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National Institute of Chemistry Slovenia Department for Materials Electrochemistry SOLID-STATE NMR -theory and pharmaceutical applications Aljaž Godec, Uroš Maver General theory of NMR For convenience the physical basis of NMR will be shown for hydrogen nuclei (proton) Proton ≈ spinning bar magnet with angular momentum, I In agreement in NMR experiments only the z component of I is known, Iz, (I is undetermined in the x-y plane), and is given by h... Planck’s constant i...spin of the proton (1/2) hi Iz = 2π General theory of NMR The angular and magnetic momentum are related by uv v µ =γI γ... gyromagnetic ratio of the nucleus (physical property of the nucleus) The z component of the magnetic momentum is then given by γ hi µz = γ I z ≡ 2π General theory of NMR In NMR experiments the sample is placed in a static external magnetic field, B0. The energy of the nucleus in B0 (E of Zeeman interaction) is hγ iB0 E = − µ z B0 ≡ − 2π -there are two energy states for a proton in B0: (i = +1/2) (i = -1/2) ↓E state ↑E state General theory of NMR The spinning axis of the proton cannot align exactly parallel or antiparallel with the static external field, but is precessing about it with angular frequency ω0 (Larmor frequency) ω0 = γ B0 hγ B0 ∆E = hν = 2π Equilibrium population ratio N −1/ 2 =e N +1/ 2 −∆E kT <1 Occurrence of bulk magnetization in +z direction General theory of NMR Bulk magnetization in +z direction M z = ( N +1/ 2 − N −1/ 2 ) µ z Mx = 0 My = 0 The equilibrium magnetization for N magnetic moments (N=N[+1/2]+N[1/2]) per unit volume, Mz0, is given by M z0 ⎛ = ⎜e ⎝ µ z B0 kT −e − µ z B0 kT − µ z B0 ⎛ µkTz B0 ⎞ e − e kT ⎜ ⎟ µ z ≡ N ⎜ µ z B0 − µ z B0 ⎠ ⎜ e kT + e kT ⎝ ⎞ ⎟ µ ≡ N µ tanh ⎛ µ z B0 ⎞ z ⎜ kT ⎟ ⎟ z ⎝ ⎠ ⎟ ⎠ General theory of NMR 2 1 Mz 0 µ z 2 B0 ⎛ µ z B0 ⎞ = N µ z tanh ⎜ ≈N ⎟ kT ⎝ kT ⎠ y=tanh(x) 0 5 0 5 y=x -1 -2 This magnetization does not build up instantaneously when the sample is placed in a static external field (or after a 90° electromagnetic pulse). ( dM z 1 = M z0 − M zt dt T1 ) T1 ...spin-lattice relaxation time −t ⎛ ⎞ T1 0 M z (t ) = M z ⎜1 − e ⎟ ⎜ ⎟ ⎝ ⎠ General theory of NMR In a static field there is no transverse component of the net magnetization (M(x)=M(y)=0). There is a way to create such a transverse magnetization using radio frequency pulsed magnetic fields. Suppose we apply not only a constant magnetic field B0 but also a rotating (circularly polarized) magnetic field B1 of frequency ω, perpendicular to B0. The total field is written as uv v v v B(t ) = B1 cos(ωt )i + B1 sin(ωt ) j + B0 k General theory of NMR The analysis of magnetization in this field can best be carried out in a noninertial rotating coordinate system, *, [ω*=ω(B1)] uv v v v B(t ) = B1 cos(ωt )i + B1 sin(ωt ) j + B0 k ? uuuv uv ⎛ uuv ⎞ ω Bef * = B1 i* + ⎜ B0 − ⎟ k * γ ⎠ ⎝ In such a system M is stationary: dM/dt=0 uuv uuv uv dM =γM ×B dt - this can happen only if B=0. The magnetic field is 0 (in *) if we add the effective field –(ω/γ)k*, so that B0k*–(ω/γ)k*=0. General theory of NMR If B1 rotates with the Larmor frequency (condition for resonance) uv ⎛ uuv uuuv ⎞ ω Bef * = B1 i* + ⎜ B0 − ⎟ k * γ ⎠ ⎝ ω (B1)= ω0= ω(*) uuuv* v* Beff = B1 i The magnetization starts to precess about B1* at rate Ω Ω=γB1 General theory of NMR the time B1 is switched on t(B1)[90°]=π/2Ω 90° pulse N(-1/2)=N(+1/2) t(B1)[180°]=π/Ω 180 ° pulse N −1/ 2 =e N +1/ 2 −∆E kT −∆E N +1/ 2 = e kT N −1/ 2 General theory of NMR For most systems the x-y magnetization decays exponentially with time dM x* dt dM y* dt =− =− M x* T2 M y* T2 M x* (t ) = M 0 e −t T2 M y* (t ) = M 0 e T2... spin-spin relaxation time −t T2 General theory of NMR The movement of the tip of the magnetization vector after a 90° pulse in the stationary coordinate system transverse relaxation M x (t ) = M 0 cos(ω0t )e M y (t ) = M 0 sin(ω0t )e N(-1/2)=N(+1/2) −∆E N −1/ 2 = e kT N +1/ 2 −t ⎛ ⎞ T1 0 M z (t ) = M z ⎜1 − e ⎟ ⎜ ⎟ ⎝ ⎠ longitudinal relaxation −t T2 −t T2 General theory of NMR Detection of the signal FID- Free Induction Decay The time domain signal is transformed into a frequency domain signal using FT. General theory of NMR Chemical shift B0 Bi i The nucleus is surrounded by electrons which act as a 3D magnetic shield. Magnetic fields induced by currents of electrons change the local field (Bloc) experienced by the nucleus. ω0i = γ Bloc i i = A, B, C µi uv uv uv B loc = B 0 − B i uv uv Bi = σ B0 uuuv uv Bloc = B 0 (1 − σ ) σ ...shielding constant SOLID-STATE NMR Spectra acquired with solution NMR equipment liquid methanol crystalline methanol Broadening of solid state spectra is due to: - dipolar interactions - chemical shift anisotropy SOLID-STATE NMR Dipolar interaction E jk DS (( )( ) = b jk 3I j ⋅ e jk 3Ik ⋅ e jk − I j ⋅ Ik ) Ij in Ik... angular momenta of spins j in k ejk ...unit vector, parallel to the internuclear vector; ejk =f(t) as the molecule rotates Dipolar coupling constantmeasure for the intensity of interaction µ0 γ j γ k h b jk = − 2 3 8π rjk E jk DS = min SOLID-STATE NMR Dipolar interaction in a static magnetic field Homonuclear: E jk DS (θ jk )= b jk 1 3cos2 θ jk −1) 3I jz Ikz − I j ⋅ Ik ( 2 ( ) Heteronuclear: DS E jk (θ jk )= b jk (3cos2 θ jk −1)I jz Ikz ( ) E jk DS ∝ 3cos 2 θ jk − 1 ( ) E jk DS θ jk = 54,74o = 0 MAGIC ANGLE In solution the interaction vanishes because of rapid reorientations of molecules (3cos2θjk-1 is integrated over all angles of a sphere). In solid state NMR molecules are fixed with respect to the static external field. SOLID-STATE NMR Chemical shift anisotropy, ∆σ σ is orientation dependent polycrystalline samples have a random distribution of all orientations of a molecule functional group oriented parallel to B0 (maximal screening) ∆σ ∝ ( 2 3cos ( θ −1) r3 functional group oriented perpendicular to B0 (minimal screening) ) ∆σ θ = 54,74o = 0 SOLID-STATE NMR Improving resolution in SS NMR 1. MAS- Magic angle spinning - rapid spinning at the magic angle causes the time average of θ to be 54,74° - the spinning frequency is between 1 and some 10 kHz - we can eliminate broadening due to dipolar interactions and chemical shift anisotropy SOLID-STATE NMR Improving resolution in SS NMR 2. CP- Cross polarization polarization = ( N +1/ 2 − N −1/ 2 ) B0 - transfer of polarization from abundant spins (1H) to rare spins (13C) γ - we can improve the signal/noise ratio for a factor γ 1 13 -occurs if we set the Hartmann-Hahn match properly γ 13 C B13 C = γ 1 H B1 H - 13C nuclei take over properties of 1H nuclei - enables more repetitions in a given time (T1(1H)<T1(13C)) H C SOLID-STATE NMR 2. CP Pulse sequence Best resolution is usually obtained with CP MAS ‘SOLID-STATE’ NMR Pharmaceutical applications of SS NMR - Investigations of polymorphism 1 conformation of IM in crystal 3 conformations of IM in crystal 13C CP/MAS NMR spectra of α (1) and γ (2) polymorphic forms of indomethacine (IM). K. Masuda et al. / International Journal of Pharmaceutics 318 (2006) 146–153 SOLID-STATE NMR - Investigations of pseudopolymorphism OH CH 3 H H H HO weight loss 13C CP/MAS NMR spectra of pseuodopolymorphs of estradiole. TGA J.-S. Park et al. / European Journal of Pharmaceutics and Biopharmaceutics 60 (2005) 407–412 SOLID-STATE NMR - Investigation of amorphous solids - broadening of signals is due to: - wide distribution of orientations of molecules - changes or disruption of hydrogen bond network - differences in intermolecular distance - wide distribution of molecular conformations (molecules are more flexible in amorphous phase with respect to the crystalline phase) 13C CP/MAS NMR spectra of amorphous (upper) and crystalline form of a drug SOLID-STATE NMR It is possible to quantify amorphous content, xa, in a binary mixture of crystalline and amorphous phase noise at frequency i spectra of amorphous form ai = Ai + ε ia spectra of crystalline form ci = Ci + ε ic spectra of binary mixture si = Si + ε is signal at frequency i Si = xa Ai + (1 − xa )Ci ≡ xa ( Ai − Ci ) + Ci Introduction of new variables Yi= si-ci in Xi= ai-ci Yi = xa X i + ε i ε i = xa (ε ic − ε ia )+ (ε is − ε ic ) Linear regression SOLID-STATE NMR Quantification of amorphous trehalose CH 2 OH O OH HO OH CH 2OH O OH HO O OH 13C CP/MAS NMR spectra of pure amorphous trehalose (6), binary mixtures (5-2) and pure crystalline trehalose Correlation between obtained and actual fraction R. Lefort, et al. Int. J. Pharm., 280 (2004) 209-219 SOLID-STATE NMR Solid-state NMR in drug design and discovery • 1. 2. 3. 4. Resolution afforded by solid-state NMR of structural details at subnanometre level: determination of structural changes after binding a small molecule at their site of action, intimate dynamic information and electronic details for bound molecules, details of the binding site, determination of chiality or the partiotioning characteristics of small molecules. SOLID-STATE NMR Computational approaches for membrane targets • NMR can reveal important details about the major secondary structure elements of receptor molecules (functionally relevant for ligand binding). • Docking programs (for example Autodock) and molecular dynamics (coupled with simulated annealing methods) are now regularly used. • NMR could be used to test the results of such simulations, and NMR-generated structural information can be included in docking routines to increase their use and applicability and to improve and refine the algorithms. SOLID-STATE NMR Solid-state NMR of large biomolecules • • • Some new high-frequency transverse relaxation-optimized spectroscopy (TROSY) NMR methods combined with 2H and 15N labelling might extend the limit (broadened spectral lines due to dipolar interactions) for full structural determinations for isolated membrane proteins in suitable small detergent micelles. Wide-line solid-state NMR has been developed to exploit anisotropic characteristics of large complexes and to give, in particular, molecular orientation in ordered systems, such as fibres or membranes. High-resolution solid-state NMR involves mechanically averaging the anisotropic spin interactions by rotating a sample in a rotor. SOLID-STATE NMR Solid-state NMR of large biomolecules • Spinning can lead to morphological changes (especially those that are induced by hidration). • The resolution of the narrow NMR spectra from spinning the sample at the magic angle (MAS) methods does not mach those of high-resolution solution-state NMR spectra (mainly because of sample disorder and slow molecular motional effects). • The mechanical averaging means that many of the informative spectral features are lost. • Heterogenous systems can also be studied. Solid-state NMR in drug discovery Chemical bonding, chirality and compositional information in the solid form Nonspecific and specific binding of a drug to a target can be identified in the solid-state NMR spectrum of a heterogenous macromolecular complex Solid-state NMR spectral parameters for a drug that is bound at its target site can give detailed insight into electronic and conformational nature and components of a binding site Dissociation constant (Kd) values can also be determined The manipulation of bioavailibility is important, either through solubility or partitioning to a membrane target through the bilayer, which can be distinguished using solid-state NMR The quality control of drug synthesis is readily monitored using solid-state NMR Patent infrigement investigations through polymorphic differences of competing drugs can be resolved Solution-state NMR Solid-state NMR For drug observation only in solution Yes NS For drug observation as solid (polymorphism determinations) NS Yes Nuclei observable 1 13 Observation of unbound drug H, 13C, 15N and 19F C, 15N, 19F, 2H and 17O Target molecular size For complete structure determination Yes (if Mr<30000 unless TROSY can be applied) NS (except for small membrane peptides so far) For direct drug observation at target binding site Yes (if Mr<40000 unless TROSY can be applied) No limit For indirecrt (rapidly exchanging into solution) drug-target observation No limit NS Sample size 10-500 µl 10 µl-1 ml Detection levels of target-drug complex (13C,15N,19F) nM (for Mr<30000) >20 nmoles* Detection levels for drug only >1 nmol >1 nmole* Temperature range Not frozen Any Isotopic-labelling requirements for target None or 13C in 15N selectively and/or uniformly None or selective target labelling (residues of a single type or a minimal number of types) only Isotopic-labelling requirements for drug Preferable for enhanced sensitivity or to aid assignments Yes for assignment and sensitivity enhancements for 13C in 15N, no for rare nuclei (such as 19F) Kd range mM do µM (for large targets); nmM to nM (for small targets) <mM (no limitations) *With proton cross-polarization to enchance sensitivity. Kd, dissociation constant; Mr, relative molecular mass; NS, not suitable; TROSY, transverse relaxation-optimized spectroscopy. SOLID-STATE NMR Isotopic substitution for drug-target studies by solidstate NMR • The identification and assignment of NMR resonances require defined chemical labelling or spectroscopic approaches that are designed for these purposes. • The overriding consideration in experimental design is how many sites need labelling (too many labels might be difficult to resolve) and where the labels should be placed. • Modelling methods (coupled with SS NMR) can help in the selection of sites for labels: 1. giving a distance between nuclei and constraining a drug structure by defining torsion angles, 2. by probing a binding site and defining the involvement of specific moieties in the binding process. SOLID-STATE NMR SOLID-STATE NMR Properties of commonly used and biologically relevant NMR-visible isotopes NMRvisible isotope Substitution Natural abundance compared with 1H Relative sensitivity Main NMR property exploited 13C 12C 1,1 % 0,016 Dipolar couplings and chemical shift 2H 1H 0,015 % 0,001 Anisotropic quadupolar interactions and dynamics 15N 14N 0,37 % 0,001 Anisotropic chemical shifts 19F No or 1H 100 % 0,83 Strong dipolar couplings 31P No 100 % 0,006 Anisotropic and isotropic chemical shifts SOLID-STATE NMR Determining Kd for ligands • The NMR spectral line heights for 13C-labelled, weakly binding ligand increase as the ligand is added to a fixed amount of target protein. • The fractional ratio of bound ligand then gives a binding isotherm and Kd. • By suppressing the NMR spectrum from isotropic, unbound ligand, an equilibrium Kd is determined directly. SOLID-STATE NMR Distance methods in solid-state NMR • • • • • Ultra-high resolution (±0,05 nm - direct result of the strong sensitivity of the magnetic dipolar coupling (b) to distance (r)). Methods are available for determining b IS between similar nuclei and different nuclei. For homonuclear recoupling, the recoupling is achieved under ‘rotational resonance’ (setting the sample spinning rate, ωR, to multiples of the frequency difference (νAB) between the NMR resonances (│νA-νB│). Mixing period (τm) Æ transfer of magnetization (reducing the spectral intensity). The decay curve of the intensity reduction as a function of the mixing time then provides a means of quantifying the dipolar interaction. ⎛ µ0 b = −⎜ ⎝ 4π ⎞ γ Iγ S h ⎟ 3 ⎠ r IS bIS…dipolar coupling between nuclei spins I and S µ0…permeability of vacuum γI,γs…are the gyromagnetic ratios of spins I and S h…Planck constant divided by 2π rIS...distance between nuclear spins I and S SOLID-STATE NMR SOLID-STATE NMR Resolving drug structures at the site of action • • Solid-state NMR in combination with sitedirected mutageneseis (SDM) and bioinformatics approaches is used for resolving binding sites. The intramolecular drug structure at the target site can be resolved with high resolution, as can the electronic environment (from NMR chemical shift perturbations). SOLID-STATE NMR Identifying bound ligand environment • • The agonist binding site is shown for the nicotinic Ach receptor, which highlights the aromatic residues (in red) that line the agonist-binding pocket, within which deuterium SS NMR studies have shown fast rotation of the agonist –(CH3)3 group. b and c – both modulate receptor function, and could potentially bind to the receptor through a cation-π interaction. SOLID-STATE NMR Partitioning behaviour of drugs • • The deuterium wide-line NMR spectra of ligands that can partition into a membrane show welldefined spectra for each motionally distinct environment. As long as the experimental conditions (particularly the relaxation delays) are sufficient, then spectral integration (the measured area, Ap and Ai, for the partitioned and isotropic spectral components) gives directly the relative concentrations of the small molecule in each phase in equilibrium. K p = A pVa / AiVm Va,Vm…aqueous and membrane volumes SOLID-STATE NMR Differential dynamics of bound ligands • • • Parts of the drug have an average position in or on its binding site, rather than a highly rigid location for the whole molecule. Deuterium substitutions give rise to either motionally broadened or a motionally narrowed spectrum. The method is sensitive enough to differentiate unbound ligand as a narrow (‘free’) signal from the tightly (Kd values in the nanomolar range) ‘bound’ ouabain when the deuterium label is carried on the steroid nucleus of ouabain. SOLID-STATE NMR