Bacteriorhodopsin is a transmembrane protein that uses light energy, absorbed by its chromophore retinal, to pump protons from the cytoplasm of bacteria such as Halobacterium salinarium into the extracellular space. It is made up of seven alpha-helices, and in the bacterium forms natural, two-dimensional crystals called purple membranes. We have analysed these crystals by electron cryo-microscopy to obtain images of bacteriorhodopsin at 3.0 A resolution. The structure covers nearly all 248 amino acids, including loops outside the membrane, and reveals the distribution of charged residues on both sides of the membrane surface. In addition, analysis of the electron-potential map produced by this method allows the determination of the charge status of these residues. On the extracellular side, four glutamate residues surround the entrance to the proton channel, whereas on the cytoplasmic side, four aspartic acids occur in a plane at the boundary of the hydrophobic-hydrophilic interface. The negative charges produced by these aspartate residues is encircled by areas of positive charge that may facilitate accumulation and lateral movement of protons on this surface.

We derive a noncommutative U(1) and U(n) gauge theory on the fuzzy sphere from a three dimensional matrix model by expanding the model around a classical solution of the fuzzy sphere. Chern-Simons term is added in the matrix model to make the fuzzy sphere as a classical solution of the model. Majorana mass term is also added to make it supersymmetric. We consider two large N limits, one corresponding to a gauge theory on a commutative sphere and the other to that on a noncommutative plane. We also investigate stability of the fuzzy sphere by calculating one-loop effective action around classical solutions. In the final part of this paper, we consider another matrix model which gives a supersymmetric gauge theory on the fuzzy sphere. In this matrix model, only Chern-Simons term is added and supersymmetry transformation is modified.

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Purple membrane suspensions change their color to blue and the absorption maximum shifts to 60% nm when the membrane is deionized on a cation exchange column or when it is washed first with 3 2 N NaCl followed by deionized water. The deionized chromophore is essentially identical with the chromophore produced by lowering the pH of the native membrane to (4.0 (pK -3.0). However. the deionized membrane docs not aggregatc andcan be obtained in the pure state. The original purple color of the membrane is restored by addition of around 1 mM Na+, K ' or 10 pM MgZt, Ca'+, Sr"+, MnZt. Pb"or La' ' when the protein concentration is 5 p,M. The required salt concentrations decrease with decreasing pH. Direct measurement of bound Ca2+ by atomic absorption spectroscopy yields a ratio of Ca2+ to protein of -2 and a binding constant of 1.4 X 10". Titration of the spectral change with salts at diffcrcnt pH values shows a linear relation between the pH and the logarithm of the salt concentration, with a 1:l ratio for Na+ and 1:2 ratio for Ca2+. These relations are well predicted by Gouy-Chapman theory: however. the accompanying release of protons, changes of the CD spectrum, the complex kinetics of the spectral change during reconstitution with salt and preliminary X-ray diffraction results all suggest that conformational changes may be occurring in the protein.

We propose gauge theory operators built using a complex Matrix scalar which are dual to brane-anti-brane systems in AdS 5 × S 5 , in the zero coupling limit of the dual Yang-Mills. The branes involved are half-BPS giant gravitons. The proposed operators dual to giant-anti-giant configurations satisfy the appropriate orthogonality properties. Projection operators in Brauer algebras are used to construct the relevant multi-trace Matrix operators. These are related to the "coupled representations" which appear in 2D Yang-Mills theory. We discuss the implications of these results for the quantum mechanics of a complex matrix model, the counting of non-supersymmetric operators and the physics of brane-anti-brane systems. The stringy exclusion principle known from the properties of half-BPS giant gravitons, has a new incarnation in this context. It involves a qualitative change in the map between brane-anti-brane states to gauge theory operators. In the case of a pair of sphere giant and anti-giant this change occurs when the sum of the magnitudes of their angular momenta reaches N.

Glu-194 near the extracellular surface of bacteriorhodopsin is indispensable for proton release to the medium upon protonation of Asp-85 during light-driven transport. As for Glu-204, its replacement with glutamine (but not aspartate) abolishes both proton release and the anomalous titration of Asp-85 that originates from coupling between the pKa of this buried aspartate and those of the other acidic groups. Unlike the case of Glu-204, however, replacement of Glu-194 with aspartate raises the pKa for proton release. In Fourier transform infrared spectra of the E194D mutant a prominent positive band is observed at 1720 cm-1. It can be assigned from [4-13C]aspartate and D2O isotope shifts to the C&dbd;O stretch of protonated Asp-194. Its rise correlates with proton transfer from the retinal Schiff base to Asp-85. Its decay coincides with the appearance of a proton at the surface, detected under similar conditions with fluorescein covalently bound to Lys-129 and with pyranine. Its amplitude decreases with increasing pH, with a pKa of about 9. We show that this pKa is likely to be that of the internal proton donor to Asp-194, the Glu-204 site, before photoexcitation, while 13C NMR titration indicates that Asp-194 has an initial pKa of about 3. We propose that there is a chain of interacting residues between the retinal Schiff base and the extracellular surface. After photoisomerization of the retinal the pKa's change so as to allow (i) Asp-85 to become protonated by the Schiff base, (ii) the Glu-204 site to transfer its proton to Asp-194 in E194D, and therefore to Glu-194 in the wild type, and (iii) residue 194 to release the proton to the medium.

It is shown that a covariant derivative on any d-dimensional manifold M can be mapped to a set of d operators acting on the space of functions on the principal Spin(d)-bundle over M. In other words, any d-dimensional manifold can be described in terms of d operators acting on an infinite dimensional space. Therefore it is natural to introduce a new interpretation of matrix models in which matrices represent such operators. In this interpretation the diffeomorphism, local Lorentz symmetry and their higher-spin analogues are included in the unitary symmetry of the matrix model. Furthermore the Einstein equation is obtained from the equation of motion, if we take the standard form of the action S=-tr([A_{a},A_{b}][A^{a},A^{b}]).Comment: 22 pages, 1 figure. V3: eqs (80) and (81) correcte

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