^{1}

^{2}

^{2}

^{*}

Conceived and designed the experiments: JSH MBK BLdG. Performed the experiments: JSH MBK. Analyzed the data: JSH MBK. Wrote the paper: JSH BLdG.

The authors have declared that no competing interests exist.

We present molecular dynamics simulations of unliganded human hemoglobin (Hb) A under physiological conditions, starting from the

As the prototypic allosteric protein, human hemoglobin (Hb) has drawn extensive scientific efforts for many decades. Human Hb exists in two quaternary conformations, the low-affinity (or deoxy)

Conformational transitions of allosteric proteins are fundamental to a variety of biological functions. For instance, quaternary transitions in hemoglobin (Hb) give rise to the cooperativity of ligand binding and have therefore drawn extensive and ongoing scientific interest over many decades

The stereochemical explanation of Hb cooperativity and the characterization of the transition pathway were originally based on the HbCO and deoxyHb crystal structures, corresponding to the

(A) X-ray structures of Hb in the

Extensive efforts aimed to identify the transition pathway of Hb in response to ligand dissociation

Molecular dynamics (MD) simulations can provide a full-atomistic picture of Hb and are therefore well suited to complement experimental efforts. Early MD efforts focused on the photodissociation of CO

So far, no spontaneous quaternary or tertiary transitions of Hb were observed during MD simulations, presumably since previous simulations were restricted to too short time scales. Here, we apply extensive MD simulations to investigate the deoxy

For the present study, Hb was simulated using five different initial configurations. (1) Starting from the

Initial structure | His(β)146 protonated | Time [ns] | # carried out | Salt bridges restrained | Name | Figures |

Yes | 200 | 3x | - | R.HC3-x | 2 | |

- | 200 | 3x | - | R.noHC3-x | S1 | |

- | 130 | 3x | - | R2-x | S2 | |

Yes | 200 | 3x | - | T.HC3-x | 3, 4 | |

- | 300 | 6x | - | T.noHC3-x | S3 | |

- | 50 | 20x | - | - | 5, S4 | |

Yes | 200 | 3x | During the first 100ns | T.SBres-x | S5 |

The simulations starting from the

In all simulations starting from the

(A–C) Projections of Hb structures during simulations R.HC3-1 to R.HC3-3 on the two eigenvectors derived from a PCA of the

The inability of the simulations to reach the

In contrast to the rather stable simulations starting from

(A–C) Projections of Hb structures during simulations T.HC3-1 to T.HC3-3 on the two eigenvectors derived from a PCA of the

The HC3 histidines have been shown to contribute ∼40% to the alkaline Bohr-effect

Complementary to the PCA projections and the rotRMSD measure, we have analyzed the quaternary

(A/B) Colored rods indicate the dimers and the spheres represent the center of mass (COM) of the four subunits as labeled in the panels A/B. Before analyzing the rotation of the α2/β2 dimer, the α1/β1 dimer of the structures were superimposed on the α1/β1 dimer of the

The arrows in

The simulations displaying full

Projection onto the quaternary transition vector connecting

To assess if the observed correlation between subunits and the Hb quaternary structure is a robust feature of

(A) Correlation between quaternary and tertiary transitions as averaged from six independent

The average MI between the subunits during the

Before the identification of functionally different tertiary states in the

The populations of the tertiary states

The tertiary states were computed from the projections of the subunit structures during simulation onto the tertiary difference vectors connecting the

Although the populations are presumably not fully converged within the simulation timescales, a number of significant conclusions can be drawn from

We have reported reproducible spontaneous quaternary transitions of human Hb A from the

A surprising result of our simulations is the instability of the

To further investigate the instability of the

We have analyzed the correlation between the quaternary and tertiary conformational transitions during six independent

The large sphere and square depict the quaternary

The initial structures for the simulations starting from the _{ε2} atom of His146 was protonated. The

All simulations were carried out using the Gromacs simulation software

In simulations with restrained salt bridges (T.BSres-1 to T.BSres-3), all salt bridges which are present in the ^{2}) between the respective pairs of atoms, with the potential equal to zero at the distance taken from the

The correlations between the tertiary transitions of the α and β subunits and the quaternary transition of Hb were measured using the (Shannon) mutual information (MI) _{X}_{Y}_{X}_{Y}

Computation of the mutual information

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PCA projections of Hb simulations starting from the R X-ray structure with deprotonated His(β)146. (A–C) Projections of Hb structures during simulations R.noHC3-1 to R.noHC3-3 on the two eigenvectors derived from a PCA of the

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PCA projections of Hb simulations starting from the R2 X-ray structure. (A–C) Projections of Hb structures during simulations R2-1 to R2-3 on the two eigenvectors derived from a PCA of the

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PCA projections of Hb simulations starting from the T X-ray structure with deprotonated His(β)146. (A–C, E–G) Projections of Hb structures during simulations T.noHC3-1 to T.noHC3-6 on the two eigenvectors derived from a PCA of the

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rotRMSD of six of the 20 50ns-simulations starting from

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PCA projections of Hb simulations starting from the T X-ray structure with restrained salt bridges during the first 100ns (termed T.SBres-x). During the first 100ns of these simulations, all salt bridges that are present in the

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Computation of the mutual information (MI) from a finite number of pairs of data points. The MI was computed by extrapolating to an infinite number of data points, corresponding to k = 0. For details, see

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Projection on the quaternary difference vector between the

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Motions along the two eigenvectors derived from a principal component analysis on the T, R, and R2 structures.

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The quaternary T→R transition during simulation T.HC3-3. The Hb backbone is show in cartoon representation, the heme groups are shown as sticks, and the iron atoms as spheres. The β1 and β2 subunits are colored in red and purple, respectively, and the α1 and α2 subunits in green and lime, respectively.

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