The free energy landscape and the folding mechanism of the C-terminal ␤-hairpin of protein G is studied by extensive replica exchange molecular dynamics simulations (40 replicas and 340 ns total simulation time), using the GROMOS96 force field and the SPC explicit water solvent. The study reveals that the system preferentially adopts a ␤-hairpin structure at biologically important temperatures, and that the helix content is low at all temperatures studied. Representing the free energy landscape as a function of several types of reaction coordinates, four local minima corresponding to the folded, partially folded, molten globule, and unfolded states are identified. The findings suggest that the folding of the ␤-hairpin occurs as the sequence: collapse of hydrophobic core 3 formation of H-bond 3 formation of the turn. Identifying the folded and molten globule states as the main conformations, the free energy landscape of the ␤-hairpin is consistent with a two-state behavior with a broad transition state. The temperature dependence of the folding-unfolding transition is investigated in some detail. The enthalpy and entropy jumps at the folding transition temperature are found to be about three times lower than the experimental estimates, indicating that the folding-unfolding transition in silico is less cooperative than its in vitro counterpart. Proteins 2005;61:795-808.

In certain physical situations, extensive interactions arise naturally in systems. We consider one such situation, namely, small-world couplings. We show that, for a fixed fraction of nonlocal couplings, synchronous chaos is always a stable attractor in the thermodynamic limit. We point out that randomness helps synchronization. We also show that there is a size dependent bifurcation in the collective behavior in such systems.

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Using a histogram Monte Carlo method and nonuniversal metric factors of a recent Letter [Phys. Rev. Lett. 75, 193 (1995)], we find that the probability for the appearance of n, n 1, 2,. .. , top to bottom percolating clusters on finite square, planar triangular, and honeycomb lattices falls on the same universal scaling functions, which show interesting behavior as the aspect ratio of the lattice increases. Our results suggest many interesting problems for further research.

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Recent experiments have shown that the Taiwan mutation (D7H) slows the fibril formation of amyloid peptides Aβ40 and Aβ42. Motivated by this finding, we have studied the influence of D7H mutation on structures of Aβ peptide monomers using the replica exchange molecular dynamics simulations with OPLS force field and implicit water model. Our study reveals that the mechanism behind modulation of aggregation rates is associated with decrease of β-content and dynamics of the salt bridge D23-K28. Estimating the bending free energy of this salt bridge, we have found that, in agreement with the experiments, the fibril formation rate of both peptides Aβ40 and Aβ42 is reduced about two times by mutation.

In the calculation of thermodynamic properties and three-dimensional structures of macromolecules, such as proteins, it is important to have an efficient algorithm for computing the solvent-accessible surface area of macromolecules. Here, we propose a new analytical method for this purpose. In the proposed algorithm we consider the transformation that maps the spherical circles formed by intersection of the atomic surfaces in three-dimensional space onto the circles on a two-dimensional plane, and the problem of computing the solvent-accessible surface area is reduced to the problem of computing the corresponding curve integrals on the plane. This allows to consider only the integrals along the circular trajectories on the plane. The algorithm is suitable for parallelization. Testings on many proteins as well as the comparison to the other analogous algorithms have shown that our method is accurate and efficient.

We consider a directed compact site lattice animal problem on the d-dimensional hypercubic lattice, and establish its equivalence with (i) the infinite-state Potts model and (ii) the enumeration of ͑d 2 1͒dimensional restricted partitions of an integer. The directed compact lattice animal problem is solved exactly in d 2, 3 using known solutions of the enumeration problem. The maximum number of lattice animals of size n grows as exp͑cn ͑d21͒͞d ͒. Also, the infinite-state Potts model solution leads to a conjectured limiting form for the generating function of restricted partitions for d . 3, the latter an unsolved problem in number theory. PACS numbers: 05.50.+q An intriguing aspect of lattice statistics is that seemingly totally different problems are sometimes related to each other, and that the solution of one problem can often be used to solve other outstanding unsolved problems. An example is the d 2 directed lattice site animals solved by Dhar [1] who used Baxter's exact solution of a hardsquare lattice gas model [2,3] to deduce its solution. In this Letter we consider a directed compact site lattice animal problem in d dimensions, and show that it is related to (i) the infinite-state Potts model in d dimensions and (ii) the enumeration of ͑d 2 1͒-dimensional restricted partitions of an integer. The known solutions of restricted partitions in two and three dimensions [4,5] now solve the corresponding compact lattice animal problems, and, similarly, the established solution of the infinite-state Potts model [6] leads to a conjectured limiting form for the generating function of restricted partitions for d . 3, which is an outstanding unsolved problem in number theory. For clarity of presentation, we present details of discussions for d 2. Considerations in higher dimensions are similar, and relevant results will be given.Directed compact lattice animals and restricted partitions of an integer.-Starting from the origin {1,1} of an L 1 3 L 2 simple quartic lattice L whose columns and rows are numbered, respectively, by i 1, . . . , L 1 and j 1, . . . , L 2 , a site animal grows in the directions of increasing i and j. In contrast to the previously considered directed animal problem [1] for which a site ͕i, j͖ can be occupied when either the site ͕i 2 1, j͖ or the site ͕i, j 2 1͖ is occupied, we introduce a more restricted growth rule. Our rule is that a site ͕i, j͖ can be occupied only when both ͕i 2 1, j͖ and ͕i, j 2 1͖ are occupied. (When applying the growth rule, sites with coordinates i 0 or j 0 are regarded as being occupied.) Com-pared to the usual directed lattice animals [1], the present model generates compact animals since it excludes configurations with unoccupied interior sites. In addition, we keep L 1 , L 2 finite, so that there exists a maximum animal size of L 1 L 2 .Let A n ͑L 1 , L 2 ͒ be the number of distinct n-site compact animals that can grow on L . In considering animal problems, one is primarily interested in finding the asymptotic behavior A n ͑L 1 , L 2 ͒ for large n. It is clear t...