Biology subjects

Fujinami, D.

Publications and source records attributed to Fujinami, D..

2 recordsLinked to original sources

bioRxiv2022

Residue-based quadratic free energy relationship is a mathematical formulation of the consistency principle of protein folding

The consistency principle represents a physicochemical condition requisite for ideal protein folding. It assumes that any pair of amino acid residues in partially folded structures has an attractive short-range interaction only if the two residues are in contact within the native structure. The residue-specific equilibrium constant, K, and the residue-specific rate constant, k (forward and backward), can be determined by NMR and hydrogen-deuterium exchange studies. Linear free energy relationships (LFER) in the rate-equilibrium free energy relationship (REFER) plots (i.e., log k vs. log K) are widely seen in protein-related phenomena, but our REFER plot differs from them in that the data points are derived from one polypeptide chain under a single condition. Here, we examined the theoretical basis of the residue-based LFER. First, we derived a basic equation, {rho}ij = [1/2]({phi}i + {phi}j), from the consistency principle, where {rho}ij is the slope of the line segment that connects residues i and j in the REFER plot, and {phi}i and {phi}j are the local fractions of the native state in the transient state ensemble (TSE). Next, we showed that the general solution is the alignment of the (log K, log k) data points on a parabolic curve in the REFER plot. Importantly, unlike LFER, the quadratic free energy relationship (QFER) is compatible with the heterogenous formation of local structures in the TSE. Residue-based LFER/QFER provides a unique insight into the TSE: A foldable polypeptide chain consists of several folding units, which are consistently coupled to undergo smooth structural changes. O_TEXTBOXSignificanceThe physicochemical basis of smooth protein folding has been theoretically explained by the consistency principle. We propose that the consistency principle is formulated by the quadratic relationship in the double logarithm plot of the residue-specific equilibrium and rate constants of a polypeptide chain. The quadratic relationship offers a procedure for the experimental verification of the consistency principle. One application is a {phi}-value analysis, free from the adverse effects of mutations. These results will trigger the development of experimental techniques that enable the determination of accurate residue-specific equilibrium and kinetic parameters for analyzing the transition states of structural changes in proteins. C_TEXTBOX

biophysics↗

bioRxiv2022

Deviation from the Residue-Based Linear Free Energy Relationship Reveals a Non-Native Structure in Protein Folding

Multiprobe measurements, such as NMR and hydrogen exchange study, can provide the equilibrium constant K and kinetic rate constant k of the structural changes of a polypeptide on a per-residue basis. We previously found a linear relationship between residue-specific log K values and residuespecific log k values for the two-state topological isomerization of a 27-residue peptide. To test the general applicability of the residue-based linear free energy relationship (rbLEFR), we performed a literature search to collect residue-specific equilibrium and kinetic constants in various exchange processes, including protein folding, coupled folding and binding of intrinsically disordered peptides, and structural fluctuations of folded proteins. The good linearity in a substantial number of log-log plots proved that the rbLFER holds for the structural changes in a wide variety of protein-related phenomena. Protein molecules quickly fold into their native structures and change their conformations smoothly. Theoretical studies and molecular simulations advocate that the physicochemical basis is the consistency principle and the minimal frustration principle: Non-native structures/interactions are absent or minimized along the folding pathway. The linearity of the residue-based free energy relationship demonstrates experimentally the absence of non-native structures in transition states. In this context, the hydrogen exchange study of apomyoglobin folding intermediates is particularly interesting. We found that the residues that deviated from the linear relationship corresponded to the non-native structure, which had been identified by other experiments. The rbLFER provides a unique and practical method to probe the dynamic aspects of the transition states of protein molecules. HighlightsO_LIA collection of equilibrium and kinetic constants of structural changes of proteins C_LIO_LIResidue-based linear free energy relationship widely holds between the two constants C_LIO_LIrbLFER indicates the absence of non-ground state structures in transition states C_LIO_LIrbLFER is an experiment proof of the consistency principle of protein folding C_LIO_LIDeviations from the linear relation suggest special structures in transition states C_LI O_FIG_DISPLAY_L [Figure 1] M_FIG_DISPLAY C_FIG_DISPLAY

biophysics↗