govern fibril assembly are present in the toy model. The monomer, which contains eight beads made from three letters (hydrophobic, polar, and charged), adopts a compact conformation in the native state. The kinetics of fibril assembly occurs in three distinct stages. In each stage there is a cascade of events that transforms the monomers and oligomers to ordered structures. In the first "burst" stage highly mobile oligomers of varying sizes form. The conversion to the aggregation-prone conformation occurs within the oligomers during the second stage. As time progresses, a dominant cluster emerges that contains a majority of the chains. In the final stage, the aggregation-prone conformation particles serve as a template onto which smaller oligomers or monomers can dock and undergo conversion to fibril structures. The overall time for growth in the latter stages is well described by the Lifshitz-Slyazov growth kinetics for crystallization from super-saturated solutions.Comment: 27 pages, 6 figure