Thermodynamic and kinetic stability of the Josephin Domain closed arrangement: evidences from replica exchange molecular dynamics

Background Molecular phenomena driving pathological aggregation in neurodegenerative diseases are not completely understood yet. Peculiar is the case of Spinocerebellar Ataxia 3 (SCA3) where the conformational properties of the AT-3 N-terminal region, also called Josephin Domain (JD), play a key role in the first step of aggregation, having the JD an amyloidogenic propensity itself. For this reason, unraveling the intimate relationship between JD structural features and aggregation tendency may lead to a step forward in understanding the pathology and rationally design a cure. In this connection, computational modeling has demonstrated to be helpful in exploring the protein molecular dynamics and mechanism of action. Results Conformational dynamics of the JD is here finely investigated by replica exchange molecular dynamics simulations able to sample the microsecond time scale and to provide both a thermodynamic and kinetic description of the protein conformational changes. Accessible structural conformations of the JD have been identified in: open, intermediate and closed like arrangement. Data indicated the closed JD arrangement as the most likely protein arrangement. The protein transition from closed toward intermediate/open states was characterized by a rate constant higher than 700 ns. This result also explains the inability of classical molecular dynamics to explore transitions from closed to open JD configuration on a time scale of hundreds of nanoseconds. Conclusion This work provides the first kinetic estimation of the JD transition pathway from open-like to closed-like arrangement and vice-versa, indicating the closed-like arrangement as the most likely configuration for a JD in water environment. More widely, the importance of our results is also underscored considering that the ability to provide a kinetic description of the protein conformational changes is a scientific challenge for both experimental and theoretical approaches to date. Reviewers This article was reviewed by Oliviero Carugo, Bojan Zagrovic. Electronic supplementary material The online version of this article (doi:10.1186/s13062-016-0173-y) contains supplementary material, which is available to authorized users.


S1.1 Replica Exchange Molecular Dynamics
The 1YZB model [1,2] of JD was selected as starting point for the present work. The 1YZB model was solvated in a dodecahedron box where the minimum distance between the protein and the edge of the box was 1 nm, resulting in a molecular system of about 40000 interacting particles. 128 replicas were simulated for temperatures ranging from 300 K to 602 K in NVT ensemble, as done in several works in literature [3][4][5]. Temperatures are distributed following the exponential spacing law suggested by a number of paper [6,7], keeping the overlap of the potential energy distributions constant across the temperature space ( Figure S2). The resulting exchange probability was 0.35. The exchange attempt time interval was set to 2 ps. Each replica was simulated for 50 ns, obtaining a cumulative simulation time of 6.4 µs. It is worth noticing that JD secondary structure is highly conserved along the REMD trajectory at 310K ( Figure S2), with the exception of α2 and (partially) α3, in agreement with data coming from literature [8,9] Figure S1. Potential energy distribution among REMD simulations. Temperatures were distributed across the replicas in a geometric progression, i.e. with the same ratio used to scale each temperature from the one below it, keeping the overlap of the potential energy distributions constant across the temperature space.
Supporting Information to Thermodynamic and Kinetic Stability of the Josephin Domain Closed Arrangement: Evidences from Replica Exchange Molecular Dynamics 3 Figure S2. Secondary structure probability calculated in case of a) Josephin Domain 1YZB model [1,2] compared with b) REMD trajectory snapshots at 310 K. JD secondary structure is highly conserved along the REMD trajectory at 310K, with the exception of α2 and partially α3.

S1.2 Thermodynamic and Kinetic Estimation
In order to obtain a reliable estimate of the JD folding rates, the kinetic description developed by van der Spoel et al [10] was applied to the REMD trajectories, as described in the main text of this paper.
The fraction of closed JD sampled along the REMD trajectories is reported in Figure S3a as function of simulation time. The red curve of Figure S3a is optimized according to Equation 5 reported in the main text of the present paper. This function depends on the mix of simulations and temperatures used in the analysis, and the results show that the red curve represents a good fit of the computational data ( Figure   S3a). From these data, together with the estimation of the forward and backward rate constants for folding, a theoretical melting curve was obtained ( Figure S3b).

S1.3 Kinetics Estimation of the Josephin Domain Open-to-Closed Transition by Unbiased Molecular Dynamics
The 1YZB [1,2] model was solvated in a dodecahedron box where the minimum distance between the protein and the edge of the box was 1 nm, resulting in a molecular system of about 40000 interacting particles. The net charge of the system was neutralized by the addition of Cl − and Na + ions. The system was first minimized by 1000 steps of the Steepest Descent energy minimization algorithm and then equilibrated at a temperature of 310K [11] and 1 atm [12]. Then, 100 replicas of the system were created by associating to the system atoms initial random velocities from a Maxwell-Boltzmann distribution at 310K. For each system a 20 ns unbiased MD was carried out for a total sampling time of 2 µs.
The analysis of the scatter plot reporting each unbiased MD trajectory snapshot ( Figure S4a