Coarse Master Equations for Binding Kinetics of Amyloid Peptide Dimers

Abstract

We characterize the kinetics of dimer formation of the short amyloid microcrystal-forming tetrapeptides NNQQ by constructing coarse master equations for the conformational dynamics of the system, using temperature replica-exchange molecular dynamics (REMD) simulations. We minimize the effects of Kramers-type recrossings by assigning conformational states based on their sequential time evolution. Transition rates are further estimated from short-time state propagators by maximizing the likelihood that the extracted rates agree with the observed atomistic trajectories without any a priori assumptions about their temperature dependence. Here, we evaluate the rates for both continuous replica trajectories that visit different temperatures and for discontinuous data corresponding to each REMD temperature. While the binding-unbinding kinetic process is clearly Markovian, the conformational dynamics of the bound NNQQ dimer has a complex character. Our kinetic analysis allows us to discriminate between short-lived encounter pairs and strongly bound conformational states. The conformational dynamics of NNQQ dimers supports a kinetically driven aggregation mechanism, in agreement with the polymorphic character reported for amyloid aggregates such as microcrystals and fibrils.

Peptide dimerization-dissociation rates from replica exchange molecular dynamics

“…Here, the states were assigned by following each replica at different temperatures, using a transition based assignment (TBA) method described and used in previous studies. 18,21,22 Our analysis of the NNQQ dimer conformational dynamics follows the approach presented in Ref. 18, and is summarized also in Fig.…”

“…7,18 Here, we use the direct transition counting (DTC) of Refs. 11 and 12 in its simplest form as a method for calculating transition rates from REMD trajectories that is easier to implement and leads to similarly accurate temperature-dependent rates as compared to the alternative, more complex and indirect methods.…”

“…11 and 12 in its simplest form as a method for calculating transition rates from REMD trajectories that is easier to implement and leads to similarly accurate temperature-dependent rates as compared to the alternative, more complex and indirect methods. 7,18 We compare the DTC results to those of the maximum likelihood propagator based (MLPB) method. We apply both methods (i.e., DTC and MLPB) to all-atom REMD simulations of dimerization of computationally and experimentally-relevant amyloid-forming NNQQ tetrapetides, 8,19 in explicit waterone of the smallest two-state-like systems featuring peptide-peptide interactions that is, nevertheless, challenging to analyze systematically using REMD.…”

“…We apply both methods (i.e., DTC and MLPB) to all-atom REMD simulations of dimerization of computationally and experimentally-relevant amyloid-forming NNQQ tetrapetides, 8,19 in explicit waterone of the smallest two-state-like systems featuring peptide-peptide interactions that is, nevertheless, challenging to analyze systematically using REMD. 18 We validate the rates extracted using the DTC method both by comparison to the corresponding MLPB rates and by analyzing the decay rates of the state autocorrelation functions of the system. [20][21][22] We assess the corresponding REMD efficiency, 23 and we obtain remarkably good agreement with the theoretically predicted errors in estimating the dimer and dissociated populations.…”

Combining pressure and temperature control in dynamics on energy landscapes

“…The determination of such regions and flows requires finding the minima of the landscape and measuring the local volume in state space contained within the basins of the landscape, and furthermore the analysis of the connectivity of the landscape including the derivation of the energetic, entropic and kinetic barriers [10,28] that separate individual minima and the multi-minima basins [2]. In the a e-mail: c.schoen@fkf.mpg.de literature, one finds two complementary approaches to identifying such landscape features: indirectly via extraction from long molecular dynamics [29][30][31] and Monte Carlo simulations [32] or even from long time sequences of experimental signals [33,34], or directly from the landscape itself using various global optimization and exploration algorithms [23]. Of course, in practice, combinations of these methods are often employed, depending on the type of system and objective of the study.…”