Investigation Of The Conformational Fluctuations In Multiple Flexible Protein Regions With Harmonic Linear Discriminant Analysis

Biomacromolecules often undergo significant conformational rearrangements during function.In proteins,these motions typically incorporate non-trivial,concerted rearrangement of multiple flexible regions.Mechanistic,thermodynamic,and kinetic predictions can be obtained via molecular dynamics simulations,provided that the simulation time is at least comparable to the relevant timescale of the process of interest.Due to the substantial computational cost,however,plain molecular dynamics simulations are often not sufficient,requiring the use of more advanced techniques.Central in many enhanced sampling methods is the definition of a small set of relevant degrees of freedom(collective variable,CV)that are able to describe the transitions between different metastable states of the system.In previous studies,successful applications of the harmonic linear discriminant analysis(HLDA)for constructing low-dimensional collective variables has been reported.Practical applications include chemical reactions,crystallization processes,and to drug unbinding.Here,the HLDA method is employed to study the free energy landscape of a monomeric protein around its native state.More precisely,the KRAS protein bound to GTP is investigated.The focus on the study lies in two flexible loops and the region associated with oncogenic mutations.The HLDA method is employed in the configurational space and the mutational space,providing two CV combination schemes.The first one provides a new viewpoint of the HLDA method.Different mutants are defined as different classifications and HLDA calculations are performed to obtain the optimal way to combine existing reaction coordinates in order to distinguish the behaviors of different mutants.The second one is a commonly used method,which constructs the combined reaction coordinates in the conformation space.Defining different conformational states as different classifications,HLDA calculations are performed to distinguish different conformational states.The results show that both schemes are able to successfully describe the thermodynamic properties of the K-Ras-GTP system.Microseconds-long biased simulations are performed on the wild type and on the G12 D,G12V,G12 C mutants,describe the resulting free-energy landscapes,and the current predictions are compared with previous experimental and computational studies.Together,the current results demonstrate the validity and efficiency of our HLDA-based protocol for the conformational sampling of multiple flexible regions in folded proteins.