We introduce a novel simulation method, model hopping, that enhances sampling of low-energy configurations in complex systems. The approach is illustrated for a protein folding problem. Thermodynamic quantities of proteins with up to 46 residues are evaluated from all-atom simulations with this method.The solution of many pharmacological and medical problems, such as rational drug design or the pathology of diseases associated with the mis-folding of proteins, requires a detailed understanding of the relation between chemical composition and structure of proteins. However, despite more than two decades of research, this so-called protein-folding problem has remained a hard computational task. This is because proteins in an all-atom representation are characterized by a rough energy landscape with a huge number of local minima separated by high energy barriers. Various numerical techniques exist that can alleviate this multiple minima problem. One popular example is parallel tempering (also known as replica exchange method) [1], a technique that was first introduced to protein studies in Ref. [2]. In its most common form, one considers an artificial system built up of N non-interacting copies of a molecule, each at a different temperature T i . In addition to standard Monte Carlo or molecular dynamics moves that affect only one copy, parallel tempering allows also the exchange of conformations between two copies i and j = i + 1 with probability w(C old → C new ) = min(1, exp(ΔβΔE)). The resulting random walk in temperature enables configurations to cross energy barriers and move out of local minima leading in this way to an enhanced sampling of lowenergy structures. Variants of parallel tempering introducing non-canonical weights have been proposed [2,3].Here, we introduce another variant of this idea, dubbed by us "model hopping" (MH), where as in the Hamilton Exchange method [4] or the Multi-Self-Overlap-Ensemble [5] the random walk in temperatures is replaced by one through an ensemble of models with slightly altered energy functions. For this we assume that the energy function can be separated in two terms: E = E A + aE B . As in parallel tempering, MH considers N non-interacting copies of the molecule, but copies are now exchanged according toHere, Δa = a j − a i and ΔE B = E B (C j ) − E B (C i ). Due to this exchange move configurations perform a random walk on a ladder of models with a 1 = 1 > a 2 > a 3 > …. > a N that differ by the relative contributions of E B to the total energy E of the molecule. For instance, barriers in the energy landscape of proteins often arise from van der Waals repulsion between atoms that come too close. Generalized-ensemble techniques circumvent the problem by performing a random walk in energy that allows crossing of these barriers. On the other hand, in MH the protein walks randomly up and down on a ladder of models with successively smaller contributions from the van der Waals energy. While the "physical" system is on one side of the ladder (at a 1 = 1), the (non-p...
We investigate the tricritical scaling behavior of the two-dimensional spin-1 Blume-Capel model by using the Wang-Landau method of measuring the joint density of states for lattice sizes up to 48×48 sites. We find that the specific heat deep in the first-order area of the phase diagram exhibits a double-peak structure of the Schottky-like anomaly appearing with the transition peak. The first-order transition curve is systematically determined by employing the method of field mixing in conjunction with finite-size scaling, showing a significant deviation from the previous data points. At the tricritical point, we characterize the tricritical exponents through finite-size-scaling analysis including the phenomenological finite-size scaling with thermodynamic variables. Our estimation of the tricritical eigenvalue exponents, yt=1.804(5), yg=0.80(1), and yh=1.925(3), provides the first Wang-Landau verification of the conjectured exact values, demonstrating the effectiveness of the density-of-states-based approach in finite-size scaling study of multicritical phenomena.
Applying the histogram reweighting method, we investigate the critical behavior of the XY model on growing scale-free networks with various degree exponents lambda. For lambda < or = 3 , the critical temperature diverges as it does for the Ising model on scale-free networks. For lambda=8 , on the other hand, we observe a second-order phase transition at finite temperature. We obtain the critical temperature T{c}=3.08(2) and the critical exponents nu=2.62(3) , gammanu=0.127(4) , and betanu=0.442(2) from a finite-size scaling analysis.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.