1 Solid State Nuclear Magnetic Resonance Determination of Protein Orientation

Solid State Nuclear Magnetic Resonance Determination of Protein OrientationBrian GustafsonREU ParticipantAdvisor: Dr. David WelikyThis report details the use of two FORTRAN computer programs to simulate the chemical shift and dipolar coupling of a peptide at various protein orientations. Examination of the plots created from these simulations provides information regarding protein structure as well as indications of the ability to predict orientation through NMR measurements of chemicals shifts and dipolar coupling.INTRODUCTIONNuclear Magnetic Resonance (NMR) is a property that can be classically thought of as a result of an associated current and magnetic moment associated with electrons and nuclei (Figure1). If you place this atom (or molecule) in a static unidirectional magnetic field, its magnetic moment (µ) will precess about the direction of the magnetic field B0 (Figure 2).Figure 1.Figure 2e-µNMR spectroscopy uses this property and others in order to learn about the composition and structure of various molecular samples.Solid state Nuclear Magnetic Resonance spectroscopy is an approach to determining atomic-level structure and dynamics of macromolecular systems. One of themost exciting areas of current research is in the field of protein structure determination. This report details simulations relevant to determining peptide plane orientations in a protein. Interpretations of these simulations are also presented.EXPERIMENTALAt this time, most solid state NMR methods specifically require 13C labeled samples. For proteins and peptides (pieces of proteins) it is often convenient to dually 13C label the carbonyls (Figure 3) at adjacent residues in the protein backbone. (In chemistry, carbonyl carbons are those carbons of a molecule that are double bonded to oxygen). Often these samples are considered to be uniaxially oriented which means that the helix axis of a peptide chain is either parallel or perpendicular to the membrane normal.C ON HCC O NH φψPeptide PlanesFigure 3.Our research has focused on the dependence carbonyl chemical shifts and intercarbonyl dipolar coupling on both peptide secondary structure and absolute orientation in the magnetic field. To determine this dependence, two computer programs were created to simulate the full range of these values for a specifically doubly carbonyl labeled protein sample. We are particularly interested with how uniquely thesesimulations can be determined by NMR measurements of the chemical shift values from the two carbonyl carbons and the dipolar coupling between them.COMPUTER PROGRAM ONE: Chemical ShiftChemical shifts are small perturbations in the Nuclear Magnetic Resonance frequency due to induced electronic magnetic fields. A simple way to understand this iswith the following analogy. If you have a solenoidal magnetic field (the NMR magnet) and place within it a loop of wire that has current flowing through it, the moving charges within the large magnetic field generates another, smaller, magnetic field. The strength of this induced magnetic field is affected by the geometry of the loop or more precisely, its relative orientation to the external magnetic field. In our case the moving electrons in the atoms that form the peptide represent the current loop. Also, the orientations of the peptide planes represent the geometric orientation of the current loop, which affects the strength of the induced magnetic field.Using a model tripeptide, with two 13C labels at carbonyl sites in the peptide backbone, a FORTRAN program was designed to calculate these chemical shifts. In this molecule, 13C has been synthesized in place of the normal 12C. 13C labels are used because of the nuclear magnetic properties of the isotope. 12C has a spin of 0 and is non-magnetic, while 13C has spin ½ and is magnetic. The protein backbone is composed of a series of planer peptide bond units with relative orientations determined by ϕ and ψ (see figure 3).There already exist, in solid state NMR, methods for determining the secondary structure (ϕ, ψ) in these samples. Often the peptides or proteins are also oriented relative to some axis (for example a membrane normal). In this research the goal has been to ascertain whether solid state NMR measurements can be used to determine this orientation.Using this knowledge of secondary structure, the values for the chemical shift at any particular orientation can be calculated. In order to do that however, the 13C labeled carbons from each site must be transformed into a common laboratory (magnetic field)reference frame. A relation can be determined between a set of Euler angles (α1-2, β1-2, and γ1-2) that relate the chemical shift 13C of site one with the 13C of site two and the dihedral angles. Euler angles are a mathematical means of transforming from one reference frame to another. There are three axes in three-dimensional space and hence three Euler angles to transform them to new axes. Further relations can be made to express the site 13C’s to the laboratory reference frame by using a second set of Euler angles (β, γ). Through these coordinate transformations, and once in the laboratory frame, calculations can be made of the chemical shift of each site. These chemical shifts are measured as small perturbations in the NMR frequency.Using the computer program, it was possible to calculate the chemical shifts for both sites with variable (β, γ) of the second set of Euler angles for specific values of the dihedral angles, ϕ and ψ. This creates, for specific ϕ and ψ, a base of values for the chemical shifts that depend upon the peptide’s orientations with respect to the laboratory frame. The angles used for ϕ and ψ were –60 and –50 respectively. These values correspond to what is known as an α-helix. The α-helix is a common secondary structure and is defined by the hydrogen bonds that lie between residues in the polypeptide chain. COMPUTER PROGRAM TWO: Dipolar CouplingDipolar coupling results from the interaction of one magnetic dipole and the field of a nearby magnetic dipole. A measurable perturbation in the NMR frequency is proportional to the magnitude of the dipolar coupling. As with the chemical shift, the orientation of the carbonyl planes relative to each other as well as the external magnetic field affect the value of the dipolar coupling.A second program was created to calculate the dipolar coupling between the two carbonyl carbons in the same model tripeptide used above. Analytically, using a vector analysis approach to a solid geometry problem, the dipolar coupling can be readily calculated as a function of the Euler angles β and γ. The equation used for the dipolar coupling (D ) is as followswith r being the distance between the carbonyls and θ being the angle between the vector of r and the external magnetic field. The variable d is the dipolar constant specific to particular carbon nuclei.RESULTSUsing the data for ϕ and ψ of an α-helix, contour plots were created for eachsite’s values of the chemical shift and also for the dipolar coupling. Plots of the chemical shifts of site one and two (Figures 4 and 5 on the following page) as a function of β and γreveal several important features. Chemical shifts are measured in parts per million of the Larmor precession frequency of the nuclear magnetic moment. The chemical shift is proportional to the magnetic field, and so the ppm shifts are independent of the field intensity.()1cos 3223−=θrd DFigure 4.Figure 5.The important result of these chemical shift simulations is in information gained regarding helix orientation. If the helix axis is parallel to the magnetic field, then the chemical shifts of both site one and site two are approximately equal to each other and to σ22. σ22 is one of the three chemical shift principle values for the carbonyl sites and in a helix the σ22’s line up with the helix axis. Thus if the helix is parallel to the magnetic field the σ22 values will be dominant. If the helix is oriented perpendicular to the magnetic field direction, the chemical shifts of both sites can have a variety of values but are anti-correlated to each other. This anti-correlation is measurable by simple two–dimensional NMR.Again, we created a contour plot for the dipolar coupling as a function of β and γ(figure 6) showing the measurable frequency perturbation in kilohertz.Figure 6.Including an analysis of the dipolar coupling with the chemical shifts, it is apparent that it does not look at all like the chemical shift plots. This reveals additional structural information as the dipolar coupling has a different (β, γ) dependence.When the chemical shift of site two of the α-helix is compared to the chemical shift of site two in anther structure, such as a β-sheet (ϕ=-139°, ψ=135°), a large difference in the pattern is apparent (Figure 7.). This illustrates a large dependence of the chemical shift on secondary structure.Figure 7.CONCLUSIONSIt appears, from this research, that the chemical shifts and dipolar coupling do exhibit a dependence upon secondary structure and absolute orientation to the magnetic field. If uniqueness can be maintained though consideration of all three measurable values (the chemical shifts for both sites and the dipolar coupling), it will be possible to take these measurements from the NMR and use them to discover the planer orientations of the peptide. This information, along with the information gained about the structure from the plots may also be useful in orienting the entire α-helix to discover whether or not it is parallel or perpendicular to the membrane normal.AKNOWLEGEMENTSI would like to thank Dr. David Weliky for the opportunity to do this project and also for his guidance along the way. Also I would like to thank the rest of the students in Dr. Weliky’s research group for their help and camaraderie during my time here.REFERENCESR. Tycko et al. “Investigation of Molecular Structure in Solids by Two Dimensional NMR Exchange Spectroscopy with Magic Angle Spinning.” J. Chem. Phys.105(18). 8 Nov. 1996.D. Weliky. Various discussions between June and August 1998。