Jarek Juraszek

Rate Constant and Reaction Coordinate of Trp-Cage Folding in Explicit Water

We report rate constant calculations and a reaction coordinate analysis of the rate-limiting folding and unfolding process of the Trp-cage mini-protein in explicit solvent using transition interface sampling. Previous transition path sampling simulations revealed that in this (un)folding process the protein maintains its compact configuration, while a (de)increase of secondary structure is observed. The calculated folding rate agrees reasonably with experiment, while the unfolding rate is 10 times higher. We discuss possible origins for this mismatch. We recomputed the rates with the forward flux sampling method, and found a discrepancy of four orders of magnitude, probably caused by the methods higher sensitivity to the choice of order parameter with respect to transition interface sampling. Finally, we used the previously computed transition path-sampling ensemble to screen combinations of many order parameters for the best model of the reaction coordinate by employing likelihood maximization. We found that a combination of the root mean-square deviation of the helix and of the entire protein was, of the set of tried order parameters, the one that best describes the reaction coordination.

Molecular Mechanism of SSR128129E, an Extracellularly Acting, Small-Molecule, Allosteric Inhibitor of FGF Receptor Signaling

The fibroblast growth factor (FGF)/fibroblast growth factor receptor (FGFR) signaling network plays an important role in cell growth, survival, differentiation, and angiogenesis. Deregulation of FGFR signaling can lead to cancer development. Here, we report an FGFR inhibitor, SSR128129E (SSR), that binds to the extracellular part of the receptor. SSR does not compete with FGF for binding to FGFR but inhibits FGF-induced signaling linked to FGFR internalization in an allosteric manner, as shown by crystallography studies, nuclear magnetic resonance, Fourier transform infrared spectroscopy, molecular dynamics simulations, free energy calculations, structure-activity relationship analysis, and FGFR mutagenesis. Overall, SSR is a small molecule allosteric inhibitor of FGF/FGFR signaling, acting via binding to the extracellular part of the FGFR.

Predicting the reaction coordinates of millisecond light-induced conformational changes in photoactive yellow protein

Understanding the dynamics of large-scale conformational changes in proteins still poses a challenge for molecular simulations. We employ transition path sampling of explicit solvent molecular dynamics trajectories to obtain atomistic insight in the reaction network of the millisecond timescale partial unfolding transition in the photocycle of the bacterial sensor photoactive yellow protein. Likelihood maximization analysis predicts the best model for the reaction coordinates of each substep as well as tentative transition states, without further simulation. We find that the unfolding of the α-helical region 43–51 is followed by sequential solvent exposure of both Glu46 and the chromophore. Which of these two residues is exposed first is correlated with the presence of a salt bridge that is part of the N-terminal domain. Additional molecular dynamics simulations indicate that the exposure of the chromophore does not result in a productive pathway. We discuss several possibilities for experimental validation of these predictions. Our results open the way for studying millisecond conformational changes in other medium-sized (signaling) proteins.

Nonlinear reaction coordinate analysis in the reweighted path ensemble

We present a flexible nonlinear reaction coordinate analysis method for the transition path ensemble based on the likelihood maximization approach developed by Peters and Trout [J. Chem. Phys. 125, 054108 (2006)]. By parametrizing the reaction coordinate by a string of images in a collective variable space, we can optimize the likelihood that the string correctly models the committor data obtained from a path sampling simulation. The collective variable space with the maximum likelihood is considered to contain the best description of the reaction. The use of the reweighted path ensemble [J. Rogal et al., J. Chem. Phys. 133, 174109 (2010)] allows a complete reaction coordinate description from the initial to the final state. We illustrate the method on a z-shaped two-dimensional potential. While developed for use with path sampling, this analysis method can also be applied to regular molecular dynamics trajectories.

Free-energy-based methods for binding profile determination in a congeneric series of CDK2 inhibitors.

Free-energy pathway methods show great promise in computing the mode of action and the free energy profile associated with the binding of small molecules with proteins, but are generally very computationally demanding. Here we apply a novel approach based on metadynamics and path collective variables. We show that this combination is able to find an optimal reaction coordinate and the free energy profile of binding with explicit solvent and full flexibility, while minimizing human intervention and computational costs. We apply it to predict the binding affinity of a congeneric series of 5 CDK2 inhibitors. The predicted binding free energy profiles are in accordance with experiment.

The reweighted path ensemble

We introduce a reweighting scheme for the path ensembles in the transition interface sampling framework. The reweighting allows for the analysis of free energy landscapes and committor projections in any collective variable space. We illustrate the reweighting scheme on a two dimensional potential with a nonlinear reaction coordinate and on a more realistic simulation of the Trp-cage folding process. We suggest that the reweighted path ensemble can be used to optimize possible nonlinear reaction coordinates.

Effects of a Mutation on the Folding Mechanism of a β-Hairpin

The folding mechanism of a protein is determined by its primary sequence. Yet, how the mechanism is changed by a mutation is still poorly understood, even for basic secondary structures such as beta-hairpins. We perform an extensive simulation study of the effects of mutating the GB1 beta-hairpin into Trpzip4 (Y5W, F12W, V14W) on the folding mechanism. While Trpzip4 has a much more stable native state due to very strong hydrophobic interactions of the side chains, its folding rate does not differ significantly from the wild type beta-hairpin. We sample the free-energy landscapes of both hairpins with Replica Exchange Molecular Dynamics (REMD) and identify the four (meta)stable states (U, H, F, and N). Using Transition Path Sampling (TPS), we then harvest ensembles of unbiased pathways between the H and F states and between the F and N states to investigate the unbiased folding mechanisms. In both hairpins, the hydrophobic collapse (U-H) is followed by the middle hydrogen bond formation (H-F), and finally a closing of the strands in a zipper-like fashion (F-N). For the Trpzip4, the path ensembles indicate that the final F-N step is much more difficult than for GB1 and involves partial unfolding, rezipping of hydrogen bonds, and rearrangement of the Trp-14 side chain. For the rate-limiting (H-F) step, the path ensembles show that in GB1 desolvation and strand closure go hand in hand, while in Trpzip4 desolvation is decoupled from strand closure. Nevertheless, likelihood maximization shows that the reaction coordinate for both hairpins remains the interstrand distance. We conclude that the folding mechanism of both hairpins is a combination of hydrophobic collapse and zipping of hydrogen bonds but that the zipper mechanism is more visible in Trpzip4. A major difference between the two hairpins is that in the transition state of the rate-limiting step for Trpzip4 one tryptophan is exposed to the solvent due to steric hindrance, making the folding mechanism more complex and leading to an increased F-N barrier. Thus, our results show in atomistic detail how a mutation leads to a different folding mechanism and results in a more frustrated folding free-energy landscape.

Un)Folding Mechanisms of the FBP28 WW Domain in Explicit Solvent Revealed by Multiple Rare Event Simulation Methods

We report a numerical study of the (un)folding routes of the truncated FBP28 WW domain at ambient conditions using a combination of four advanced rare event molecular simulation techniques. We explore the free energy landscape of the native state, the unfolded state, and possible intermediates, with replica exchange molecular dynamics. Subsequent application of bias-exchange metadynamics yields three tentative unfolding pathways at room temperature. Using these paths to initiate a transition path sampling simulation reveals the existence of two major folding routes, differing in the formation order of the two main hairpins, and in hydrophobic side-chain interactions. Having established that the hairpin strand separation distances can act as reasonable reaction coordinates, we employ metadynamics to compute the unfolding barriers and find that the barrier with the lowest free energy corresponds with the most likely pathway found by transition path sampling. The unfolding barrier at 300 K is approximately 17 k(B)T approximately 42 kJ/mol, in agreement with the experimental unfolding rate constant. This work shows that combining several powerful simulation techniques provides a more complete understanding of the kinetic mechanism of protein folding.

Predicting the Reaction Coordinates of Millisecond Light-Induced Conformational Changes in Photoactive Yellow Protein

Understanding the dynamics of large-scale conformational changes in proteins still poses a challenge for molecular simulation, as such processes occur on long time scales. The transition path sampling method aims to sample reactive paths connecting two stable states. We used transition path sampling to investigate the mechanisms underlying the millisecond timescale partial unfolding transition in the photocycle of the bacterial sensor Photoactive Yellow Protein. This reaction is characterized by loss of alpha-helical structure and solvent exposure of the chromophore binding pocket. Advanced analysis methods predict the best model for the reaction coordinates of each step in the unfolding reactions as well as tentative transition states.We find that the unfolding of the alpha-helical region 43-51 is followed by sequential solvent exposure of Glu46 and the chromophore. Solvent exposure of the chromophore can also occur first, but is a dead-end route. Which of these two residues is exposed first, is correlated with the presence of a salt bridge that is part of the N-terminal domain.

Sampling the unfolding pathways towards the signaling state of Photoactive Yellow Protein

When receiving a signal trigger, sensor proteins undergo conformational changes resulting in the formation of a signaling state. Photoactive Yellow Protein (PYP) is a bacterial blue light sensor, 125 amino acids in size, including para-coumaric acid as a chromophore. Upon absorbing a blue-light photon, PYP undergoes a series of rearrangements to form a signaling state. The last step in this process is partial unfolding of the protein, occurring on a sub-millisecond timescale.Molecular simulation can provide detailed insight into the mechanisms underlying protein conformational changes and is complementary to experiments. Studying a protein folding reaction at atomistic resolution with conventional atomistic Molecular Dynamics (MD) is unpractical due to the long time scales involved. These long time scales originate from the presence of local free energy minima from which it is not trivial to escape.Advanced simulations enabled us to investigate the equilibrium characteristics, as well as the dynamical pathways of conformational changes linked to the formation of the signaling state of PYP.Replica exchange MD resulted in the identification of several intermediates during the light induced unfolding. Using these state as input for transition path sampling and subsequent reaction coordinate analysis led to new mechanistic insights in this conformational change. The conformational change starts with the unfolding of a helix in the chromophore binding pocket, followed by the solvent exposure of either the chromophore or glutamate at position 46. Furthermore, our simulations indicate that it is more likely that Glu46 becomes solvent exposed first.To our knowledge this is the first simulation study of unbiased dynamical pathways of a sub-millisecond timescale process of a biologically relevant protein. This work opens up the way for investigating conformational changes in other interesting systems in high detail.