Replica Exchange Molecular Dynamics of Diphenylalanine Amyloid Peptides in Electric Fields

Abstract

The self-assembling propensity of amyloid peptides such as diphenylalanine (FF) allows them to form ordered, nanoscale structures, with biocompatible properties important for biomedical applications. Moreover, piezoelectric properties allow FF molecules and their aggregates (e.g., FF nanotubes) to be aligned in a controlled way by the application of external electric fields. However, while the behavior of FF nanostructures emerges from the biophysical properties of the monomers, the detailed responses of individual peptides to both temperature and electric fields are not fully understood. Here, we study the temperature-dependent conformational dynamics of FF peptides solvated in explicit water molecules, an environment relevant to biomedical applications, by using an enhanced sampling method, replica exchange molecular dynamics (REMD), in conjunction with applied electric fields. Our simulations highlight and overcome possible artifacts that may occur during the setup of REMD simulations of explicitly solvated peptides in the presence of external electric fields, a problem particularly important in the case of short peptides such as FF. The presence of the external fields could overstabilize certain conformational states in one or more REMD replicas, leading to distortions of the underlying potential energy distributions observed at each temperature. This can be overcome by correcting the REMD initial conditions to include the lower-energy conformations induced by the external field. We show that the converged REMD data can be analyzed using a Markovian description of conformational states and show that a rather complex, 3-state, temperature-dependent conformational dynamics in the absence of electric fields collapses to only one of these states in the presence of the electric fields. These details on the temperature- and electric-field-dependent thermodynamic and kinetic properties of small FF amyloid peptides can be useful in understanding and devising new methods to control their aggregation-prone biophysical properties and, possibly, the structural and biophysical properties of FF molecular nanostructures.

Figure 1

Representative conformations of FF peptides in the absence of externally applied electric fields. Values of the d_ee distances (i.e., distances between the C_ζ atoms at the ends of the two side chains, in Å) are shown in black.

Figure 2

(a) Distributions of potential energy values (U, in kcal/mol) calculated from REMD simulations in the presence of an external electric field with an intensity of E = 30 kcal/(mol Å e). (b) Illustration of the problems that could occur when attempting REMD simulations in external electric fields. The presence of the field can induce some (in this case the first two) replicas to adopt conformations that are significantly lower in energy than the corresponding initial conformational states of the other replicas. This is a serious artifact, as illustrated in part a, as it changes the expected equilibrium U distributions.

Figure 3

Distributions of potential energy values (U, in kcal/mol) calculated from REMD simulations (a) at E = 0 kcal/(mol Å e) and (b) with corrected initial conditions in the presence of an external electric field with an intensity of E = 30 kcal/(mol Å e).

Figure 4

Distributions of RMSD values calculated for the heavy atoms of FF peptides for conformations from REMD simulations in the presence of external electric fields with intensities of (a) E = 0, (b) E = 30, and (c) E = 45 kcal/(mol Å e).

Figure 5

Distributions of the dipole moment magnitude (Debye units), calculated for FF peptides for conformations from REMD simulations in the presence of external electric fields with intensities of (a) E = 0, (b) E = 30, and (c) E = 45 kcal/(mol Å e).

Figure 6

Replica exchange equilibrium distributions of side chain–side chain distances of FF amyloid peptides, with no external electric field applied, (a) for each replica (R-trajectories) and (b) at each temperature (T-trajectories) of the REMD simulation set.

Figure 7

Distributions of side chain-to-side chain distances, d_ee, for simulations with an applied electric field of 30 kcal/(mol Å e), (a) for each replica (R-trajectories) and (b) at each temperature (T-trajectories) of the REMD simulation set. Note that, at this field intensity, the conformational dynamics is restricted to an extended structure with a most probable d_ee value of ∼8.9 Å.

Figure 8

Distributions of d_ee values for simulations with an applied electric field of 45 kcal/(mol Å e), (a) for each replica (R-trajectories) and (b) at each temperature (T-trajectories) of the REMD simulation set. At this field intensity, the conformational dynamics is restricted further to a single extended structure with a most probable d_ee value of ∼10 Å.

Figure 9

Representative conformations of FF amyloid peptides derived by kinetic analysis of REMD simulations at different electric fields. In the absence of electric fields, the FF peptide adopts three main Markovian conformational states, S₁, S₂, and S₃ (top), with the corresponding state probabilities (in %) given next to each state label. The corresponding equilibrium transition rates between these states (blue arrows, see text) are also shown, as numbers. These REMD rates are for the data corresponding to all the replicas (all R-trajectories). Each arrow’s thickness is proportional to the magnitude of its corresponding transition rate. On the bottom are shown the representative conformations, S₂′ and S₂″, adopted in the presence of external electric fields with intensities of E = 30 and E = 45 kcal/(mol Å e), respectively.