Microcanonical Analyses of Peptide Aggregation Processes

Abstract

We propose the use of microcanonical analyses for numerical studies of peptide aggregation transitions. Performing multicanonical Monte Carlo simulations of a simple hydrophobic-polar continuum model for interacting heteropolymers of finite length, we find that the microcanonical entropy behaves convex in the transition region, leading to a negative microcanonical specific heat. As this effect is also seen in first-order-like transitions of other finite systems, our results provide clear evidence for recent hints that the characterisation of phase separation in first-order-like transitions of finite systems profits from this microcanonical view.PACS numbers: 87.15.Aa, 87.15.Cc Thermodynamic phase transitions in macroscopic, infinitely large systems are typically analysed in the thermodynamic limit of a canonical ensemble, i.e., the temperature T is treated as an intensive external control parameter adjusted by the heat bath, and the total system energy E is distributed according to the BoltzmannGibbs statistics. The probability for a macrostate with energy E is given by p(E) = g(E) exp(−E/k B T )/Z, where g(E) is the density of states, Z the partition sum, and k B the Boltzmann constant. As long as the microcanonical entropy S(E) = k B ln g(E) is a concave function of E, the microcanonical (caloric) temperature T (E) = (∂S(E)/∂E) −1 for fixed volume V and particle number N is a monotonically increasing function of E. Consequently, the microcanonical specific heat2 ) is positive. The specific heat can only become negative in an energetic regime, where S(E) is convex. In this region, the caloric T (E) curve exhibits a typical backbending, which means that the system becomes colder with increasing total energy. For this reason, the temperature T is not the most appropriate control parameter and the analysis of such, in particular finite, systems is more adequately performed in the microcanonical ensemble, where the system energy E is considered as the adjustable external parameter [1,2].It is a surprising fact that the backbending effect is indeed observed in transitions with phase separation. Although this phenomenon has already been known for a long time from astrophysical systems [3], it has been widely ignored since then as somehow "exotic" effect. Recently, however, experimental evidence was found from melting studies of sodium clusters by photofragmentation [4]. Bimodality and negative specific heats are also known from nuclei fragmentation experiments and models [5,6], as well as from spin models on finite lattices which experience first-order transitions in the thermodynamic limit [7,8]. This phenomenon is also observed in a large number of other isolated finite model systems for evaporation and melting effects [9,10].In this Letter, we demonstrate the usefulness of the microcanonical ensemble for studies of the aggregation process of small proteins (peptides), which, due to the fixed inhomogeneous sequence of amino acids, are necessarily systems of finite size. Understanding protein aggregation is esse...

Microcanonical Approach to the Simulation of First-Order Phase Transitions

“…For both, we obtain accurate results in systems with more than 10 6 spins (preexisting methods handle 10 4 spins). Envisaged applications include first-order transitions with quenched disorder [16,28], colloid crystallization [29], peptide aggregation [30] and the condensation transition [11].…”

Thermodynamics of Protein Folding from Coarse-Grained Models’ Perspectives

“…Actually, a multicanonical computer simulation reveals very clear indications for a single conformational transition, the aggregation transition [86,87]. This means that the peptide-peptide aggregation and the folding into a compact peptide complex are not separate transitions (at least in this example).…”

“…A mesoscopic model for the aggregation of multiple chains can simply be defined by assuming that the same type-dependent Lennard-Jones like potentials used in the single-chain form (18) describe also the inter-monomeric interaction, i.e., the interaction among monomers of different chains [86]. For the analysis of the aggregation transition let us consider the example of a complex of two identical AB peptides with sequence AB 2 AB 2 ABAB 2 AB [86,87].…”

“…For the analysis of the aggregation transition let us consider the example of a complex of two identical AB peptides with sequence AB 2 AB 2 ABAB 2 AB [86,87]. We suppose that the aggregation of the peptides should be signaled by strong fluctuations of the relative distance of the centers of masses of the individual chains.…”

Generalized Replica Exchange Method

“…In many finite size systems, such as spins, 29 nuclei fragmentations, 30,31 model proteins, [32][33][34] and atomic clusters, 8,35,36 S͑E͒ shows a convex dip, i.e., ‫ץ‬ 2 S / ‫ץ‬E 2 Ͼ 0, 30 across the transition region, as sketched in Fig. 1͑a͒.…”