HSQC spectra for three proteins

HSQC spectra for three proteins SH3 domain from Abp1p Kinase domain from EphB2 apo Calmodulin What do the spectra tell you about the three proteins?

HSQC spectra for three proteins Small protein Big protein Diffuse peaks in the middle of the spectrum indicate aggregation Medium sized protein SH3 domain from Abp1p Kinase domain from EphB2 Apo calmodulin What does the spectra tell you about the three proteins?

Shielding and the chemical shift ν = γb 0 1 σ 2π DSS (4,4-dimethyl-4-silapentane-1-sulfonic acid) δ = ν ν rrr ν rrr 10 6 ppp Referencing of chemical shifts in proteins 1 H, 2 H, 13 C: methyl groups of DSS are reference frequencies 15 N: liquid ammonia at 25 C is reference frequency

1. Local effects 2. Ring current effects Local effects are largely casued by electron withdrawing or electron donating groups. The importance is strongly correlated with electronegativity of atoms within a few covalent bonds.

3. Hydrogen bonds electrons H N C O H N Lower chemical shift Higher chemical shift 4. Charges electrons H N H N M + Lower chemical shift Higher chemical shift

5. Dihedral angles Certain chemical shifts, e.g. 13 Cα, 13 Cβ, 13 CO and 1 Hα, are very sensitive to the dihedral angles ϕ and ψ.

Chemical shift ranges for protons in proteins The 1 H spectrum of ubiquitin illustrates the chemical shift range for protons on proteins,

Chemical shift ranges for 13 C in proteins methyl carbonyl aromatic alpha aliphatic Chemical shift (ppm) 13 C NMR spectrum of a protein

Important contributions to the chemical shift of different nuclei in proteins Nucleus Residue ϕ/ψ χ 1 Ring H-bonds type currents 13 C α X X 13 C β X X 13 C O X X X 1 H α X X X X 1 H N X X X X X 15 N X X X X The chemical shifts of different nuclei are sensitive to different effects. As can be seen for chemical shifts of the nuclei of the protein backbone (and 13 C β ) all are dependent on the type of amino acid residue. However, while the chemical shifts of some nuclei depend on a multitude of additional factors, others, most notably 13 C α and 13 C β, largely only depend on one additional effect. Thus if you know the chemical shifts of 13 C α and 13 C β, for a particular alanine residue you also know whether this residue is located in an α-helix, β-strand or random coil.

Secondary structure of E140Q-Tr2C An SSP score of 1 indicates a fully developed helix whereas a value of -1 indicates a fully extended structure.

The CS-ROSETTA protocol Assembled fragments. Energy minimized structure. Sequence of protein of interest. Matching fragments from proteins in database.

Two protein structures calculated with CS-ROSETTA A thioredoxin domain from human Grx3. The structure calculated using CS-ROSETTA is overlaid with a structure calculated by other means. CS-ROSETTA structure Cystal structure RMSD = 0.6 Å A PDZ domain from human SAP97

Spin couplings Definition: An interaction that modifies the energy levels of a (nuclear) spin Types of spin couplings Zeeman coupling the interaction with an external magnetic field (MHz) Quadupolar coupling a coupling of electrical origin* (MHz) Dipolar coupling the (direct) interaction with another nuclear spin (khz) Chemical shift coupling the interaction with an induced field (Hz-kHz) Scalar coupling the indirect interaction with another nuclear spin (Hz) *only exists for nuclei with spin I 1. We will not consider it further in this course.

The dipolar coupling B 0 B 0 Expression for the dipolar coupling constant A θ r AX X A θ r AX X D = μ 0 4π ħγ A γ X 3 3ccc 2 θ 1 r AA Depends on: Distance between the nuclei Angle between internuclear vector and the static magnetic field Higher energy Lower energy The direct dipole-dipole coupling between two nuclei, black and red arrows, depends on the angle the internuclear vector makes with the external field B 0 as indicated by a green arrow. For a rapidly rotating molecule the dipolar coupling averages to zero.

The scalar coupling Mediated by electrons Only important for nuclei that sit 4 covalent bonds apart Independent of direction, i.e. survives for molecules in solution

Energy levels for an isolated spin and an AX spin I=½ system A A X E A A A X X A X The spin state ( up or down ) of X affects the energy of A! ppm ppm ν A = γ AB 0 1 σ A π J AA m X X

Pascal s triangle helps us determine multiplet structures and their relative intensities Molecule (X is I=½) A AX AX 2 AX 3 AX 4 Multiplet structure singlet doublet triplet quartet pentet Relative intensities 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 Pascal s triangle can be used to help memorize the multiplet structure of the spectrum of nucleus A when it is coupled to n nuclei X. It is important to observe that for Pascal s triangle to be valid X (but not A) must be a spin I=½ nucleus. A new row is constructed by adding the coefficients to the left and to the right on the row above. If there is no element to the left or to the right above, add zero. For those of you interested in mathematics: The entries are also called binomial coefficients and are important in many areas outside of science. For instance, they can be used to work out an expression like (x+y) 7 in a hurry or tell you the odds of getting eleven correct results at stryktipset simply by chance.

Examples of multiplet structures You should learn how to determine these and similar patterns! The first four examples on the top row show multiplet structures that are given by straightforward application of Pascal s triangle. The last example on the top row and the first three examples on the bottom row show slightly more complicated structures since the A nucleus is coupled to nucleus X with one coupling constant and to nucleus M with another coupling constant. However, if J AX >>J AM or vice versa, the multiplet structure can easily be determined by repeated use of Pascal s triangle. The last two examples show examples where A is coupled to nuclei I>½. In these cases Pascal s triangle is not applicable and the multiplet structures must be worked out by other means.

Three examples of what J- couplings may be used for 1. Determination of the structure of small organic molecules. Characteristic multiplet structures shows how different groups are connected. 2. Determination of dihedral angles and thus secondary structure in proteins 3. Transfer of magnetization. If two nuclei are coupled it should be, and is, possible to transfer magnetization between the two. We will return to this when discussing 2D NMR.

Multiplet patterns report on structure of organic molecules

Backbone dihedral angles and the Ramachandran plot A B A) While the omega angle is always trans (except for sometimes in Pro residues), the angles phi and psi may adopt different angles. B) The allowed values of phi and psi constitute the Ramachandran plot. The most favored regions (red) and the additionally allowed region (yellow) are highlighted.

Measurement of 3 J HNHA enables characterization of protein secondary structure J = A + B cos(φ) + C cos 2 (φ) J=10 Hz β-strand J=3Hz α-helix The scalar coupling between 1 HN and 1 Hα ( 3 J HNHA ) depends on the dihedral angle phi. The dependence is described by the Karplus relation, which is shown by the figure. As the figure suggest, the size of the coupling is different for α-helical and β-strand structures, making it a reporter on secondary structure.

Scalar couplings for Tr2C-E140Q Residue 3 J HNHA (Hz) Met76 Lys77 Asp78 6.2 Thr79 7.0 Asp80 6.8 Ser81 5.7 Glu82 4.0 Glu83 4.0 Glu84 4.7 Ile85 5.4 Arg86 3.8 Glu87 4.4 Ala88 6.8 Phe89 --- Arg90 5.5 Val91 7.3 Phe92 9.4 Asp93 7.4 Lys94 6.3 Asp95 7.6 Residue 3 J HNHA (Hz) Gly96 --- Asn97 --- Gly98 --- Tyr99 9.9 Ile100 8.2 Ser101 6.8 Ala102 3.8 Ala103 4.1 Glu104 5.6 Leu105 4.5 Arg106 4.9 His107 7.7 Val108 4.8 Met109 4.7 Thr110 4.8 Asn111 5.7 Leu112 6.4 Gly113 --- Glu114 7.2 Lys115 7.6 Residue 3 J HNHA (Hz) Leu116 7.2 Thr117 6.9 Asp118 3.7 Glu119 4.1 Glu120 4.9 Val121 4.6 Asp122 4.2 Glu123 4.4 Met124 4.3 Ile125 8.5 Arg126 4.3 Glu127 4.6 Ala128 6.7 Asp129 6.6 Ile130 3.1 Asp131 6.4 Gly132 --- Asp133 7.9 Gly134 --- Gln135 8.8 Residue 3 J HNHA (Hz) Val136 9.3 Asn137 --- Tyr138 --- Glu139 4.0 Gln140 4.1 Phe141 --- Val142 5.3 Gln143 4.9 Met144 4.8 Met145 5.5 Thr146 7.4 Ala147 5.8 Lys148 7.5 Do you think the scalar couplings suggest the same secondary structure as the chemical shifts? Which parameter (chemical shifts or scalar couplings) do you find the more faithful reporter of secondary structure?

Magnetization transfer in the HSQC experiment 1 H 15 N 15 N 1 H 1 H τ τ τ τ t 2 15 N t 1 DECOUPLE Pulse sequence for the HSQC experiment. Narrow and wide rectangles correspond to 90 and 180 pulses, respectively. The triangle represent recording of the FID while the block marked DECOUPLE represents broad-band decoupling on 15 N. By tuning the delay τ to 1/4J NH complete magnetization transfer occurs during 2τ as indicated in the figure.

Magnitude of scalar couplings, transfer of magnetization and relative sensitivity of experiments The transfer time of magnetization from one nucleus to another is t=1/(2j) Small couplings mean long transfer times and more time for the magnetization to decay (relax) and thus to less sensitive experiments. Experiment Smallest coupling Sensitivity HSQC 15 N- 1 H N 92 Hz Very sensitive HNCO 15 N- 13 C O 15 Hz Fairly sensitive HNCA 15 N- 13 C α 10 Hz Not so sensitive

Decoupling Although the spectral appearance because of the scalar coupling is very important since it reports on molecular structure, it has however two negative consequences. The first one is that it reduces sensitivity, since the components of a doublet only have half the intensity of a singlet and the situation for other multiplets is even worse. The second negative consequence is spectral crowding since you will get more NMR signals than there are NMR active nuclei in the molecule. It is therefore often desirable to record NMR experiments in a fashion so that the effect of the scalar coupling is not visible. Immediately after the pulse on A and as soon as we start collecting the signal we start apply many 180 pulses on X, one after the other. This means that the X spins that originally were up will be down after the first 180 pulse and vice versa. It turns out that if we repeat the 180 pulses sufficiently rapidly, the A spin will simply see the average of up and down of X, i.e. it is like of X was not there at all and the signal would be collapsed into a singlet. The benefits would be better signal to noise and a simplified spectrum. The benefits of decoupling are two-fold: The number of peaks are reduced and the sensitivity is increased.

The spectrum of 13 C 1 H 2 H 2 ( 13 CHD 2 ) in calmodulin No deuterium decoupling* Deuterium decoupling* *Proton is decoupled in both spectra. What would the spectrum look like if neither proton or deuterium were decoupled?

Weak and strong forms of the scalar coupling What has been stated so far is only true in the weak coupling limit which is defined as J<<δν, where δν is the seperation in resonance frequencies between the two coupled nuclei. If this condition is violated the spins are strongly coupled and the appearance of the spectrum will change as a function of δν/j. When the spins have the identical chemical shifts there is no signature in the spectrum of a coupling.

Chemical and magnetic equivalence Nuclei that have the identical chemical shifts because of molecular symmetry are chemically equivalent. If the nuclei in addition have identical couplings to all other nuclei in the molecule they are magnetically equivalent. All nuclei that form a scalar coupled network comprise a spin system. Note that it is not necessary for all nuclei in the spin system to be mutually coupled. Example of chemical equivalence: The protons (or 19 F) in CHF=CHF Example of magnetic equivalence: The protons (or 19 F) in CH 2 F 2 Example of a spin system: All protons in the amino acid leucine

The residual dipolar coupling If a protein in solution can be partially aligned, for about 0.1% of time, the dipolar coupling will not be averaged to zero but will be scaled down. This is the residual dipolar coupling (RDC). As can be seen from the figure it can be used to determine relative bond angles. These are used in structure calculations where the aim is to minimize the difference between oobserved and backcalculated RDCs. Calculated versus observed RDCs for a certain protein are shown in the chart. PROTEIN N H D (3cos 2 (20 )-1) = 1.65 N H N H D (3cos 2 (90 )-1) = -1 D (3cos 2 (110 )-1) = -0.65

Note that we now know three NMR parameters that contain structural information: 1) The chemical shift, that reports on dihedral angles 2) The scalar coupling, that reports on dihedral angles 3) The residual dipolar coupling that reports on angles between bond vectors

On the sensitivity of NMR experiments on different nuclei The sensitivity of an NMR is increased both if it is started and detected on a nucleus with a high gyromagnetic ratio. Here is the argument: 1) The equilibrium magnetization is dependent on the population difference between spin up and spin down. This is roughly proportional to γ. (start) 2) It is also dependent on the magnetic moment of the nuclear spins. This is exactly proportional to γ. (start) 3) The current that is induced in a coil by a rotating magnetization is proportional to the resonance frequency which is exactly proprtional to γ. (detection) 4) Unfortunately, the noise in the coil is proportional to γ. (detection) Taking all this into account we see that the sensitivity (S/N) scales as γ 5/2 if the experiment is started and detected on a particular nucleus.