Therefore, we elaborate below about this important issue that has been ignored to a large extent in the literature but has been given considerable thought by us over the course of the years. II.4 On the practical definition of a microstateĬalculating populations, p m or ratios p m/ p n by the various techniques cannot be achieved without first establishing a practical definition of a microstate, which is however not trivial. This analysis requires calculating the relative populations, p m/ p n, which are also needed for a correct analysis of nuclear magnetic resonance (NMR) and x-ray data of flexible macromolecules. It is of interest, for example, to know whether the conformational change adopted by a loop (a side chain, ligand, etc.) upon protein binding has been induced by the other protein (induced fit ) or alternatively the free loop already interconverts among different microstates where one of them is selected upon binding (selected fit ). On the other hand, a peptide can populate significantly several of the most stable microstates in thermodynamic equilibrium.įree energy calculations are also required in problems which are less challenging than protein folding, i.e., in cases of intermediate flexibility, where a flexible protein segment (e.g., a side chain or a surface loop), a cyclic peptide, or a ligand bound to an enzyme populates significantly several microstates in thermodynamic equilibrium. If F 2 is also the global free energy minimum of a protein, Ω 2 is expected to describe the native microstate (assuming a perfect force field) and a simulation started from Ω 2 will keep the protein in this microstate for a long time. The figure suggests that the second microstate is the more stable among the two due to lower energy and higher entropy (Ω 2 is larger than Ω 1) hence lower free energy. The partition function Z m of microstate m is obtained by integrating exp over Ω m where F m = - k B T ln Z m is the microstate's free energy. Each microstate consists of many localized potential wells denoted intermittently by solid and dashed lines. The two large potential energy wells are defined over the corresponding microstates denoted Ω 1 and Ω 2. Schematic one-dimensional representation of part of the energy surface of a peptide or a protein, as a function of a coordinate X. It is noted further that F m of non-stable microstates, such as a transition state, might also be of interest. A central aim of computational structural biology is to fold a protein, i.e., to identify its ( single) Ω m with global minimum F m (out of trillions of microstates) – an unsolved optimization task. MD studies have shown that a molecule will visit a localized well only for a very short time (as short as several fs) while staying for a much longer time within a microstate, meaning that the microstates are of a greater physical significance than the localized wells. 1) a microstate can be represented by a sample (trajectory) generated by a local MD simulation (e.g., the α-helical region of a peptide, see further discussion in II.4 below). More specifically, this surface is “decorated” by a tremendous number of localized energy wells and “wider” ones that are defined over microstates (regions Ω m), each consisting of many localized wells ( Fig. While the difficulty in calculating the absolute S ( F) discussed above is common to all systems, biological macromolecules such as peptides and proteins, are particularly challenging due to their rugged potential energy surface, E( x). II.3 Microstates and intermediate flexibility The present article constitutes a substantial extension of a concise review appeared recently. We summarize here mainly recent developments in this area of research where the emphasis is on methodology issues and less on applications. While significant progress has been made (see reviews in ), in many cases the efficiency (or accuracy) of existing methods is unsatisfactory and the need for new ideas has kept this field highly active. However, calculation of F( S) by computer simulation is extremely difficult, and considerable attention has thus been devoted in the last 50 years to this subject. The free energy defines the binding affinities of protein-protein and protein-ligand interactions, it also quantifies many other important processes such as enzymatic reactions, electron transfer, ion transport through membranes, and the solvation of small molecules. F constitutes the criterion of stability, which is essential for studying the structure and function of peptides, proteins, nucleic acids, and other biological macromolecules. S is a measure of order where changes in the S of water lead to the hydrophobic interaction – the main driving force in protein folding. The absolute entropy, S and the absolute Helmholtz free energy, F (or G – Gibbs free energy) are fundamental quantities in statistical mechanics with a special importance in structural biology.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |