Gel filtration experiments suggest that Ma
Pgb* exists as a dimer in solution at the concentrations employed in all of the experiments reported herein (Figure S2
). The dimerization state of the protein in solution is further indicated by Dynamic Light Scattering analysis. Stability of the quaternary assembly is suggested by the strong interactions and the large contact surface between the two molecules in the crystallographic unit cell, which comprises mostly residues belonging to the G- and H-helices, to the H0
-helix, partly to the Z-helix and to the BC and FG hinges 
. The buried interface calculated on the dimer derived from the Ma
Pgb*crystal structure (pdb-code 2VEB) is of 1847 Å2
, with a free energy of dissociation ΔGdiss
24.8 kcal/mol (with 24 potential hydrogen bonds and 10 salt bridges across the interface) as calculated by the program PISA (http://www.ebi.ac.uk/msd-srv/prot_int/pistart.html
corresponds to the free energy difference between dissociated and associated states and, therefore, assemblies with ΔGdiss
>0 are thermodynamically stable. The dimeric structure of Ma
Pgb* is also suggested by the presence of an identical quaternary assembly in a different crystal form (pdb-code 2VEE, four dimers in the asymmetric unit) and a similar dimeric structure in the closely related globin coupled sensors 
. In particular, analysis of the dimeric interface of the globin domain of the GCS from B. Subtilis
(pdb-code 1OR4 
), indicate a buried interface area, a ΔGdiss
, and a number of potential hydrogen bonds and salt bridges across the interface (1825 Å2
, 17.6 kcal/mol, 19 and 15 respectively) comparable to those calculated for Ma
Minimal reaction scheme for the observed kinetics. After photodissociation of bound state, a mixture of MaPgb*rCO (≈70%) and MaPgb*tCO (≈30%), CO can migrate from the primary docking site (MaPgb*r:CO)1/(MaPgb*t:CO)1 to a secondary docking site (MaPgb*r:CO)2/(MaPgb*t:CO)2 or exit to the solvent (MaPgb*r + CO)/(MaPgb*t + CO). Rebinding occurs through two distinct pathways involving either MaPgb*t or MaPgb*r. Different equilibrium constants connect MaPgb*t with MaPgb*r and MaPgb*rCO with MaPgb*rCO.
Using Scheme 1 we were able to reproduce accurately the CO binding kinetics (in flash photolysis and stopped flow) for all tested experimental conditions (Ma
Pgb* in solution, Ma
Pgb* + CO gels, and COMa
Pgb* gels). Other schemes failed to describe the body of experimental data we have accumulated. reports representative fits to CO rebinding kinetics to Ma
Pgb* in solution after nanosecond laser photolysis, under selected experimental conditions. Besides showing the good agreement between the kinetic model and the experimental data, plots in also offer the time courses of the reaction intermediates, as detailed in the Figure caption. The complete list of microscopic rate constants at 20°C is given in , which also contains the activation free energies (ΔG‡
) at 20°C estimated from the activation enthalpies (ΔH‡
) and entropies (ΔS‡
) (Table S1
Representative analysis of CO rebinding kinetics to MaPgb*.
As can be appreciated from the sample fits in , migration to a temporary docking site occurs in low yield, and modulates the geminate phase in the tens of nanoseconds. The low efficiency of this reaction branch is due to comparatively high exit (kout
) and rebinding (kg,r
) rates. Population of the temporary docking site is likely coupled to some structural rearrangement early on the reaction pathway. A spectroscopic trace of this fact is identified in the early time course of the amplitude of the second SVD component, reported in panel B of . This may arise from conformational rearrangements of the aromatic residues surrounding the distal and the proximal sides, a process which may gate diffusion to the binding site. Given the short time scale over which these processes occur, it is unlikely that the location of the temporary docking site is far from the binding site. A possible candidate is the core cavity of about 75 Å3
, located between the distal and proximal haem sides 
, although the presence of four mutually hydrogen-bonded water molecules in the crystal structure suggests that the photodissociated CO may not be easily accommodated.
The value of the exit rate kout
is remarkably high, and demonstrates that the photodissociated ligand has a facile way out from the distal haem pocket, meaning that an open connections to the solvent is available, immediately after photodissociation of the ligand. The retrieved rebinding rates kin,r
are similar to those observed for other haemoglobins such as human neuroglobin 
, and plant non symbiotic haemoglobin 1 from Arabidopsis thaliana
, but larger than the values for human HbA 
and horse heart Mb 
Unlike other known haemoglobins, for which approximately 30% of the haem surface is solvent accessible, the haem in Ma
Pgb* is completely shielded from the solvent, being surrounded by the distal B-, C- and E-helices, and by the proximal F-helix. This peculiar structural feature is related to the conformation of the 1–20 N-terminal segment, and to the extended CE and FG loops 
. As a consequence of this three-dimensional outline, diatomic ligand diffusion to the haem pocket cannot exploit the well known distal His(E7)-gate, which is operative in Mb 
The two hydrophobic tunnels, identified in the three-dimensional structure 
, are the most likely candidates to support an efficient escape from the distal haem pocket and warrant high exit rate. A straight apolar protein matrix tunnel connects the protein surface to the haem distal cavity and is located between the B- and G-helices (tunnel 1). A second tunnel is located between the B- and the E-helices, and is partly defined by Tyr(B10)61 (tunnel 2). Access to neither of them appears to be restricted by the dimer contact surface. These tunnels thus provide direct connections between the haem distal pocket and the solvent in a similar fashion to what was recently reported for type 1 non symbiotic Hbs from Arabidopsis thaliana
and rice 
The analysis of extended Molecular Dynamics simulations of Ma
Pgb* dimers has shown that while tunnel 2 is always open, ligand accessibility through tunnel 1 may be regulated by Phe(145)G8, which can adopt open and closed conformations 
. Dimerization and ligand binding strongly affect the ratio between open and closed states. Sensing of the ligand is mediated by Phe(93)E11, and the steric hindrance between Phe(93)E11 and the haem bound ligand alters the structural and dynamical behavior of helices B and E, which facilitates opening of tunnel 1.
Both Phe(145)G8 side-chain mobility and the ligand sensing properties of Phe(93)E11 suggest a structural basis to understand the nature of the fast and the slow rebinding conformations. In the open conformation, tunnel 1 leaves an additional open access from the solvent, thus resulting in higher probability (kin,r) for rebinding. At variance, for the unliganded state only tunnel 2 is open and the corresponding entry rate (kin,t) is lower. Investigations on mutants at positions E11 and G8 will provide key tests to understand the functional role of the residues Phe(93)E11 and Phe(145)G8.
At present it is difficult to fully understand the structural and dynamical basis for the change in Fe affinity for CO upon ligand binding. Further computational analysis and additional experimental evidence collected with mutated proteins is necessary to gain insight into the role of specific interactions between amino acid residues in the distal pocket in tuning association and dissociation rate constants.
It is worth comparing the apparent rate constants for binding (kON
) using the retrieved microscopic rates for the two pathways, kON,t~kin,tkg,t
) with those determined from stopped flow experiments. The values we obtain are kON,r
, and compare very well with those determined by stopped flow.
On the microsecond time scales, the photodissociated protein MaPgb*r
relaxes with rate k3
towards the lower affinity state MaPgb*t
, a process which is competitive with rebinding of CO from the solvent. Given the high rebinding rates (kg,r
), and the back reaction rate k−3
, relaxation populates the slow reacting species to nearly 40–50% of the photodissociated molecules (i.e. MaPgb*rMaPgb*t
does not fully relax to equilibrium before CO rebinding occurs,). This can be visually appreciated in , where the concentration of MaPgb*t
is plotted as a function of time (magenta curves). The microscopic rates k−3
define an equilibrium constant of 3 for the reaction MaPgb*rMaPgb*t
, showing that at equilibrium a substantial fraction (more than 70%) of the deoxy molecules are in the slow rebinding conformation MaPgb*t
. An identical equilibrium exists between (MaPgb*r:CO
(equilibrium constant k2
2.4). The estimated equilibrium constant affords populations of fast (25%) and slow (75%) rebinding species which are roughly in agreement with the population of the fast and slow rebinding species observed in stopped flow experiments.
Structural relaxation from time resolved spectra and numerical analysis of CO rebinding.
The corresponding equilibrium for the internal rates k−1
is more difficult to assess but suggests that COMaPgb*r
is favored over COMaPgb*t
in the presence of the ligand (equilibrium constant k1
0.3). Consistently, this figure compares well with the equilibrium constant determined from the fractions of slow and fast phases in the CO dissociation kinetics (0.49).
Relaxation of the equilibrium between species MaPgb*r and MaPgb*t can be visually appreciated in . The magenta lines clearly show that MaPgb*t is formed to a larger extent when the CO concentration is decreased () and that formation and decay of this species is a thermally activated process (both forward and reverse reactions become faster as temperature is increased, ).
Gel experiments allow to slightly but significantly affect the equilibrium between MaPgb*r
. In comparison to the experiments in solution (for which k3
3), relaxation of MaPgb*r
is kinetically favored in MaPgb*+CO gels, with the rate k3
increasing to 105
(and the equilibrium constant to 4.4). On the contrary, for COMa
Pgb* gels the equilibrium is slightly shifted towards MaPgb*r
, the equilibrium constant decreasing to 2.8.
This effect can be clearly distinguished in , where the time course of MaPgb*t is shown for MaPgb* solutions, COMaPgb* gels and MaPgb* + CO gels. The combination of rate constants is such that MaPgb*t is formed to a maximum extent after photolysis of MaPgb* + CO gels, while MaPgb*t is formed with the lowest efficiency for COMaPgb* gels. The case of COMaPgb* solutions appears as an intermediate case.
also compares the time courses of MaPgb*t
with the time evolution of the amplitude of the second spectral component retrieved from the SVD analysis (already reported in ). The striking similarity of the time courses is a strong indication that the spectral change obtained from the time resolved spectra reflects the structural relaxation leading the protein from MaPgb*r
. A non perfect matching between the black dotted curve and the progress curve for MaPgb*t
retrieved for COMa
Pgb* solutions most likely arises from a maybe too drastic assumption that structural relaxation is a purely exponential process. Fitting of the second SVD component is best obtained with a sum of stretching exponential relaxations (Figure S5
). This supports the idea that the structural relaxation is extended in time in a similar fashion to what is observed for Mb 
and human HbA 
The substantial free energy barriers for the forward and reverse rates of the tertiary relaxation are mostly entropic, with only modest (k−3
) or negligible (k−1
) enthalpic contributions (Table S1
). This is an indication that the conformational change does not involve major rearrangements of the structure. For comparison, coordination (and dissociation) of the haem iron by the distal His, a process involving substantial molecular reshaping, has enthalpic barriers on the order of 14.1±0.9 kcal/mol (17±3 kcal/mol for the dissociation) for human Cygb 
and 13 kcal/mol (18 kcal/mol for the dissociation) for human Ngb 
As expected, free energy barriers indicate that MaPgb*t is more stable than MaPgb*r, while COMaPgb*r is more stable than COMaPgb*t.
Activation energies for the forward and reverse rates allow to build a free energy diagram for the reaction scheme (). The barrier between MaPgb*t and (MaPgb*t:CO)1 is larger than the corresponding barrier separating MaPgb*r and (MaPgb*r:CO)1, accounting for the higher second order rebinding rate observed for the latter reaction. The free energies of the unliganded species are lower for MaPgb*t than for MaPgb*r, in agreement with the idea that in the absence of an exogenous ligand the protein spontaneously relaxes towards the conformation with lower binding and higher dissociation rates, resulting in lower affinity for CO. The reverse occurs for the liganded species.