Rank and k-nullity of contact manifolds

We prove that the dimension of the 1-nullity distribution N(1) on a closed Sasakian manifold M of rankl is at least equal to 2l−1 provided that M has an isolated closed characteristic. The result is then used to provide some examples of k-contact manifolds which are not Sasakian. On a closed, 2n+1-dimensional Sasakian manifold of positive bisectional curvature, we show that either the dimension of N(1) is less than or equal to n+1 or N(1) is the entire tangent bundle TM. In the latter case, the Sasakian manifold Mis isometric to a quotient of the Euclidean sphere under a finite group of isometries. We also point out some interactions between k-nullity, Weinstein conjecture, and minimal unit vector fields.

Conformational dynamics associated with ligand binding to vertebrate hexa-coordinate hemoglobins

Neuroglobin (Ngb) and cytoglobin (Cygb) are two new additions to the globin family, exhibiting heme iron hexa-coordination, a disulfide bond and large internal cavities. These proteins are implicated in cytoprotection under hypoxic-ischemic conditions, but the molecular basis of their cytoprotective function is unclear. Herein, a photothermal and spectroscopic study of the interactions of diatomic ligands with Ngb, Cygb, myoglobin and hemoglobin is presented. The impact of the disulfide bond in Ngb and Cygb and role of conserved residues in Ngb His64, Val68, Cys55, Cys120 and Tyr44 on conformational dynamics associated with ligand binding/dissociation were investigated. Transient absorption and photoacoustic calorimetry studies indicate that CO photo-dissociation from Ngb leads to a volume expansion (13.4±0.9 mL mol-1), whereas a smaller volume change was determined for Ngb with reduced Cys (ΔV=4.6±0.3 mL mol-1). Furthermore, Val68 side chain regulates ligand migration between the distal pocket and internal hydrophobic cavities since Val68Phe geminate quantum yield is ∼2.7 times larger than that of WT Ngb. His64Gln and Tyr44Phe mutations alter the thermodynamic parameters associated with CO photo-release indicating that electrostatic/hydrogen binding network that includes heme propionate groups, Lys 67, His64, and Tyr 44 in Ngb modulates the energetics of CO photo-dissociation. In Cygb, CO escape from the protein matrix is fast (< 40 ns) with a ΔH of 18±2 kcal mol-1 in Cygbred, whereas disulfide bridge formation promotes a biphasic ligand escape associated with an overall enthalpy change of 9±4 kcal mol-1. Therefore, the disulfide bond modulates conformational dynamics in Ngb and Cygb. I propose that in Cygb with reduced Cys the photo-dissociated ligand escapes through the hydrophobic tunnel as occurs in Ngb, whereas the CO preferentially migrates through the His64 gate in Cygbox. To characterize Cygb surface 1,8-ANS interactions with Cygb were investigated employing fluorescence spectroscopy, ITC and docking simulations. Two 1,8-ANS binding sites were identified. One binding site is located close to the extended N-terminus of Cygb and was also identified as a binding site for oleate. Furthermore, guanidinium hydrochloride-induced unfolding studies of Cygb reveal that the disulfide bond does not impact Cygb stability, whereas binding of cyanide slightly increases the protein stability.