pH and the Breast Cancer Recurrent Mutation D538G Affect the Process of Activation of Estrogen Receptor α.

Estrogen receptor α (ERα) is a regulatory protein that can access a set of distinct structural configurations. ERα undergoes extensive remodeling as it interacts with different agonists and antagonists, as well as transcription activation and repression factors. Moreover, breast cancer tumors resistant to hormone therapy have been associated with the imbalance between the active and inactive ERα states. Cancer-activating mutations in ERα play a crucial role in this imbalance and can promote the progression of cancer. However, the rate of this progression can also be increased by dysregulated pH in the tumor microenvironment. Many molecular aspects of the process of activation of ERα that can be affected by these pH changes and mutations are still unclear. Thus, we applied computational and experimental techniques to explore the activation process dynamics of ER for environments with different pHs and in the presence of one of the most recurrent cancer-activating mutations, D538G. Our results indicated that the effect of the pH increase associated with the D538G mutation promoted a robust stabilization of the active state of ER. We were also able to determine the main protein regions that have the most potential to influence the activation process under different pH conditions, which may provide targets of future therapeutics for the treatment of hormone-resistant breast cancer tumors. Finally, the approach used here can be applied for proteins associated with the proliferation of other cancer types, which can also have their function affected by small pH changes.

Distinguishing Biomolecular Pathways and Metastable States.

Protein folding occurs in a high dimensional phase space, and the representation of the associated energy landscape is nontrivial. A widely applied approach to studying folding landscapes is to describe the dynamics along a small number of reaction coordinates. However, other strategies involve more elaborate analysis of the complex phase space. There have been many attempts to obtain a more detailed representation of all available conformations for a given system. In this work, we address this problem using a metric based on internal distances between amino acids to describe the differences between any two conformations. Using an effective projection method, we are able to go beyond the typical one-dimensional representation and provide intuitive two dimensional visualizations of the landscape. We refer to this method as the energy landscape visualization method (ELViM). We have applied this methodology using a Cα structure-based model to study the folding of two well-known proteins: SH3 domain and protein-A. Our visualization method yields a detailed description of the folding process, making possible the identification of transition state regions, and establishing the paths that lead to the native state. For SH3, we have analyzed structural differences in the distribution of folding routes. The competition between the native and mirror structures in protein A is also discussed. Finally, the method is applied to study conformational changes in the protein elongation factor thermally unstable. Distinct features of ELViM are that it does not require or assume a reaction coordinate, and it does not require analysis of kinetic aspects of the system.

Drift-diffusion (DrDiff) framework determines kinetics and thermodynamics of two-state folding trajectory and tunes diffusion models.

The stochastic drift-diffusion (DrDiff) theory is an approach used to characterize the dynamical properties of simulation data. With new features in transition times analyses, the framework characterized the thermodynamic free-energy profile [F(Q)], the folding time (τf), and transition path time (τTP) by determining the coordinate-dependent drift-velocity [v(Q)] and diffusion [D(Q)] coefficients from trajectory time traces. In order to explore the DrDiff approach and to tune it with two other methods (Bayesian analysis and fep1D algorithm), a numerical integration of the Langevin equation with known D(Q) and F(Q) was performed and the inputted coefficients were recovered with success by the diffusion models. DrDiff was also applied to investigate the prion protein (PrP) kinetics and thermodynamics by analyzing folding/unfolding simulations. The protein structure-based model, the well-known Go¯-model, was employed in a coarse-grained Cα level to generate long constant-temperature time series. PrP was chosen due to recent experimental single-molecule studies in D and τTP that stressed the importance and the difficulty of probing these quantities and the rare transition state events related to prion misfolding and aggregation. The PrP thermodynamic double-well F(Q) profile, the "X" shape of τf(T), and the linear shape of τTP(T) were predicted with v(Q) and D(Q) obtained by the DrDiff algorithm. With the advance of single-molecule techniques, the DrDiff framework might be a useful ally for determining kinetic and thermodynamic properties by analyzing time observables of biomolecular systems. The code is freely available at https://github.com/ronaldolab/DrDiff.

The origin of nonmonotonic complex behavior and the effects of nonnative interactions on the diffusive properties of protein folding.

We present a method for calculating the configurational-dependent diffusion coefficient of a globular protein as a function of the global folding process. Using a coarse-grained structure-based model, we determined the diffusion coefficient, in reaction coordinate space, as a function of the fraction of native contacts formed Q for the cold shock protein (TmCSP). We find nonmonotonic behavior for the diffusion coefficient, with high values for the folded and unfolded ensembles and a lower range of values in the transition state ensemble. We also characterized the folding landscape associated with an energetically frustrated variant of the model. We find that a low-level of frustration can actually stabilize the native ensemble and increase the associated diffusion coefficient. These findings can be understood from a mechanistic standpoint, in that the transition state ensemble has a more homogeneous structural content when frustration is present. Additionally, these findings are consistent with earlier calculations based on lattice models of protein folding and more recent single-molecule fluorescence measurements.

Coordinate and time-dependent diffusion dynamics in protein folding.

We developed both analytical and simulation methods to explore the diffusion dynamics in protein folding. We found the diffusion as a quantitative measure of escape from local traps along the protein folding funnel with chosen reaction coordinates has two remarkable effects on kinetics. At a fixed coordinate, local escape time depends on the distribution of barriers around it, therefore the diffusion is often time distributed. On the other hand, the environments (local escape barriers) change along the coordinates, therefore diffusion is coordinate dependent. The effects of time-dependent diffusion on folding can lead to non-exponential kinetics and non-Poisson statistics of folding time distribution. The effects of coordinate dependent diffusion on folding can lead to the change of the kinetic barrier height as well as the position of the corresponding transition state and therefore modify the folding kinetic rates as well as the kinetic routes. Our analytical models for folding are based on a generalized Fokker-Planck diffusion equation with diffusion coefficient both dependent on coordinate and time. Our simulation for folding are based on structure-based folding models with a specific fast folding protein CspTm studied experimentally on diffusion and folding with single molecules. The coordinate and time-dependent diffusion are especially important to be considered in fast folding and single molecule studies, when there is a small or no free energy barrier and kinetics is controlled by diffusion while underlying statistics of kinetics become important. Including the coordinate dependence of diffusion will challenge the transition state theory of protein folding. The classical transition state theory will have to be modified to be consistent. The more detailed folding mechanistic studies involving phi value analysis based on the classical transition state theory will also have to be quantitatively modified. Complex kinetics with multiple time scales may allow us not only to explore the folding kinetics but also probe the local landscape and barrier height distribution with single-molecule experiments.