Effect of the abolition of intersubunit salt bridges on allosteric protein structural dynamics†

A salt bridge, one of the representative structural factors established by non-covalent interactions, plays a crucial role in stabilizing the structure and regulating the protein function, but its role in dynamic processes has been elusive. Here, to scrutinize the structural and functional roles of the salt bridge in the process of performing the protein function, we investigated the effects of salt bridges on the allosteric structural transition of homodimeric hemoglobin (HbI) by applying time-resolved X-ray solution scattering (TRXSS) to the K30D mutant, in which the interfacial salt bridges of the wild type (WT) are abolished. The TRXSS data of K30D are consistent with the kinetic model that requires one monomer intermediate in addition to three structurally distinct dimer intermediates (I1, I2, and I3) observed in WT and other mutants. The kinetic and structural analyses show that K30D has an accelerated biphasic transition from I2 to I3 by more than nine times compared to WT and lacks significant structural changes in the transition from R-like I2 to T-like I3 observed in WT, unveiling that the loss of the salt bridges interrupts the R–T allosteric transition of HbI. Besides, the correlation between the bimolecular CO recombination rates in K30D, WT, and other mutants reveals that the bimolecular CO recombination is abnormally decelerated in K30D, indicating that the salt bridges also affect the cooperative ligand binding in HbI. These comparisons of the structural dynamics and kinetics of K30D and WT show that the interfacial salt bridges not only assist the physical connection of two subunits but also play a critical role in the global structural signal transduction of one subunit to the other subunit via a series of well-organized structural transitions.


Data processing
Two-dimensional x-ray scattering patterns were azimuthally integrated to obtain onedimensional scattering curves as a function of the magnitude of the momentum transfer vector, . To convert the scattering angle (2θ) to q, the center-of-mass position (4 / ) sin(2 / 2) q     of the undulator spectrum was used as the reference wavelength (λ). Since a majority of scattering signal comes from solvent pairs or bulk solvent, the laser-induced scattering intensity changes are less than a few percent of the static scattering intensity. To extract the underlying scattering signal from solute molecules, we obtained time-resolved difference x-ray solution scattering curves at the time delay of t, ΔS(q, t), shown in Fig. S6 after careful normalization.
As a normalization reference, we used a q position of 2.07 Å -1 , which is the isosbestic point of the water scattering curves with respect to the temperature increase, so that the difference scattering intensity at this q value is zero. The scattering contribution arising from the solvent heating in the time-resolved difference x-ray solution scattering curves was removed by the following procedures. In Fig. S8, the solution scattering difference curve at 10 ms is presented as an example confirming that the difference scattering at late time delays is mainly attributed to solvent heating. The difference scattering curve is similar to the scattering curve arising from the water thermal heating, indicating that the contribution from transiently generated species is

General scheme for the kinetic analysis using SVD and PCA
To extract kinetics information of intermediates and their structures from ΔS(q, t), we followed the well-established procedure, which had been applied to previous TRXSS studies on WT and various mutants of HbI, consisting of kinetic analysis using singular value decomposition (SVD) and principal component analysis (PCA). First, SVD, which is a factorization method to separate the time-dependent information from the time-independent information, was performed on the ΔS(q, t) matrix for the entire time points of 100 ps -10 ms and the q range of 0. 17  of the corresponding intermediates.

SVD Analysis
To determine the kinetic model, we need to examine the number of distinct transient species in the dynamic process of interest and their associated rate coefficients. For this purpose, we applied the singular value decomposition (SVD) analysis and the subsequent kinetic analysis to our experimental data. From the experimental scattering curves measured at various time delays, we can build matrix A, where n q is the number of q points in the q t n n  scattering curve at a given time-delay point and n t is the number of time-delay points. For the data in this work, n q and n t are 406 and 33, respectively. Then, the matrix A can be decomposed while satisfying the relationship of A = USV T , where U is an matrix whose columns are q t n n  called left singular vectors (lSVs) and contain time-independent q spectra, V is an matrix t t n n  whose columns are called right singular vectors (rSVs) and contain time-dependent amplitude changes of the corresponding lSVs, and S is a diagonal matrix whose diagonal elements assigned to I 1 , I 2 , and I 3 , respectively, model (6) is the same as the kinetic framework of WT, F97Y, T72V, and I114F. It should be noted that the I 2 -to-I 3 biphasic transition originates from the existence of both fully photolyzed and partially photolyzed forms. The fully photolyzed form converts faster than the partially photolyzed form due to the allosteric effect. One cannot rule out the possibility of model (7), but we consider this model highly unlikely because it is difficult to find any reason justifying why only the dimer of K30D shows such a drastically different kinetic framework. intermediates of WT HbI in half and assuming that the same structural changes occurring in the WT dimer occur in the WT monomer (Fig. S3). Surprisingly, even if the monomer is half the dimer's size, the difference scattering intensity of the monomer is similar to that of the dimer in the q range of 0.17 -1.0 Å -1 , or even larger in certain q regions. Therefore, the kinetic analysis was performed assuming a framework that included the photoinduced structural change of the dimeric form of K30D HbI(CO) 2 and the monomeric form of K30D HbI(CO) 2 .

Assignment of time constants for bimolecular CO recombination
To discuss the kinetic model containing the monomer, we consider the issue of A TRXSS study of Mb shows that its CO recombination rate (230 mM -1 s -1 ) 15 is faster than that of WT HbI (95 mM -1 s -1 ). This consideration renders that the monomer of K30D is likely to have faster CO recombination than the dimer. Besides, it is natural that the fraction of the monomer is higher than that of the dimer under our experimental condition, and thus we can exclude model (b) where the monomer is almost absent (~0.3%, shown in Fig. S11b). (1)

Kinetic analysis
where A' is an matrix that contains the theoretical difference scattering curve  (Table S1) and extract the time-independent SADSs (Fig. 3b) and timedependent concentration changes (Fig. 3c) of the four intermediates.

Generation of the template structures for the structural analysis
Up to date, TRXSS studies on HbI have been performed with structure refinement applied with a rigid-body modeling approach using crystallographic structures as template structures. [22][23][24][25] In the case of K30D, however, this method could not be applied because crystallographic structures were not reported, unlike WT or other mutants. HbI is a homodimeric protein with two symmetric subunits consisting of 16 α-helices, 14 linkers, and two heme groups. The proportion of α-helices accounts for about 80% of the total number of residues, and the protein is considered to be a relatively rigid protein because the α-helices are closely packed together. Also, the visible absorption spectra and circular dichroism spectra of WT and K30D HbI are nearly identical to each other for both liganded and unliganded forms, indicating high similarity in the local structure near the heme pocket in WT and K30D HbI. 3 We, therefore, assumed that the backbone of WT and K30D would be quite similar to each other and generated hypothetical crystallographic structures of K30D by incorporating single amino acid residue replacements from the crystallographic structure formed at 5 ns after the photolysis of carbonyl ligand (PDB ID: 2GRZ) and the crystallographic structure of the carboxy form of WT HbI (PDB ID: 3SDH). The resulting structures were used as template structures in the structure refinement for K30D. The original crystallographic structures were modified using PyMol software by replacing Lys30 residues of two subunits of the HbI with Asp30 residues.

Structure refinement
The structure refinement using SADSs of all intermediates of the K30D was performed.
The positions and orientations of the rigid bodies were randomly generated based on a Monte Carlo simulation algorithm and refined to minimize the discrepancy between the theoretical difference scattering curve calculated from the refined structure and the SADSs of the dimer and monomer intermediates. For each intermediate, the refinement process was repeated for 360 different initial structures whose rigid bodies were randomly displaced from the template.
We selected 195, 167, 200, and 196 candidate structures for the I 1 , I 2 , I 3 and i, respectively, which exhibited χ 2 values (a quantified value of the discrepancy between the experimental and theoretical difference scattering curves) below a certain threshold. The theoretical difference scattering curves for the refined candidate structures are shown in Fig. S4.

Supporting information table and figures
Table S1 Kinetic parameters obtained from the kinetic analysis of TRXSS data of K30D.               The SAPPA kinetic profiles of (a) shown in a different style to facilitate easy comparison with the kinetic profiles from candidate kinetic models of (c). The profiles of the first, second, and third basis components are shown in black, red, and blue, respectively.
(c) The simulated kinetic profiles of three intermediates for the nine candidate kinetic models shown in Fig. S14. Comparison of the kinetic profiles in (c) and the SAPPA kinetic profiles in (b) show that only models (6) and (7) are compatible with the experimental data, ruling out the other models.