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178-930: The principle of NMR usually involves three sequential steps: Similarly, biochemists use NMR to identify proteins and other complex molecules. Besides identification, NMR spectroscopy provides detailed information about the structure, dynamics, reaction state, and chemical environment of molecules. The most common types of NMR are proton and carbon-13 NMR spectroscopy, but it is applicable to any kind of sample that contains nuclei possessing spin . NMR spectra are unique, well-resolved, analytically tractable and often highly predictable for small molecules . Different functional groups are obviously distinguishable, and identical functional groups with differing neighboring substituents still give distinguishable signals. NMR has largely replaced traditional wet chemistry tests such as color reagents or typical chromatography for identification. The most significant drawback of NMR spectroscopy

356-905: A m ∗ b m = ∑ m = − j j ( ∑ n = − j j U n m a n ) ∗ ( ∑ k = − j j U k m b k ) , {\displaystyle \sum _{m=-j}^{j}a_{m}^{*}b_{m}=\sum _{m=-j}^{j}\left(\sum _{n=-j}^{j}U_{nm}a_{n}\right)^{*}\left(\sum _{k=-j}^{j}U_{km}b_{k}\right),} ∑ n = − j j ∑ k = − j j U n p ∗ U k q = δ p q . {\displaystyle \sum _{n=-j}^{j}\sum _{k=-j}^{j}U_{np}^{*}U_{kq}=\delta _{pq}.} Mathematically speaking, these matrices furnish

534-516: A carboxyl group, and a variable side chain are bonded . Only proline differs from this basic structure as it contains an unusual ring to the N-end amine group, which forces the CO–NH amide moiety into a fixed conformation. The side chains of the standard amino acids, detailed in the list of standard amino acids , have a great variety of chemical structures and properties; it is the combined effect of all of

712-470: A gene may be duplicated before it can mutate freely. However, this can also lead to complete loss of gene function and thus pseudo-genes . More commonly, single amino acid changes have limited consequences although some can change protein function substantially, especially in enzymes . For instance, many enzymes can change their substrate specificity by one or a few mutations. Changes in substrate specificity are facilitated by substrate promiscuity , i.e.

890-482: A helium-4 atom in the ground state has spin 0 and behaves like a boson, even though the quarks and electrons which make it up are all fermions. This has some profound consequences: The spin–statistics theorem splits particles into two groups: bosons and fermions , where bosons obey Bose–Einstein statistics , and fermions obey Fermi–Dirac statistics (and therefore the Pauli exclusion principle ). Specifically,

1068-461: A molecule , particularly for molecules that are too complicated to work with using one-dimensional NMR. The first two-dimensional experiment, COSY, was proposed by Jean Jeener, a professor at Université Libre de Bruxelles, in 1971. This experiment was later implemented by Walter P. Aue, Enrico Bartholdi and Richard R. Ernst , who published their work in 1976. A variety of physical circumstances do not allow molecules to be studied in solution, and at

1246-574: A better sensitivity and higher resolution of the peaks, and it is preferred for research purposes. Credit for the discovery of NMR goes to Isidor Isaac Rabi , who received the Nobel Prize in Physics in 1944. The Purcell group at Harvard University and the Bloch group at Stanford University independently developed NMR spectroscopy in the late 1940s and early 1950s. Edward Mills Purcell and Felix Bloch shared

1424-427: A charged elementary particle, possesses a nonzero magnetic moment . One of the triumphs of the theory of quantum electrodynamics is its accurate prediction of the electron g -factor , which has been experimentally determined to have the value −2.002 319 304 360 92 (36) , with the digits in parentheses denoting measurement uncertainty in the last two digits at one standard deviation . The value of 2 arises from

1602-552: A combination of sequence, structure and function, and they can be combined in many different ways. In an early study of 170,000 proteins, about two-thirds were assigned at least one domain, with larger proteins containing more domains (e.g. proteins larger than 600 amino acids having an average of more than 5 domains). Most proteins consist of linear polymers built from series of up to 20 different L -α- amino acids. All proteinogenic amino acids possess common structural features, including an α-carbon to which an amino group,

1780-403: A defined conformation . Proteins can interact with many types of molecules, including with other proteins , with lipids , with carbohydrates , and with DNA . It has been estimated that average-sized bacteria contain about 2 million proteins per cell (e.g. E. coli and Staphylococcus aureus ). Smaller bacteria, such as Mycoplasma or spirochetes contain fewer molecules, on

1958-834: A detailed review of the vegetable proteins at the Connecticut Agricultural Experiment Station . Then, working with Lafayette Mendel and applying Liebig's law of the minimum , which states that growth is limited by the scarcest resource, to the feeding of laboratory rats, the nutritionally essential amino acids were established. The work was continued and communicated by William Cumming Rose . The difficulty in purifying proteins in large quantities made them very difficult for early protein biochemists to study. Hence, early studies focused on proteins that could be purified in large quantities, including those of blood, egg whites, and various toxins, as well as digestive and metabolic enzymes obtained from slaughterhouses. In

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2136-468: A few steps are allowed: for many qualitative purposes, the complexity of the spin quantum wavefields can be ignored and the system properties can be discussed in terms of "integer" or "half-integer" spin models as discussed in quantum numbers below. Quantitative calculations of spin properties for electrons requires the Dirac relativistic wave equation . As the name suggests, spin was originally conceived as

2314-470: A given kind have the same magnitude of spin angular momentum, though its direction may change. These are indicated by assigning the particle a spin quantum number . The SI units of spin are the same as classical angular momentum (i.e., N · m · s , J ·s, or kg ·m ·s ). In quantum mechanics, angular momentum and spin angular momentum take discrete values proportional to the Planck constant . In practice, spin

2492-592: A kind of " torque " on an electron by putting it in a magnetic field (the field acts upon the electron's intrinsic magnetic dipole moment —see the following section). The result is that the spin vector undergoes precession , just like a classical gyroscope. This phenomenon is known as electron spin resonance (ESR). The equivalent behaviour of protons in atomic nuclei is used in nuclear magnetic resonance (NMR) spectroscopy and imaging. Mathematically, quantum-mechanical spin states are described by vector-like objects known as spinors . There are subtle differences between

2670-478: A little ambiguous and can overlap in meaning. Protein is generally used to refer to the complete biological molecule in a stable conformation , whereas peptide is generally reserved for a short amino acid oligomers often lacking a stable 3D structure. But the boundary between the two is not well defined and usually lies near 20–30 residues. Polypeptide can refer to any single linear chain of amino acids, usually regardless of length, but often implies an absence of

2848-428: A molecule change slightly between solvents, and therefore the solvent used is almost always reported with chemical shifts. Proton NMR spectra are often calibrated against the known solvent residual proton peak as an internal standard instead of adding tetramethylsilane (TMS), which is conventionally defined as having a chemical shift of zero. To detect the very small frequency shifts due to nuclear magnetic resonance,

3026-531: A non-zero magnetic moment despite being electrically neutral. This fact was an early indication that the neutron is not an elementary particle. In fact, it is made up of quarks , which are electrically charged particles. The magnetic moment of the neutron comes from the spins of the individual quarks and their orbital motions. Neutrinos are both elementary and electrically neutral. The minimally extended Standard Model that takes into account non-zero neutrino masses predicts neutrino magnetic moments of: where

3204-599: A nuclear magnetic resonance response – a free induction decay (FID) – is obtained. It is a very weak signal and requires sensitive radio receivers to pick up. A Fourier transform is carried out to extract the frequency-domain spectrum from the raw time-domain FID. A spectrum from a single FID has a low signal-to-noise ratio , but it improves readily with averaging of repeated acquisitions. Good H NMR spectra can be acquired with 16 repeats, which takes only minutes. However, for elements heavier than hydrogen,

3382-410: A particular cell or cell type is known as its proteome . The chief characteristic of proteins that also allows their diverse set of functions is their ability to bind other molecules specifically and tightly. The region of the protein responsible for binding another molecule is known as the binding site and is often a depression or "pocket" on the molecular surface. This binding ability is mediated by

3560-500: A protein carries out its function: for example, enzyme kinetics studies explore the chemical mechanism of an enzyme's catalytic activity and its relative affinity for various possible substrate molecules. By contrast, in vivo experiments can provide information about the physiological role of a protein in the context of a cell or even a whole organism . In silico studies use computational methods to study proteins. Proteins may be purified from other cellular components using

3738-411: A protein is defined by the sequence of a gene, which is encoded in the genetic code . In general, the genetic code specifies 20 standard amino acids; but in certain organisms the genetic code can include selenocysteine and—in certain archaea — pyrrolysine . Shortly after or even during synthesis, the residues in a protein are often chemically modified by post-translational modification , which alters

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3916-539: A protein that fold into distinct structural units. Domains usually also have specific functions, such as enzymatic activities (e.g. kinase ) or they serve as binding modules (e.g. the SH3 domain binds to proline-rich sequences in other proteins). Short amino acid sequences within proteins often act as recognition sites for other proteins. For instance, SH3 domains typically bind to short PxxP motifs (i.e. 2 prolines [P], separated by two unspecified amino acids [x], although

4094-486: A role in biological recognition phenomena involving cells and proteins. Receptors and hormones are highly specific binding proteins. Transmembrane proteins can also serve as ligand transport proteins that alter the permeability of the cell membrane to small molecules and ions. The membrane alone has a hydrophobic core through which polar or charged molecules cannot diffuse . Membrane proteins contain internal channels that allow such molecules to enter and exit

4272-560: A rotation by angle θ in the plane with normal vector θ ^ {\textstyle {\hat {\boldsymbol {\theta }}}} , U = e − i ℏ θ ⋅ S , {\displaystyle U=e^{-{\frac {i}{\hbar }}{\boldsymbol {\theta }}\cdot \mathbf {S} },} where θ = θ θ ^ {\textstyle {\boldsymbol {\theta }}=\theta {\hat {\boldsymbol {\theta }}}} , and S

4450-437: A separate lock unit, which is essentially an additional transmitter and RF processor tuned to the lock nucleus (deuterium) rather than the nuclei of the sample of interest. In modern NMR spectrometers shimming is adjusted automatically, though in some cases the operator has to optimize the shim parameters manually to obtain the best possible resolution. Upon excitation of the sample with a radio frequency (60–1000 MHz) pulse,

4628-406: A series of purification steps may be necessary to obtain protein sufficiently pure for laboratory applications. To simplify this process, genetic engineering is often used to add chemical features to proteins that make them easier to purify without affecting their structure or activity. Here, a "tag" consisting of a specific amino acid sequence, often a series of histidine residues (a " His-tag "),

4806-430: A significant broadening of spectral lines. A variety of techniques allows establishing high-resolution conditions, that can, at least for C spectra, be comparable to solution-state NMR spectra. Two important concepts for high-resolution solid-state NMR spectroscopy are the limitation of possible molecular orientation by sample orientation, and the reduction of anisotropic nuclear magnetic interactions by sample spinning. Of

4984-420: A single quantum state, even after torque is applied. Rotating a spin-2 particle 180° can bring it back to the same quantum state, and a spin-4 particle should be rotated 90° to bring it back to the same quantum state. The spin-2 particle can be analogous to a straight stick that looks the same even after it is rotated 180°, and a spin-0 particle can be imagined as sphere, which looks the same after whatever angle it

5162-727: A smaller percentage of hydrogen atoms, which are the atoms usually observed in NMR spectroscopy, and because nucleic acid double helices are stiff and roughly linear, they do not fold back on themselves to give "long-range" correlations. The types of NMR usually done with nucleic acids are H or proton NMR , C NMR , N NMR , and P NMR . Two-dimensional NMR methods are almost always used, such as correlation spectroscopy (COSY) and total coherence transfer spectroscopy (TOCSY) to detect through-bond nuclear couplings, and nuclear Overhauser effect spectroscopy (NOESY) to detect couplings between nuclei that are close to each other in space. Parameters taken from

5340-432: A solution known as a crude lysate . The resulting mixture can be purified using ultracentrifugation , which fractionates the various cellular components into fractions containing soluble proteins; membrane lipids and proteins; cellular organelles , and nucleic acids . Precipitation by a method known as salting out can concentrate the proteins from this lysate. Various types of chromatography are then used to isolate

5518-400: A spin quantum number of 1/2, are of great significance in NMR spectroscopy. Examples include H, C, N, and P. Some atoms with very high spin (as 9/2 for Tc atom) are also extensively studied with NMR spectroscopy. When placed in a magnetic field, NMR active nuclei (such as H or C) absorb electromagnetic radiation at a frequency characteristic of the isotope . The resonant frequency, energy of

Nuclear magnetic resonance spectroscopy - Misplaced Pages Continue

5696-429: A spinning sample-holder inside a very strong magnet, a radio-frequency emitter, and a receiver with a probe (an antenna assembly) that goes inside the magnet to surround the sample, optionally gradient coils for diffusion measurements, and electronics to control the system. Spinning the sample is usually necessary to average out diffusional motion, however, some experiments call for a stationary sample when solution movement

5874-403: A unitary projective representation of the rotation group SO(3) . Each such representation corresponds to a representation of the covering group of SO(3), which is SU(2) . There is one n -dimensional irreducible representation of SU(2) for each dimension, though this representation is n -dimensional real for odd n and n -dimensional complex for even n (hence of real dimension 2 n ). For

6052-441: A variety of techniques such as ultracentrifugation , precipitation , electrophoresis , and chromatography ; the advent of genetic engineering has made possible a number of methods to facilitate purification. To perform in vitro analysis, a protein must be purified away from other cellular components. This process usually begins with cell lysis , in which a cell's membrane is disrupted and its internal contents released into

6230-959: A very strong, large and expensive liquid-helium -cooled superconducting magnet, because resolution directly depends on magnetic field strength. Higher magnetic field also improves the sensitivity of the NMR spectroscopy, which depends on the population difference between the two nuclear levels, which increases exponentially with the magnetic field strength. Less expensive machines using permanent magnets and lower resolution are also available, which still give sufficient performance for certain applications such as reaction monitoring and quick checking of samples. There are even benchtop nuclear magnetic resonance spectrometers . NMR spectra of protons (H nuclei) can be observed even in Earth magnetic field . Low-resolution NMR produces broader peaks, which can easily overlap one another, causing issues in resolving complex structures. The use of higher-strength magnetic fields result in

6408-479: Is a development of ordinary NMR. In two-dimensional NMR , the emission is centered around a single frequency, and correlated resonances are observed. This allows identifying the neighboring substituents of the observed functional group, allowing unambiguous identification of the resonances. There are also more complex 3D and 4D methods and a variety of methods designed to suppress or amplify particular types of resonances. In nuclear Overhauser effect (NOE) spectroscopy,

6586-541: Is a matter of interpretation whether the Hamiltonian must include such a term, and whether this aspect of classical mechanics extends into quantum mechanics (any particle's intrinsic spin angular momentum, S , is a quantum number arising from a " spinor " in the mathematical solution to the Dirac equation , rather than being a more nearly physical quantity, like orbital angular momentum L ). Nevertheless, spin appears in

6764-405: Is also possible. The timescale of NMR is relatively long, and thus it is not suitable for observing fast phenomena, producing only an averaged spectrum. Although large amounts of impurities do show on an NMR spectrum, better methods exist for detecting impurities, as NMR is inherently not very sensitive – though at higher frequencies, sensitivity is higher. Correlation spectroscopy

6942-463: Is also useful for probing the binding of nucleic acid molecules to other molecules, such as proteins or drugs, by seeing which resonances are shifted upon binding of the other molecule. Carbohydrate NMR spectroscopy addresses questions on the structure and conformation of carbohydrates . The analysis of carbohydrates by 1H NMR is challenging due to the limited variation in functional groups, which leads to 1H resonances concentrated in narrow bands of

7120-693: Is an intrinsic form of angular momentum carried by elementary particles , and thus by composite particles such as hadrons , atomic nuclei , and atoms. Spin is quantized, and accurate models for the interaction with spin require relativistic quantum mechanics or quantum field theory . The existence of electron spin angular momentum is inferred from experiments, such as the Stern–Gerlach experiment , in which silver atoms were observed to possess two possible discrete angular momenta despite having no orbital angular momentum. The relativistic spin–statistics theorem connects electron spin quantization to

7298-477: Is an important variable. For instance, measurements of diffusion constants ( diffusion ordered spectroscopy or DOSY) are done using a stationary sample with spinning off, and flow cells can be used for online analysis of process flows. The vast majority of molecules in a solution are solvent molecules, and most regular solvents are hydrocarbons and so contain NMR-active hydrogen-1 nuclei. In order to avoid having

Nuclear magnetic resonance spectroscopy - Misplaced Pages Continue

7476-406: Is attached to one terminus of the protein. As a result, when the lysate is passed over a chromatography column containing nickel , the histidine residues ligate the nickel and attach to the column while the untagged components of the lysate pass unimpeded. A number of different tags have been developed to help researchers purify specific proteins from complex mixtures. Spin (physics) Spin

7654-421: Is called the dispersion. It is rather small for H signals, but much larger for other nuclei. NMR signals are reported relative to a reference signal, usually that of TMS ( tetramethylsilane ). Additionally, since the distribution of NMR signals is field-dependent, these frequencies are divided by the spectrometer frequency. However, since we are dividing Hz by MHz, the resulting number would be too small, and thus it

7832-411: Is centered on the peak of an individual nucleus; if its magnetic field is correlated with another nucleus by through-bond (COSY, HSQC, etc.) or through-space (NOE) coupling, a response can also be detected on the frequency of the correlated nucleus. Two-dimensional NMR spectra provide more information about a molecule than one-dimensional NMR spectra and are especially useful in determining the structure of

8010-562: Is dictated by the nucleotide sequence of their genes , and which usually results in protein folding into a specific 3D structure that determines its activity. A linear chain of amino acid residues is called a polypeptide . A protein contains at least one long polypeptide. Short polypeptides, containing less than 20–30 residues, are rarely considered to be proteins and are commonly called peptides . The individual amino acid residues are bonded together by peptide bonds and adjacent amino acid residues. The sequence of amino acid residues in

8188-628: Is found in hard or filamentous structures such as hair , nails , feathers , hooves , and some animal shells . Some globular proteins can also play structural functions, for example, actin and tubulin are globular and soluble as monomers, but polymerize to form long, stiff fibers that make up the cytoskeleton , which allows the cell to maintain its shape and size. Other proteins that serve structural functions are motor proteins such as myosin , kinesin , and dynein , which are capable of generating mechanical forces. These proteins are crucial for cellular motility of single celled organisms and

8366-469: Is higher in prokaryotes than eukaryotes and can reach up to 20 amino acids per second. The process of synthesizing a protein from an mRNA template is known as translation . The mRNA is loaded onto the ribosome and is read three nucleotides at a time by matching each codon to its base pairing anticodon located on a transfer RNA molecule, which carries the amino acid corresponding to the codon it recognizes. The enzyme aminoacyl tRNA synthetase "charges"

8544-461: Is inefficient for polypeptides longer than about 300 amino acids, and the synthesized proteins may not readily assume their native tertiary structure . Most chemical synthesis methods proceed from C-terminus to N-terminus, opposite the biological reaction. Most proteins fold into unique 3D structures. The shape into which a protein naturally folds is known as its native conformation . Although many proteins can fold unassisted, simply through

8722-399: Is its poor sensitivity (compared to other analytical methods, such as mass spectrometry ). Typically 2–50 mg of a substance is required to record a decent-quality NMR spectrum. The NMR method is non-destructive, thus the substance may be recovered. To obtain high-resolution NMR spectra, solid substances are usually dissolved to make liquid solutions, although solid-state NMR spectroscopy

8900-510: Is multiplied by a million. This operation therefore gives a locator number called the "chemical shift" with units of parts per million. The chemical shift provides structural information. The conversion of chemical shifts (and J's, see below) is called assigning the spectrum. For diamagnetic organic compounds, assignments of H and C NMR spectra are extremely sophisticated because of the large databases and easy computational tools. In general, chemical shifts for protons are highly predictable, since

9078-399: Is now a common tool for the determination of Conformation Activity Relationships where the structure before and after interaction with, for example, a drug candidate is compared to its known biochemical activity. Proteins are orders of magnitude larger than the small organic molecules discussed earlier in this article, but the basic NMR techniques and some NMR theory also applies. Because of

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9256-404: Is often enormous—as much as 10 -fold increase in rate over the uncatalysed reaction in the case of orotate decarboxylase (78 million years without the enzyme, 18 milliseconds with the enzyme). The molecules bound and acted upon by enzymes are called substrates . Although enzymes can consist of hundreds of amino acids, it is usually only a small fraction of the residues that come in contact with

9434-420: Is often the only way to distinguish different nuclei. The magnitude of the coupling (the coupling constant J ) is an effect of how strongly the nuclei are coupled to each other. For simple cases, this is an effect of the bonding distance between the nuclei, the magnetic moment of the nuclei, and the dihedral angle between them. The above description assumes that the coupling constant is small in comparison with

9612-503: Is pointing in the + z or − z directions respectively, and are often referred to as "spin up" and "spin down". For a spin- ⁠ 3 / 2 ⁠ particle, like a delta baryon , the possible values are + ⁠ 3 / 2 ⁠ , + ⁠ 1 / 2 ⁠ , − ⁠ 1 / 2 ⁠ , − ⁠ 3 / 2 ⁠ . For a given quantum state , one could think of a spin vector ⟨ S ⟩ {\textstyle \langle S\rangle } whose components are

9790-412: Is proportional to the magnetic field ( Zeeman effect ). Δ E is also sensitive to electronic environment of the nucleus, giving rise to what is known as the chemical shift, δ. The simplest types of NMR graphs are plots of the different chemical shifts of the nuclei being studied in the molecule. The value of δ is often expressed in terms of "shielding": shielded nuclei have higher Δ E . The range of δ values

9968-454: Is rotated. It is clear that the transformation law must be linear, so we can represent it by associating a matrix with each rotation, and the product of two transformation matrices corresponding to rotations A and B must be equal (up to phase) to the matrix representing rotation AB. Further, rotations preserve the quantum-mechanical inner product, and so should our transformation matrices: ∑ m = − j j

10146-1855: Is the Levi-Civita symbol . It follows (as with angular momentum ) that the eigenvectors of S ^ 2 {\displaystyle {\hat {S}}^{2}} and S ^ z {\displaystyle {\hat {S}}_{z}} (expressed as kets in the total S basis ) are S ^ 2 | s , m s ⟩ = ℏ 2 s ( s + 1 ) | s , m s ⟩ , S ^ z | s , m s ⟩ = ℏ m s | s , m s ⟩ . {\displaystyle {\begin{aligned}{\hat {S}}^{2}|s,m_{s}\rangle &=\hbar ^{2}s(s+1)|s,m_{s}\rangle ,\\{\hat {S}}_{z}|s,m_{s}\rangle &=\hbar m_{s}|s,m_{s}\rangle .\end{aligned}}} The spin raising and lowering operators acting on these eigenvectors give S ^ ± | s , m s ⟩ = ℏ s ( s + 1 ) − m s ( m s ± 1 ) | s , m s ± 1 ⟩ , {\displaystyle {\hat {S}}_{\pm }|s,m_{s}\rangle =\hbar {\sqrt {s(s+1)-m_{s}(m_{s}\pm 1)}}|s,m_{s}\pm 1\rangle ,} where S ^ ± = S ^ x ± i S ^ y {\displaystyle {\hat {S}}_{\pm }={\hat {S}}_{x}\pm i{\hat {S}}_{y}} . But unlike orbital angular momentum,

10324-628: Is the Planck constant , and ℏ = h 2 π {\textstyle \hbar ={\frac {h}{2\pi }}} is the reduced Planck constant. In contrast, orbital angular momentum can only take on integer values of s ; i.e., even-numbered values of n . Those particles with half-integer spins, such as ⁠ 1 / 2 ⁠ , ⁠ 3 / 2 ⁠ , ⁠ 5 / 2 ⁠ , are known as fermions , while those particles with integer spins, such as 0, 1, 2, are known as bosons . The two families of particles obey different rules and broadly have different roles in

10502-532: Is the code for methionine . Because DNA contains four nucleotides, the total number of possible codons is 64; hence, there is some redundancy in the genetic code, with some amino acids specified by more than one codon. Genes encoded in DNA are first transcribed into pre- messenger RNA (mRNA) by proteins such as RNA polymerase . Most organisms then process the pre-mRNA (also known as a primary transcript ) using various forms of post-transcriptional modification to form

10680-1566: Is the vector of spin operators . Working in the coordinate system where θ ^ = z ^ {\textstyle {\hat {\theta }}={\hat {z}}} , we would like to show that S x and S y are rotated into each other by the angle θ . Starting with S x . Using units where ħ = 1 : S x → U † S x U = e i θ S z S x e − i θ S z = S x + ( i θ ) [ S z , S x ] + ( 1 2 ! ) ( i θ ) 2 [ S z , [ S z , S x ] ] + ( 1 3 ! ) ( i θ ) 3 [ S z , [ S z , [ S z , S x ] ] ] + ⋯ {\displaystyle {\begin{aligned}S_{x}\rightarrow U^{\dagger }S_{x}U&=e^{i\theta S_{z}}S_{x}e^{-i\theta S_{z}}\\&=S_{x}+(i\theta )\left[S_{z},S_{x}\right]+\left({\frac {1}{2!}}\right)(i\theta )^{2}\left[S_{z},\left[S_{z},S_{x}\right]\right]+\left({\frac {1}{3!}}\right)(i\theta )^{3}\left[S_{z},\left[S_{z},\left[S_{z},S_{x}\right]\right]\right]+\cdots \end{aligned}}} Using

10858-851: Is then the sum of the orbital angular momentum and the spin. The quantum-mechanical operators associated with spin- ⁠ 1 / 2 ⁠ observables are S ^ = ℏ 2 σ , {\displaystyle {\hat {\mathbf {S} }}={\frac {\hbar }{2}}{\boldsymbol {\sigma }},} where in Cartesian components S x = ℏ 2 σ x , S y = ℏ 2 σ y , S z = ℏ 2 σ z . {\displaystyle S_{x}={\frac {\hbar }{2}}\sigma _{x},\quad S_{y}={\frac {\hbar }{2}}\sigma _{y},\quad S_{z}={\frac {\hbar }{2}}\sigma _{z}.} For

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11036-426: Is therefore with a set of complex numbers corresponding to amplitudes of finding a given value of projection of its intrinsic angular momentum on a given axis. For instance, for a spin- ⁠ 1 / 2 ⁠ particle, we would need two numbers a ±1/2 , giving amplitudes of finding it with projection of angular momentum equal to + ⁠ ħ / 2 ⁠ and − ⁠ ħ / 2 ⁠ , satisfying

11214-425: Is to obtain high resolution 3-dimensional structures of the protein, similar to what can be achieved by X-ray crystallography . In contrast to X-ray crystallography, NMR spectroscopy is usually limited to proteins smaller than 35 kDa , although larger structures have been solved. NMR spectroscopy is often the only way to obtain high resolution information on partially or wholly intrinsically unstructured proteins . It

11392-463: Is turned through. Spin obeys commutation relations analogous to those of the orbital angular momentum : [ S ^ j , S ^ k ] = i ℏ ε j k l S ^ l , {\displaystyle \left[{\hat {S}}_{j},{\hat {S}}_{k}\right]=i\hbar \varepsilon _{jkl}{\hat {S}}_{l},} where ε jkl

11570-427: Is usually given as a dimensionless spin quantum number by dividing the spin angular momentum by the reduced Planck constant ħ . Often, the "spin quantum number" is simply called "spin". The earliest models for electron spin imagined a rotating charged mass, but this model fails when examined in detail: the required space distribution does not match limits on the electron radius : the required rotation speed exceeds

11748-475: The μ ν are the neutrino magnetic moments, m ν are the neutrino masses, and μ B is the Bohr magneton . New physics above the electroweak scale could, however, lead to significantly higher neutrino magnetic moments. It can be shown in a model-independent way that neutrino magnetic moments larger than about 10   μ B are "unnatural" because they would also lead to large radiative contributions to

11926-403: The Dirac equation , a fundamental equation connecting the electron's spin with its electromagnetic properties; and the deviation from −2 arises from the electron's interaction with the surrounding quantum fields, including its own electromagnetic field and virtual particles . Composite particles also possess magnetic moments associated with their spin. In particular, the neutron possesses

12104-448: The Dirac equation , and thus the relativistic Hamiltonian of the electron, treated as a Dirac field , can be interpreted as including a dependence in the spin S . Spin obeys the mathematical laws of angular momentum quantization . The specific properties of spin angular momenta include: The conventional definition of the spin quantum number is s = ⁠ n / 2 ⁠ , where n can be any non-negative integer . Hence

12282-480: The Pauli exclusion principle : observations of exclusion imply half-integer spin, and observations of half-integer spin imply exclusion. Spin is described mathematically as a vector for some particles such as photons, and as a spinor or bispinor for other particles such as electrons. Spinors and bispinors behave similarly to vectors : they have definite magnitudes and change under rotations; however, they use an unconventional "direction". All elementary particles of

12460-486: The amino acid leucine for which he found a (nearly correct) molecular weight of 131 Da . Early nutritional scientists such as the German Carl von Voit believed that protein was the most important nutrient for maintaining the structure of the body, because it was generally believed that "flesh makes flesh." Around 1862, Karl Heinrich Ritthausen isolated the amino acid glutamic acid . Thomas Burr Osborne compiled

12638-413: The expectation values of the spin components along each axis, i.e., ⟨ S ⟩ = [ ⟨ S x ⟩ , ⟨ S y ⟩ , ⟨ S z ⟩ ] {\textstyle \langle S\rangle =[\langle S_{x}\rangle ,\langle S_{y}\rangle ,\langle S_{z}\rangle ]} . This vector then would describe

12816-644: The muscle sarcomere , with a molecular mass of almost 3,000 kDa and a total length of almost 27,000 amino acids. Short proteins can also be synthesized chemically by a family of methods known as peptide synthesis , which rely on organic synthesis techniques such as chemical ligation to produce peptides in high yield. Chemical synthesis allows for the introduction of non-natural amino acids into polypeptide chains, such as attachment of fluorescent probes to amino acid side chains. These methods are useful in laboratory biochemistry and cell biology , though generally not for commercial applications. Chemical synthesis

12994-436: The reduced Planck constant , such that the state function of the particle is, say, not ψ = ψ ( r ) {\displaystyle \psi =\psi (\mathbf {r} )} , but ψ = ψ ( r , s z ) {\displaystyle \psi =\psi (\mathbf {r} ,s_{z})} , where s z {\displaystyle s_{z}} can take only

13172-484: The relaxation of the resonances is observed. As NOE depends on the proximity of the nuclei, quantifying the NOE for each nucleus allows construction of a three-dimensional model of the molecule. NMR spectrometers are relatively expensive; universities usually have them, but they are less common in private companies. Between 2000 and 2015, an NMR spectrometer cost around 0.5–5 million  USD . Modern NMR spectrometers have

13350-645: The sperm of many multicellular organisms which reproduce sexually . They also generate the forces exerted by contracting muscles and play essential roles in intracellular transport. A key question in molecular biology is how proteins evolve, i.e. how can mutations (or rather changes in amino acid sequence) lead to new structures and functions? Most amino acids in a protein can be changed without disrupting activity or function, as can be seen from numerous homologous proteins across species (as collected in specialized databases for protein families , e.g. PFAM ). In order to prevent dramatic consequences of mutations,

13528-944: The spin operator commutation relations , we see that the commutators evaluate to i S y for the odd terms in the series, and to S x for all of the even terms. Thus: U † S x U = S x [ 1 − θ 2 2 ! + ⋯ ] − S y [ θ − θ 3 3 ! ⋯ ] = S x cos ⁡ θ − S y sin ⁡ θ , {\displaystyle {\begin{aligned}U^{\dagger }S_{x}U&=S_{x}\left[1-{\frac {\theta ^{2}}{2!}}+\cdots \right]-S_{y}\left[\theta -{\frac {\theta ^{3}}{3!}}\cdots \right]\\&=S_{x}\cos \theta -S_{y}\sin \theta ,\end{aligned}}} as expected. Note that since we only relied on

13706-1074: The wavefunction ψ ( r 1 , σ 1 , … , r N , σ N ) {\displaystyle \psi (\mathbf {r} _{1},\sigma _{1},\dots ,\mathbf {r} _{N},\sigma _{N})} for a system of N identical particles having spin s must change upon interchanges of any two of the N particles as ψ ( … , r i , σ i , … , r j , σ j , … ) = ( − 1 ) 2 s ψ ( … , r j , σ j , … , r i , σ i , … ) . {\displaystyle \psi (\dots ,\mathbf {r} _{i},\sigma _{i},\dots ,\mathbf {r} _{j},\sigma _{j},\dots )=(-1)^{2s}\psi (\dots ,\mathbf {r} _{j},\sigma _{j},\dots ,\mathbf {r} _{i},\sigma _{i},\dots ).} Thus, for bosons

13884-409: The z  axis. One can see that there are 2 s + 1 possible values of s z . The number " 2 s + 1 " is the multiplicity of the spin system. For example, there are only two possible values for a spin- ⁠ 1 / 2 ⁠ particle: s z = + ⁠ 1 / 2 ⁠ and s z = − ⁠ 1 / 2 ⁠ . These correspond to quantum states in which the spin component

14062-466: The "direction" in which the spin is pointing, corresponding to the classical concept of the axis of rotation . It turns out that the spin vector is not very useful in actual quantum-mechanical calculations, because it cannot be measured directly: s x , s y and s z cannot possess simultaneous definite values, because of a quantum uncertainty relation between them. However, for statistically large collections of particles that have been placed in

14240-399: The (signed) intensity as a function of pulse width. It follows a sine curve and, accordingly, changes sign at pulse widths corresponding to 180° and 360° pulses. Decay times of the excitation, typically measured in seconds, depend on the effectiveness of relaxation, which is faster for lighter nuclei and in solids, slower for heavier nuclei and in solutions, and can be very long in gases. If

14418-493: The 1700s by Antoine Fourcroy and others, who often collectively called them " albumins ", or "albuminous materials" ( Eiweisskörper , in German). Gluten , for example, was first separated from wheat in published research around 1747, and later determined to exist in many plants. In 1789, Antoine Fourcroy recognized three distinct varieties of animal proteins: albumin , fibrin , and gelatin . Vegetable (plant) proteins studied in

14596-562: The 1950s, the Armour Hot Dog Company purified 1 kg of pure bovine pancreatic ribonuclease A and made it freely available to scientists; this gesture helped ribonuclease A become a major target for biochemical study for the following decades. The understanding of proteins as polypeptides , or chains of amino acids, came through the work of Franz Hofmeister and Hermann Emil Fischer in 1902. The central role of proteins as enzymes in living organisms that catalyzed reactions

14774-530: The 1952 Nobel Prize in Physics for their inventions. The key determinant of NMR activity in atomic nuclei is the nuclear spin quantum number ( I ). This intrinsic quantum property, similar to an atom's " spin ", characterizes the angular momentum of the nucleus. To be NMR-active, a nucleus must have a non-zero nuclear spin ( I ≠ 0). It is this non-zero spin that enables nuclei to interact with external magnetic fields and show signals in NMR. Atoms with an odd sum of protons and neutrons exhibit half-integer values for

14952-498: The 20,000 or so proteins encoded by the human genome, only 6,000 are detected in lymphoblastoid cells. Proteins are assembled from amino acids using information encoded in genes. Each protein has its own unique amino acid sequence that is specified by the nucleotide sequence of the gene encoding this protein. The genetic code is a set of three-nucleotide sets called codons and each three-nucleotide combination designates an amino acid, for example AUG ( adenine – uracil – guanine )

15130-491: The 4 H sites of 1,2-dichlorobenzene divide into two chemically equivalent pairs by symmetry, but an individual member of one of the pairs has different couplings to the spins making up the other pair. Magnetic inequivalence can lead to highly complex spectra, which can only be analyzed by computational modeling. Such effects are more common in NMR spectra of aromatic and other non-flexible systems, while conformational averaging about C−C bonds in flexible molecules tends to equalize

15308-516: The EC number system provides a functional classification scheme. Similarly, the gene ontology classifies both genes and proteins by their biological and biochemical function, but also by their intracellular location. Sequence similarity is used to classify proteins both in terms of evolutionary and functional similarity. This may use either whole proteins or protein domains , especially in multi-domain proteins . Protein domains allow protein classification by

15486-798: The NMR spectrum. In other words, there is poor spectral dispersion. The anomeric proton resonances are segregated from the others due to fact that the anomeric carbons bear two oxygen atoms. For smaller carbohydrates, the dispersion of the anomeric proton resonances facilitates the use of 1D TOCSY experiments to investigate the entire spin systems of individual carbohydrate residues. Knowledge of energy minima and rotational energy barriers of small molecules in solution can be found using NMR, e.g. looking at free ligand conformational preferences and conformational dynamics, respectively. This can be used to guide drug design hypotheses, since experimental and calculated values are comparable. For example, AstraZeneca uses NMR for its oncology research & development. One of

15664-709: The ability of many enzymes to bind and process multiple substrates . When mutations occur, the specificity of an enzyme can increase (or decrease) and thus its enzymatic activity. Thus, bacteria (or other organisms) can adapt to different food sources, including unnatural substrates such as plastic. Methods commonly used to study protein structure and function include immunohistochemistry , site-directed mutagenesis , X-ray crystallography , nuclear magnetic resonance and mass spectrometry . The activities and structures of proteins may be examined in vitro , in vivo , and in silico . In vitro studies of purified proteins in controlled environments are useful for learning how

15842-473: The acidic hydroxyl proton often results in a loss of coupling information. Coupling to any spin-1/2 nuclei such as phosphorus-31 or fluorine-19 works in this fashion (although the magnitudes of the coupling constants may be very different). But the splitting patterns differ from those described above for nuclei with spin greater than 1/2 because the spin quantum number has more than two possible values. For instance, coupling to deuterium (a spin-1 nucleus) splits

16020-405: The addition of a single methyl group to a binding partner can sometimes suffice to nearly eliminate binding; for example, the aminoacyl tRNA synthetase specific to the amino acid valine discriminates against the very similar side chain of the amino acid isoleucine . Proteins can bind to other proteins as well as to small-molecule substrates. When proteins bind specifically to other copies of

16198-814: The allowed values of s are 0, ⁠ 1 / 2 ⁠ , 1, ⁠ 3 / 2 ⁠ , 2, etc. The value of s for an elementary particle depends only on the type of particle and cannot be altered in any known way (in contrast to the spin direction described below). The spin angular momentum S of any physical system is quantized . The allowed values of S are S = ℏ s ( s + 1 ) = h 2 π n 2 ( n + 2 ) 2 = h 4 π n ( n + 2 ) , {\displaystyle S=\hbar \,{\sqrt {s(s+1)}}={\frac {h}{2\pi }}\,{\sqrt {{\frac {n}{2}}{\frac {(n+2)}{2}}}}={\frac {h}{4\pi }}\,{\sqrt {n(n+2)}},} where h

16376-595: The alpha carbons are roughly coplanar . The other two dihedral angles in the peptide bond determine the local shape assumed by the protein backbone. The end with a free amino group is known as the N-terminus or amino terminus, whereas the end of the protein with a free carboxyl group is known as the C-terminus or carboxy terminus (the sequence of the protein is written from N-terminus to C-terminus, from left to right). The words protein , polypeptide, and peptide are

16554-531: The amino acid side chains in a protein that ultimately determines its three-dimensional structure and its chemical reactivity. The amino acids in a polypeptide chain are linked by peptide bonds . Once linked in the protein chain, an individual amino acid is called a residue, and the linked series of carbon, nitrogen, and oxygen atoms are known as the main chain or protein backbone. The peptide bond has two resonance forms that contribute some double-bond character and inhibit rotation around its axis, so that

16732-482: The angle between the spin vector and the detector increases, until at an angle of 180°—that is, for detectors oriented in the opposite direction to the spin vector—the expectation of detecting particles from the collection reaches a minimum of 0%. As a qualitative concept, the spin vector is often handy because it is easy to picture classically. For instance, quantum-mechanical spin can exhibit phenomena analogous to classical gyroscopic effects . For example, one can exert

16910-560: The angular momentum of a field, Hans C. Ohanian showed that "spin is essentially a wave property ... generated by a circulating flow of charge in the wave field of the electron". This same concept of spin can be applied to gravity waves in water: "spin is generated by subwavelength circular motion of water particles". Unlike classical wavefield circulation, which allows continuous values of angular momentum, quantum wavefields allow only discrete values. Consequently, energy transfer to or from spin states always occurs in fixed quantum steps. Only

17088-412: The angular momentum of a particle possesses not only a magnitude (how fast the body is rotating), but also a direction (either up or down on the axis of rotation of the particle). Quantum-mechanical spin also contains information about direction, but in a more subtle form. Quantum mechanics states that the component of angular momentum for a spin- s particle measured along any direction can only take on

17266-406: The applied magnetic field must be extremely uniform throughout the sample volume. High-resolution NMR spectrometers use shims to adjust the homogeneity of the magnetic field to parts per billion ( ppb ) in a volume of a few cubic centimeters. In order to detect and compensate for inhomogeneity and drift in the magnetic field, the spectrometer maintains a "lock" on the solvent deuterium frequency with

17444-534: The atomic dipole moments spontaneously align locally, producing a macroscopic, non-zero magnetic field from the domain. These are the ordinary "magnets" with which we are all familiar. In paramagnetic materials, the magnetic dipole moments of individual atoms will partially align with an externally applied magnetic field. In diamagnetic materials, on the other hand, the magnetic dipole moments of individual atoms align oppositely to any externally applied magnetic field, even if it requires energy to do so. The study of

17622-730: The background noise, although the integrated area under the peaks remains constant. In most high-field NMR, however, the distortions are usually modest, and the characteristic distortions ( roofing ) can in fact help to identify related peaks. Some of these patterns can be analyzed with the method published by John Pople , though it has limited scope. Second-order effects decrease as the frequency difference between multiplets increases, so that high-field (i.e. high-frequency) NMR spectra display less distortion than lower-frequency spectra. Early spectra at 60 MHz were more prone to distortion than spectra from later machines typically operating at frequencies at 200 MHz or above. Furthermore, as in

17800-491: The behavior of spinors and vectors under coordinate rotations . For example, rotating a spin- ⁠ 1 / 2 ⁠ particle by 360° does not bring it back to the same quantum state, but to the state with the opposite quantum phase ; this is detectable, in principle, with interference experiments. To return the particle to its exact original state, one needs a 720° rotation. (The plate trick and Möbius strip give non-quantum analogies.) A spin-zero particle can only have

17978-541: The behavior of such " spin models " is a thriving area of research in condensed matter physics . For instance, the Ising model describes spins (dipoles) that have only two possible states, up and down, whereas in the Heisenberg model the spin vector is allowed to point in any direction. These models have many interesting properties, which have led to interesting results in the theory of phase transitions . In classical mechanics,

18156-574: The binding of a substrate molecule to an enzyme's active site , or the physical region of the protein that participates in chemical catalysis. In solution, proteins also undergo variation in structure through thermal vibration and the collision with other molecules. Proteins can be informally divided into three main classes, which correlate with typical tertiary structures: globular proteins , fibrous proteins , and membrane proteins . Almost all globular proteins are soluble and many are enzymes. Fibrous proteins are often structural, such as collagen ,

18334-570: The body of a multicellular organism. These proteins must have a high binding affinity when their ligand is present in high concentrations, but must also release the ligand when it is present at low concentrations in the target tissues. The canonical example of a ligand-binding protein is haemoglobin , which transports oxygen from the lungs to other organs and tissues in all vertebrates and has close homologs in every biological kingdom . Lectins are sugar-binding proteins which are highly specific for their sugar moieties. Lectins typically play

18512-558: The cell is as enzymes , which catalyse chemical reactions. Enzymes are usually highly specific and accelerate only one or a few chemical reactions. Enzymes carry out most of the reactions involved in metabolism , as well as manipulating DNA in processes such as DNA replication , DNA repair , and transcription . Some enzymes act on other proteins to add or remove chemical groups in a process known as posttranslational modification. About 4,000 reactions are known to be catalysed by enzymes. The rate acceleration conferred by enzymatic catalysis

18690-436: The cell surface and an effector domain within the cell, which may have enzymatic activity or may undergo a conformational change detected by other proteins within the cell. Antibodies are protein components of an adaptive immune system whose main function is to bind antigens , or foreign substances in the body, and target them for destruction. Antibodies can be secreted into the extracellular environment or anchored in

18868-752: The cell's machinery through the process of protein turnover . A protein's lifespan is measured in terms of its half-life and covers a wide range. They can exist for minutes or years with an average lifespan of 1–2 days in mammalian cells. Abnormal or misfolded proteins are degraded more rapidly either due to being targeted for destruction or due to being unstable. Like other biological macromolecules such as polysaccharides and nucleic acids , proteins are essential parts of organisms and participate in virtually every process within cells . Many proteins are enzymes that catalyse biochemical reactions and are vital to metabolism . Proteins also have structural or mechanical functions, such as actin and myosin in muscle and

19046-450: The cell. Many ion channel proteins are specialized to select for only a particular ion; for example, potassium and sodium channels often discriminate for only one of the two ions. Structural proteins confer stiffness and rigidity to otherwise-fluid biological components. Most structural proteins are fibrous proteins ; for example, collagen and elastin are critical components of connective tissue such as cartilage , and keratin

19224-727: The chemical and spatial structures of small molecules in a supercritical fluid environment, using state parameters as a driving force for such changes. Related methods of nuclear spectroscopy : Protein Proteins are large biomolecules and macromolecules that comprise one or more long chains of amino acid residues . Proteins perform a vast array of functions within organisms, including catalysing metabolic reactions , DNA replication , responding to stimuli , providing structure to cells and organisms , and transporting molecules from one location to another. Proteins differ from one another primarily in their sequence of amino acids, which

19402-621: The chemical properties of their amino acids, others require the aid of molecular chaperones to fold into their native states. Biochemists often refer to four distinct aspects of a protein's structure: Proteins are not entirely rigid molecules. In addition to these levels of structure, proteins may shift between several related structures while they perform their functions. In the context of these functional rearrangements, these tertiary or quaternary structures are usually referred to as " conformations ", and transitions between them are called conformational changes. Such changes are often induced by

19580-441: The chief actors within the cell, said to be carrying out the duties specified by the information encoded in genes. With the exception of certain types of RNA , most other biological molecules are relatively inert elements upon which proteins act. Proteins make up half the dry weight of an Escherichia coli cell, whereas other macromolecules such as DNA and RNA make up only 3% and 20%, respectively. The set of proteins expressed in

19758-442: The connectivity of atoms in a molecule. The multiplicity of the splitting is an effect of the spins of the nuclei that are coupled and the number of such nuclei involved in the coupling. Coupling to n equivalent spin-1/2 nuclei splits the signal into a n  + 1 multiplet with intensity ratios following Pascal's triangle as described in the table. Coupling to additional spins leads to further splittings of each component of

19936-490: The construction of enormously complex signaling networks. As interactions between proteins are reversible, and depend heavily on the availability of different groups of partner proteins to form aggregates that are capable to carry out discrete sets of function, study of the interactions between specific proteins is a key to understand important aspects of cellular function, and ultimately the properties that distinguish particular cell types. The best-known role of proteins in

20114-592: The couplings between protons on adjacent carbons, reducing problems with magnetic inequivalence. Correlation spectroscopy is one of several types of two-dimensional nuclear magnetic resonance (NMR) spectroscopy or 2D-NMR . This type of NMR experiment is best known by its acronym , COSY . Other types of two-dimensional NMR include J-spectroscopy, exchange spectroscopy (EXSY), Nuclear Overhauser effect spectroscopy (NOESY), total correlation spectroscopy (TOCSY), and heteronuclear correlation experiments, such as HSQC , HMQC , and HMBC . In correlation spectroscopy, emission

20292-408: The derivative unit kilodalton (kDa). The average size of a protein increases from Archaea to Bacteria to Eukaryote (283, 311, 438 residues and 31, 34, 49 kDa respectively) due to a bigger number of protein domains constituting proteins in higher organisms. For instance, yeast proteins are on average 466 amino acids long and 53 kDa in mass. The largest known proteins are the titins , a component of

20470-421: The difference in NMR frequencies between the inequivalent spins. If the shift separation decreases (or the coupling strength increases), the multiplet intensity patterns are first distorted, and then become more complex and less easily analyzed (especially if more than two spins are involved). Intensification of some peaks in a multiplet is achieved at the expense of the remainder, which sometimes almost disappear in

20648-400: The double helix does not have a compact interior and does not fold back upon itself. NMR is also useful for investigating nonstandard geometries such as bent helices , non-Watson–Crick basepairing, and coaxial stacking . It has been especially useful in probing the structure of natural RNA oligonucleotides, which tend to adopt complex conformations such as stem-loops and pseudoknots . NMR

20826-421: The eigenvectors are not spherical harmonics . They are not functions of θ and φ . There is also no reason to exclude half-integer values of s and m s . All quantum-mechanical particles possess an intrinsic spin s {\displaystyle s} (though this value may be equal to zero). The projection of the spin s {\displaystyle s} on any axis is quantized in units of

21004-447: The erroneous conclusion that they might be composed of a single type of (very large) molecule. The term "protein" to describe these molecules was proposed by Mulder's associate Berzelius; protein is derived from the Greek word πρώτειος ( proteios ), meaning "primary", "in the lead", or "standing in front", + -in . Mulder went on to identify the products of protein degradation such as

21182-420: The existence of spin in the Hamiltonian will produce an actual angular velocity, and hence an actual physical rotation – that is, a change in the phase-angle, θ , over time. However, whether this holds true for free electrons is ambiguous, since for an electron, | S | ² is a constant ⁠ 1  / 2 ⁠   ℏ , and one might decide that since it cannot change, no partial ( ∂ ) can exist. Therefore it

21360-603: The figure to the right, J-coupling can be used to identify ortho-meta-para substitution of a ring. Ortho coupling is the strongest at 15 Hz, Meta follows with an average of 2 Hz, and finally para coupling is usually insignificant for studies. More subtle effects can occur if chemically equivalent spins (i.e., nuclei related by symmetry and so having the same NMR frequency) have different coupling relationships to external spins. Spins that are chemically equivalent but are not indistinguishable (based on their coupling relationships) are termed magnetically inequivalent. For example,

21538-587: The first scientific works devoted to the use of pressure as a variable parameter in NMR experiments was the work of J. Jonas published in the journal Annual Review of Biophysics in 1994. The use of high pressures in NMR spectroscopy was primarily driven by the desire to study biochemical systems, where the use of high pressure allows controlled changes in intermolecular interactions without significant perturbations. Of course, attempts have been made to solve scientific problems using high-pressure NMR spectroscopy. However, most of them were difficult to reproduce due to

21716-509: The interaction of different spin states through the chemical bonds of a molecule and results in the splitting of NMR signals. For a proton, the local magnetic field is slightly different depending on whether an adjacent nucleus points towards or against the spectrometer magnetic field, which gives rise to two signals per proton instead of one. These splitting patterns can be complex or simple and, likewise, can be straightforwardly interpretable or deceptive. This coupling provides detailed insight into

21894-525: The late 1700s and early 1800s included gluten , plant albumin , gliadin , and legumin . Proteins were first described by the Dutch chemist Gerardus Johannes Mulder and named by the Swedish chemist Jöns Jacob Berzelius in 1838. Mulder carried out elemental analysis of common proteins and found that nearly all proteins had the same empirical formula , C 400 H 620 N 100 O 120 P 1 S 1 . He came to

22072-600: The latter approach, fast spinning around the magic angle is a very prominent method, when the system comprises spin-1/2 nuclei. Spinning rates of about 20 kHz are used, which demands special equipment. A number of intermediate techniques, with samples of partial alignment or reduced mobility, is currently being used in NMR spectroscopy. Applications in which solid-state NMR effects occur are often related to structure investigations on membrane proteins, protein fibrils or all kinds of polymers, and chemical analysis in inorganic chemistry, but also include "exotic" applications like

22250-435: The magnetic fields generated by the particles themselves. The intrinsic magnetic moment μ of a spin- ⁠ 1 / 2 ⁠ particle with charge q , mass m , and spin angular momentum S is where the dimensionless quantity g s is called the spin g -factor . For exclusively orbital rotations, it would be 1 (assuming that the mass and the charge occupy spheres of equal radius). The electron, being

22428-478: The major component of connective tissue, or keratin , the protein component of hair and nails. Membrane proteins often serve as receptors or provide channels for polar or charged molecules to pass through the cell membrane . A special case of intramolecular hydrogen bonds within proteins, poorly shielded from water attack and hence promoting their own dehydration , are called dehydrons . Many proteins are composed of several protein domains , i.e. segments of

22606-443: The mature mRNA, which is then used as a template for protein synthesis by the ribosome . In prokaryotes the mRNA may either be used as soon as it is produced, or be bound by a ribosome after having moved away from the nucleoid . In contrast, eukaryotes make mRNA in the cell nucleus and then translocate it across the nuclear membrane into the cytoplasm , where protein synthesis then takes place. The rate of protein synthesis

22784-405: The membranes of specialized B cells known as plasma cells . Whereas enzymes are limited in their binding affinity for their substrates by the necessity of conducting their reaction, antibodies have no such constraints. An antibody's binding affinity to its target is extraordinarily high. Many ligand transport proteins bind particular small biomolecules and transport them to other locations in

22962-427: The modern particle-physics era, where abstract quantum properties derived from symmetry properties dominate. Concrete interpretation became secondary and optional. The first classical model for spin proposed a small rigid particle rotating about an axis, as ordinary use of the word may suggest. Angular momentum can be computed from a classical field as well. By applying Frederik Belinfante 's approach to calculating

23140-617: The molecule. Subsequently, the distances obtained are used to generate a 3D structure of the molecule by solving a distance geometry problem. NMR can also be used to obtain information on the dynamics and conformational flexibility of different regions of a protein. Nucleic acid NMR is the use of NMR spectroscopy to obtain information about the structure and dynamics of poly nucleic acids , such as DNA or RNA . As of 2003, nearly half of all known RNA structures had been determined by NMR spectroscopy. Nucleic acid and protein NMR spectroscopy are similar but differences exist. Nucleic acids have

23318-404: The most important applications of the special relativity theory". Particles with spin can possess a magnetic dipole moment , just like a rotating electrically charged body in classical electrodynamics . These magnetic moments can be experimentally observed in several ways, e.g. by the deflection of particles by inhomogeneous magnetic fields in a Stern–Gerlach experiment , or by measuring

23496-401: The much higher number of atoms present in a protein molecule in comparison with a small organic compound, the basic 1D spectra become crowded with overlapping signals to an extent where direct spectral analysis becomes untenable. Therefore, multidimensional (2, 3 or 4D) experiments have been devised to deal with this problem. To facilitate these experiments, it is desirable to isotopically label

23674-642: The multiplet, e.g. coupling to two different spin-1/2 nuclei with significantly different coupling constants leads to a doublet of doublets (abbreviation: dd). Note that coupling between nuclei that are chemically equivalent (that is, have the same chemical shift) has no effect on the NMR spectra, and couplings between nuclei that are distant (usually more than 3 bonds apart for protons in flexible molecules) are usually too small to cause observable splittings. Long-range couplings over more than three bonds can often be observed in cyclic and aromatic compounds, leading to more complex splitting patterns. For example, in

23852-422: The neutrino mass. Since the neutrino masses are known to be at most about 1 eV/ c , fine-tuning would be necessary in order to prevent large contributions to the neutrino mass via radiative corrections. The measurement of neutrino magnetic moments is an active area of research. Experimental results have put the neutrino magnetic moment at less than 1.2 × 10  times the electron's magnetic moment. On

24030-496: The nobel prize in 1972, solidified the thermodynamic hypothesis of protein folding, according to which the folded form of a protein represents its free energy minimum. With the development of X-ray crystallography , it became possible to determine protein structures as well as their sequences. The first protein structures to be solved were hemoglobin by Max Perutz and myoglobin by John Kendrew , in 1958. The use of computers and increasing computing power also supported

24208-479: The nuclear spin quantum number ( I = 1/2, 3/2, 5/2, and so on). These atoms are NMR-active because they possess non-zero nuclear spin. Atoms with an even sum but both an odd number of protons and an odd number of neutrons exhibit integer nuclear spins ( I = 1, 2, 3, and so on). Conversely, atoms with an even number of both protons and neutrons have a nuclear spin quantum number of zero ( I = 0), and therefore are not NMR-active. NMR-active nuclei, particularly those with

24386-500: The order of 50,000 to 1 million. By contrast, eukaryotic cells are larger and thus contain much more protein. For instance, yeast cells have been estimated to contain about 50 million proteins and human cells on the order of 1 to 3 billion. The concentration of individual protein copies ranges from a few molecules per cell up to 20 million. Not all genes coding proteins are expressed in most cells and their number depends on, for example, cell type and external stimuli. For instance, of

24564-465: The other hand, elementary particles with spin but without electric charge, such as the photon and Z boson , do not have a magnetic moment. In ordinary materials, the magnetic dipole moments of individual atoms produce magnetic fields that cancel one another, because each dipole points in a random direction, with the overall average being very near zero. Ferromagnetic materials below their Curie temperature , however, exhibit magnetic domains in which

24742-430: The phase of the particle depends on the angle as e i S θ   , {\displaystyle e^{iS\theta }\ ,} for rotation of angle θ around the axis parallel to the spin S . This is equivalent to the quantum-mechanical interpretation of momentum as phase dependence in the position, and of orbital angular momentum as phase dependence in the angular position. For fermions,

24920-440: The physical and chemical properties, folding, stability, activity, and ultimately, the function of the proteins. Some proteins have non-peptide groups attached, which can be called prosthetic groups or cofactors . Proteins can also work together to achieve a particular function, and they often associate to form stable protein complexes . Once formed, proteins only exist for a certain period and are then degraded and recycled by

25098-515: The picture is less clear: From the Ehrenfest theorem , the angular velocity is equal to the derivative of the Hamiltonian to its conjugate momentum , which is the total angular momentum operator J = L + S . Therefore, if the Hamiltonian H has any dependence on the spin S , then   ⁠ ∂  H   / ∂  S   ⁠   must be non-zero; consequently, for classical mechanics ,

25276-521: The plant leaves and fuel cells. For example, Rahmani et al. studied the effect of pressure and temperature on the bicellar structures' self-assembly using deuterium NMR spectroscopy. Solid-state NMR is usefull also for metal structure understanding in case of X-ray amorphous metal samples (like nano-size refractory metal Tc) . Much of the innovation within NMR spectroscopy has been within the field of protein NMR spectroscopy, an important technique in structural biology . A common goal of these investigations

25454-449: The prefactor (−1) will reduce to +1, for fermions to −1. This permutation postulate for N -particle state functions has most important consequences in daily life, e.g. the periodic table of the chemical elements. As described above, quantum mechanics states that components of angular momentum measured along any direction can only take a number of discrete values. The most convenient quantum-mechanical description of particle's spin

25632-421: The problem of equipment for creating and maintaining high pressure. In the most common types of NMR cells for realization of high-pressure NMR experiments are given. High-pressure NMR spectroscopy has been widely used for a variety of applications, mainly related to the characterization of the structure of protein molecules. However, in recent years, software and design solutions have been proposed to characterize

25810-424: The process of cell signaling and signal transduction . Some proteins, such as insulin , are extracellular proteins that transmit a signal from the cell in which they were synthesized to other cells in distant tissues . Others are membrane proteins that act as receptors whose main function is to bind a signaling molecule and induce a biochemical response in the cell. Many receptors have a binding site exposed on

25988-534: The protein or proteins of interest based on properties such as molecular weight, net charge and binding affinity. The level of purification can be monitored using various types of gel electrophoresis if the desired protein's molecular weight and isoelectric point are known, by spectroscopy if the protein has distinguishable spectroscopic features, or by enzyme assays if the protein has enzymatic activity. Additionally, proteins can be isolated according to their charge using electrofocusing . For natural proteins,

26166-406: The protein with C and N because the predominant naturally occurring isotope C is not NMR-active and the nuclear quadrupole moment of the predominant naturally occurring N isotope prevents high resolution information from being obtained from this nitrogen isotope. The most important method used for structure determination of proteins utilizes NOE experiments to measure distances between atoms within

26344-427: The proteins in the cytoskeleton , which form a system of scaffolding that maintains cell shape. Other proteins are important in cell signaling, immune responses , cell adhesion , and the cell cycle . In animals, proteins are needed in the diet to provide the essential amino acids that cannot be synthesized . Digestion breaks the proteins down for metabolic use. Proteins have been studied and recognized since

26522-488: The proton spectrum for ethanol, the CH 3 group is split into a triplet with an intensity ratio of 1:2:1 by the two neighboring CH 2 protons. Similarly, the CH 2 is split into a quartet with an intensity ratio of 1:3:3:1 by the three neighboring CH 3 protons. In principle, the two CH 2 protons would also be split again into a doublet to form a doublet of quartets by the hydroxyl proton, but intermolecular exchange of

26700-519: The radiation absorbed, and the intensity of the signal are proportional to the strength of the magnetic field. For example, in a 21- tesla magnetic field, hydrogen nuclei ( protons ) resonate at 900 MHz. It is common to refer to a 21 T magnet as a 900  MHz magnet, since hydrogen is the most common nucleus detected. However, different nuclei will resonate at different frequencies at this field strength in proportion to their nuclear magnetic moments . An NMR spectrometer typically consists of

26878-515: The range is hundreds of ppm. In paramagnetic NMR spectroscopy , the samples are paramagnetic, i.e. they contain unpaired electrons. The paramagnetism gives rise to very diverse chemical shifts. In H NMR spectroscopy, the chemical shift range can span up to thousands of ppm. Some of the most useful information for structure determination in a one-dimensional NMR spectrum comes from J-coupling, or scalar coupling (a special case of spin–spin coupling ), between NMR active nuclei. This coupling arises from

27056-515: The relaxation time and thus the required delay between pulses. A 180° pulse, an adjustable delay, and a 90° pulse is transmitted. When the 90° pulse exactly cancels out the signal, the delay corresponds to the time needed for 90° of relaxation. Inversion recovery is worthwhile for quantitative C, D and other time-consuming experiments. NMR signals are ordinarily characterized by three variables: chemical shift, spin–spin coupling, and relaxation time. The energy difference Δ E between nuclear spin states

27234-462: The relaxation time is rather long, e.g. around 8 seconds for C. Thus, acquisition of quantitative heavy-element spectra can be time-consuming, taking tens of minutes to hours. Following the pulse, the nuclei are, on average, excited to a certain angle vs. the spectrometer magnetic field. The extent of excitation can be controlled with the pulse width, typically about 3–8 μs for the optimal 90° pulse. The pulse width can be determined by plotting

27412-442: The requirement | a + 1 / 2 | 2 + | a − 1 / 2 | 2 = 1. {\displaystyle |a_{+1/2}|^{2}+|a_{-1/2}|^{2}=1.} For a generic particle with spin s , we would need 2 s + 1 such parameters. Since these numbers depend on the choice of the axis, they transform into each other non-trivially when this axis

27590-415: The rotation of a particle around some axis. Historically orbital angular momentum related to particle orbits. While the names based on mechanical models have survived, the physical explanation has not. Quantization fundamentally alters the character of both spin and orbital angular momentum. Since elementary particles are point-like, self-rotation is not well-defined for them. However, spin implies that

27768-582: The same molecule, they can oligomerize to form fibrils; this process occurs often in structural proteins that consist of globular monomers that self-associate to form rigid fibers. Protein–protein interactions also regulate enzymatic activity, control progression through the cell cycle , and allow the assembly of large protein complexes that carry out many closely related reactions with a common biological function. Proteins can also bind to, or even be integrated into, cell membranes. The ability of binding partners to induce conformational changes in proteins allows

27946-435: The same pure quantum state, such as through the use of a Stern–Gerlach apparatus , the spin vector does have a well-defined experimental meaning: It specifies the direction in ordinary space in which a subsequent detector must be oriented in order to achieve the maximum possible probability (100%) of detecting every particle in the collection. For spin- ⁠ 1 / 2 ⁠ particles, this probability drops off smoothly as

28124-411: The same time not by other spectroscopic techniques to an atomic level, either. In solid-phase media, such as crystals, microcrystalline powders, gels, anisotropic solutions, etc., it is in particular the dipolar coupling and chemical shift anisotropy that become dominant to the behaviour of the nuclear spin systems. In conventional solution-state NMR spectroscopy, these additional interactions would lead to

28302-573: The sample, allowing scientists to obtain more information and analyze larger structures. Computational protein structure prediction of small protein structural domains has also helped researchers to approach atomic-level resolution of protein structures. As of April 2024 , the Protein Data Bank contains 181,018 X-ray, 19,809 EM and 12,697 NMR protein structures. Proteins are primarily classified by sequence and structure, although other classifications are commonly used. Especially for enzymes

28480-434: The second excitation pulse is sent prematurely before the relaxation is complete, the average magnetization vector has not decayed to ground state, which affects the strength of the signal in an unpredictable manner. In practice, the peak areas are then not proportional to the stoichiometry; only the presence, but not the amount of functional groups is possible to discern. An inversion recovery experiment can be done to determine

28658-430: The sequencing of complex proteins. In 1999, Roger Kornberg succeeded in sequencing the highly complex structure of RNA polymerase using high intensity X-rays from synchrotrons . Since then, cryo-electron microscopy (cryo-EM) of large macromolecular assemblies has been developed. Cryo-EM uses protein samples that are frozen rather than crystals, and beams of electrons rather than X-rays. It causes less damage to

28836-546: The shifts are primarily determined by shielding effects (electron density). The chemical shifts for many heavier nuclei are more strongly influenced by other factors, including excited states ("paramagnetic" contribution to shielding tensor). This paramagnetic contribution, which is unrelated to paramagnetism ) not only disrupts trends in chemical shifts, which complicates assignments, but it also gives rise to very large chemical shift ranges. For example, most H NMR signals for most organic compounds are within 15 ppm. For P NMR,

29014-516: The signal into a 1:1:1 triplet because the spin 1 has three spin states. Similarly, a spin-3/2 nucleus such as Cl splits a signal into a 1:1:1:1 quartet and so on. Coupling combined with the chemical shift (and the integration for protons) tells us not only about the chemical environment of the nuclei, but also the number of neighboring NMR active nuclei within the molecule. In more complex spectra with multiple peaks at similar chemical shifts or in spectra of nuclei other than hydrogen, coupling

29192-476: The signals from solvent hydrogen atoms overwhelm the experiment and interfere in analysis of the dissolved analyte, deuterated solvents are used where >99% of the protons are replaced with deuterium (hydrogen-2). The most widely used deuterated solvent is deuterochloroform (CDCl 3 ), although other solvents may be used for various reasons, such as solubility of a sample, desire to control hydrogen bonding , or melting or boiling points. The chemical shifts of

29370-740: The special case of spin- ⁠ 1 / 2 ⁠ particles, σ x , σ y and σ z are the three Pauli matrices : σ x = ( 0 1 1 0 ) , σ y = ( 0 − i i 0 ) , σ z = ( 1 0 0 − 1 ) . {\displaystyle \sigma _{x}={\begin{pmatrix}0&1\\1&0\end{pmatrix}},\quad \sigma _{y}={\begin{pmatrix}0&-i\\i&0\end{pmatrix}},\quad \sigma _{z}={\begin{pmatrix}1&0\\0&-1\end{pmatrix}}.} The Pauli exclusion principle states that

29548-479: The spectrum, mainly NOESY cross-peaks and coupling constants , can be used to determine local structural features such as glycosidic bond angles, dihedral angles (using the Karplus equation ), and sugar pucker conformations. For large-scale structure, these local parameters must be supplemented with other structural assumptions or models, because errors add up as the double helix is traversed, and unlike with proteins,

29726-488: The speed of light. In the Standard Model , the fundamental particles are all considered "point-like": they have their effects through the field that surrounds them. Any model for spin based on mass rotation would need to be consistent with that model. Wolfgang Pauli , a central figure in the history of quantum spin, initially rejected any idea that the "degree of freedom" he introduced to explain experimental observations

29904-405: The substrate, and an even smaller fraction—three to four residues on average—that are directly involved in catalysis. The region of the enzyme that binds the substrate and contains the catalytic residues is known as the active site . Dirigent proteins are members of a class of proteins that dictate the stereochemistry of a compound synthesized by other enzymes. Many proteins are involved in

30082-706: The surrounding amino acids may determine the exact binding specificity). Many such motifs has been collected in the Eukaryotic Linear Motif (ELM) database. Topology of a protein describes the entanglement of the backbone and the arrangement of contacts within the folded chain. Two theoretical frameworks of knot theory and Circuit topology have been applied to characterise protein topology. Being able to describe protein topology opens up new pathways for protein engineering and pharmaceutical development, and adds to our understanding of protein misfolding diseases such as neuromuscular disorders and cancer. Proteins are

30260-400: The tRNA molecules with the correct amino acids. The growing polypeptide is often termed the nascent chain . Proteins are always biosynthesized from N-terminus to C-terminus . The size of a synthesized protein can be measured by the number of amino acids it contains and by its total molecular mass , which is normally reported in units of daltons (synonymous with atomic mass units ), or

30438-472: The tertiary structure of the protein, which defines the binding site pocket, and by the chemical properties of the surrounding amino acids' side chains. Protein binding can be extraordinarily tight and specific; for example, the ribonuclease inhibitor protein binds to human angiogenin with a sub-femtomolar dissociation constant (<10 M) but does not bind at all to its amphibian homolog onconase (> 1 M). Extremely minor chemical changes such as

30616-538: The theorem requires that particles with half-integer spins obey the Pauli exclusion principle while particles with integer spin do not. As an example, electrons have half-integer spin and are fermions that obey the Pauli exclusion principle, while photons have integer spin and do not. The theorem was derived by Wolfgang Pauli in 1940; it relies on both quantum mechanics and the theory of special relativity . Pauli described this connection between spin and statistics as "one of

30794-426: The values where S i is the spin component along the i -th axis (either x , y , or z ), s i is the spin projection quantum number along the i -th axis, and s is the principal spin quantum number (discussed in the previous section). Conventionally the direction chosen is the z  axis: where S z is the spin component along the z  axis, s z is the spin projection quantum number along

30972-529: The values of the following discrete set: s z ∈ { − s ℏ , − ( s − 1 ) ℏ , … , + ( s − 1 ) ℏ , + s ℏ } . {\displaystyle s_{z}\in \{-s\hbar ,-(s-1)\hbar ,\dots ,+(s-1)\hbar ,+s\hbar \}.} One distinguishes bosons (integer spin) and fermions (half-integer spin). The total angular momentum conserved in interaction processes

31150-582: The world around us. A key distinction between the two families is that fermions obey the Pauli exclusion principle : that is, there cannot be two identical fermions simultaneously having the same quantum numbers (meaning, roughly, having the same position, velocity and spin direction). Fermions obey the rules of Fermi–Dirac statistics . In contrast, bosons obey the rules of Bose–Einstein statistics and have no such restriction, so they may "bunch together" in identical states. Also, composite particles can have spins different from their component particles. For example,

31328-412: Was insulin , by Frederick Sanger , in 1949. Sanger correctly determined the amino acid sequence of insulin, thus conclusively demonstrating that proteins consisted of linear polymers of amino acids rather than branched chains, colloids , or cyclols . He won the Nobel Prize for this achievement in 1958. Christian Anfinsen 's studies of the oxidative folding process of ribonuclease A, for which he won

31506-581: Was not fully appreciated until 1926, when James B. Sumner showed that the enzyme urease was in fact a protein. Linus Pauling is credited with the successful prediction of regular protein secondary structures based on hydrogen bonding , an idea first put forth by William Astbury in 1933. Later work by Walter Kauzmann on denaturation , based partly on previous studies by Kaj Linderstrøm-Lang , contributed an understanding of protein folding and structure mediated by hydrophobic interactions . The first protein to have its amino acid chain sequenced

31684-411: Was related to rotation. He called it "classically non-describable two-valuedness". Later, he allowed that it is related to angular momentum, but insisted on considering spin an abstract property. This approach allowed Pauli to develop a proof of his fundamental Pauli exclusion principle , a proof now called the spin-statistics theorem . In retrospect, this insistence and the style of his proof initiated

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