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102-417: Lysozyme ( EC 3.2.1.17 , muramidase, N -acetylmuramide glycanhydrolase ; systematic name peptidoglycan N -acetylmuramoylhydrolase ) is an antimicrobial enzyme produced by animals that forms part of the innate immune system . It is a glycoside hydrolase that catalyzes the following process: Peptidoglycan is the major component of gram-positive bacterial cell wall. This hydrolysis in turn compromises

204-437: A founder named "Artemis") were developed to produce milk with human lysozyme to protect children from diarrhea if they can't get the benefits of human breastfeeding. Since lysozyme is a natural form of protection from Gram-positive pathogens like Bacillus and Streptococcus , it plays an important role in immunology of infants in human milk feeding. Whereas the skin is a protective barrier due to its dryness and acidity,

306-469: A closed inactive state. The catalytic relevance was examined with single walled carbon nanotubes (SWCN) field effect transistors (FETs), where a singular lysozyme was bound to the SWCN FET. Electronically monitoring the lysozyme showed two conformations, an open active site and a closed inactive site. In its active state lysozyme is able to processively hydrolyze its substrate, breaking on average 100 bonds at

408-445: A competitive inhibition of lysozyme. In Gram-negative bacteria , the lipopolysaccharide acts as a non-competitive inhibitor by highly favored binding with lysozyme. Despite that the muramidase activity of lysozyme has been supposed to play the key role for its antibacterial properties, evidence of its non-enzymatic action was also reported. For example, blocking the catalytic activity of lysozyme by mutation of critical amino acid in

510-468: A correction factor. For isotope effects involving elements other than hydrogen, many of these simplifications are not valid, and the magnitude of the isotope effect may depend strongly on some or all of the neglected factors. Thus, KIEs for elements other than hydrogen are often much harder to rationalize or interpret. In many cases and especially for hydrogen-transfer reactions, contributions to KIEs from tunneling are significant (see below). In some cases,

612-463: A covalent intermediate. Evidence for the ESI-MS and X-ray structures indicate the existence of covalent intermediate, but primarily rely on using a less active mutant or non-native substrate. Thus, QM/MM molecular dynamics provides the unique ability to directly investigate the mechanism of wild-type HEWL and native substrate. The calculations revealed that the covalent intermediate from the covalent mechanism

714-464: A few criteria are considered: Also for reactions where isotopes include H, D and T, a criterion of tunneling is the Swain-Schaad relations which compare the rate constants ( k ) of the reactions where H, D or T are exchanged: In organic reactions, this proton tunneling effect has been observed in such reactions as the deprotonation and iodination of nitropropane with hindered pyridine base with

816-497: A further rate enhancement is seen for the lighter isotope, possibly due to quantum tunneling . This is typically only observed for reactions involving bonds to hydrogen. Tunneling occurs when a molecule penetrates through a potential energy barrier rather than over it. Though not allowed by classical mechanics , particles can pass through classically forbidden regions of space in quantum mechanics based on wave–particle duality . Tunneling can be analyzed using Bell's modification of

918-471: A greater energy input needed for heavier isotopologues to reach the transition state (or, in rare cases, dissociation limit ), and therefore, a slower reaction rate. The study of KIEs can help elucidate reaction mechanisms , and is occasionally exploited in drug development to improve unfavorable pharmacokinetics by protecting metabolically vulnerable C-H bonds. KIE is considered one of the most essential and sensitive tools for studying reaction mechanisms,

1020-417: A larger isotope effect is observed for a stiffer ("stronger") C–H/D bond. For most reactions of interest, a hydrogen atom is transferred between two atoms, with a transition-state [A···H···B] and vibrational modes at the transition state need to be accounted for. Nevertheless, it is still generally true that cleavage of a bond with a higher vibrational frequency will give a larger isotope effect. To calculate

1122-524: A lower ZPE, more energy must be supplied to break the bond, resulting in a higher activation energy for bond cleavage, which in turn lowers the measured rate (see, for example, the Arrhenius equation ). A primary kinetic isotope effect (PKIE) may be found when a bond to the isotopically labeled atom is being formed or broken. Depending on the way a KIE is probed (parallel measurement of rates vs. intermolecular competition vs. intramolecular competition),

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1224-517: A pre-equilibrium, so that the C-H bond cleavage occurs somewhere before the rate-determining step.) This type of experiment, uses the same substrates as used in Experiment A, but they are allowed in to react in the same container, instead of two separate containers. The KIE in this experiment is determined by the relative amount of products formed from C-H versus C-D functionalization (or it can be inferred from

1326-503: A rate of 15 per second. In order to bind a new substrate and move from the closed inactive state to the open active state requires two conformation step changes, while inactivation requires one step. The conventional C-type lysozyme is part of a larger group of structurally and mechanistically related enzymes termed the lysozyme superfamily . This family unites GH22 C-type ("chicken") lysozymes with plant chitinase GH19 , G-type ("goose") lysozyme GH23 , V-type ("viral") lysozyme GH24 and

1428-435: A reported KIE of 25 at 25°C: and in a 1,5-sigmatropic hydrogen shift , though it is observed that it is hard to extrapolate experimental values obtained at high temperature to lower temperatures: It has long been speculated that high efficiency of enzyme catalysis in proton or hydride ion transfer reactions could be due partly to the quantum mechanical tunneling effect. Environment at the active site of an enzyme positions

1530-406: A stronger nucleophile than water, which then attacks the glycosyl enzyme intermediate, to give the product of hydrolysis and leaving the enzyme unchanged. This type of covalent mechanism for enzyme catalysis was first proposed by Koshland . More recently, quantum mechanics/ molecular mechanics (QM/MM) molecular dynamics simulations have been using the crystal of HEWL and predict the existence of

1632-591: A tool in the expression of toxic recombinant proteins. Expressing recombinant proteins in BL21(DE3) strains is typically accomplished by the T7-RNA-polymerase. Via IPTG induction, the UV-5 repressor is inhibited, leading to the transcription of the T7-RNA-polymerase and thereby of the protein of interest. Nonetheless, a basal level of the T7-RNA-polymerase is observable even without induction. T7 lysozyme acts as an inhibitor of

1734-412: A variety of ways. In many cases, the rate difference can be rationalized by noting that the mass of an atom affects the vibrational frequency of the chemical bond that it forms, even if the potential energy surface for the reaction is nearly identical. Heavier isotopes will ( classically ) lead to lower vibration frequencies, or, viewed quantum mechanically , have lower zero-point energy (ZPE). With

1836-475: Is 10.5–11. The enzyme functions by hydrolyzing glycosidic bonds in peptidoglycans . The enzyme can also break glycosidic bonds in chitin , although not as effectively as true chitinases . Lysozyme's active site binds the peptidoglycan molecule in the prominent cleft between its two domains. It attacks peptidoglycans (found in the cell walls of bacteria, especially Gram-positive bacteria ), its natural substrate , between N -acetylmuramic acid (NAM) and

1938-510: Is also applicable to heavier elements) is given below. It employs transition state theory and a statistical mechanical treatment of translational, rotational, and vibrational levels for the calculation of rate constants k H and k D . However, this formula is "semi-classical" in that it neglects the contribution from quantum tunneling, which is often introduced as a separate correction factor. Bigeleisen's formula also does not deal with differences in non-bonded repulsive interactions caused by

2040-503: Is an active inhibitor of lysis. Similar observations have been seen with the use of potassium salts. Slight variations are present due to differences in bacterial strains. A consequence of the use of lysozyme in extracting recombinant proteins for protein crystallization is that the crystal may be contaminated with units of lysozyme, producing a physiologically irrelevant combination. In fact, some proteins simply cannot crystalize without such contamination. Furthermore, lysozyme can serve as

2142-593: Is being generated one carbon atom away (a β SKIE). These isotope effects have a theoretical maximum of k H / k D = 2 ≈ 1.4. For a SKIE at the α position, rehybridization from sp to sp produces a normal isotope effect, while rehybridization from sp to sp results in an inverse isotope effect with a theoretical minimum of k H / k D = 2 ≈ 0.7. In practice, k H / k D ~ 1.1-1.2 and k H /k D ~ 0.8-0.9 are typical for α SKIEs, while k H / k D ~ 1.15-1.3 are typical for β SKIE. For reactants containing several isotopically substituted β-hydrogens,

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2244-440: Is created as a result of the glycosidic bond breaking. Thus distortion causing the substrate molecule to adopt a strained conformation similar to that of the transition state will lower the energy barrier of the reaction. The proposed oxo-carbonium intermediate was speculated to be electrostatically stabilized by aspartate and glutamate residues in the active site by Arieh Warshel in 1978. The electrostatic stabilization argument

2346-432: Is greatest for small barrier widths. Optimal tunneling distances of protons between donor and acceptor atom is 40 pm. Tunneling is a quantum effect tied to the laws of wave mechanics, not kinetics . Therefore, tunneling tends to become more important at low temperatures, where even the smallest kinetic energy barriers may not be overcome but can be tunneled through. Peter S. Zuev et al. reported rate constants for

2448-469: Is now fairly routine. Moreover, several qualitative and semi-quantitative models allow rough estimates of deuterium isotope effects to be made without calculations, often providing enough information to rationalize experimental data or even support or refute different mechanistic possibilities. Starting materials containing H are often commercially available, making the synthesis of isotopically enriched starting materials relatively straightforward. Also, due to

2550-477: Is observed when no bond to the isotopically labeled atom in the reactant is broken or formed. SKIEs tend to be much smaller than PKIEs; however, secondary deuterium isotope effects can be as large as 1.4 per H atom, and techniques have been developed to measure heavy-element isotope effects to very high precision, so SKIEs are still very useful for elucidating reaction mechanisms. For the aforementioned nucleophilic substitution reactions, secondary hydrogen KIEs at

2652-451: Is often found that tunneling is a major factor when they do exceed such values. A value of k H / k D ~ 10 is thought to be maximal for a semi-classical PKIE (no tunneling) for reactions at ≈298 K. (The formula for k H / k D has a temperature dependence, so larger isotope effects are possible at lower temperatures.) Depending on the nature of the transition state of H-transfer (symmetric vs. "early" or "late" and linear vs. bent);

2754-440: Is part of the innate immune system. Reduced lysozyme levels have been associated with bronchopulmonary dysplasia in newborns. Piglets fed with human lysozyme milk can recover from diarrheal disease caused by E. coli faster. The concentration of lysozyme in human milk is 1,600 to 3,000 times greater than the concentration in livestock milk. Human lysozyme is more active than hen egg white lysozyme. A transgenic line of goats (with

2856-453: Is related to formation of the oxo-carbenium intermediate. There were some contradictory results to indicate the exact RDS. By tracing the formation of product ( p-nitrophenol ), it was discovered that the RDS can change over different temperatures, which was a reason for those contradictory results. At a higher temperature the RDS is formation of glycosyl enzyme intermediate and at a lower temperature

2958-417: Is the reaction carried out by alcohol dehydrogenase . Competitive KIEs for the hydrogen transfer step at 25°C resulted in 3.6 and 10.2 for primary and secondary KIEs, respectively. Isotopic effect expressed with the equations given above only refer to reactions that can be described with first-order kinetics . In all instances in which this is not possible, transient KIEs should be taken into account using

3060-446: Is unique to the transition state). The simplified formula above, predicts a maximum for k H / k D as 6.9. If the complete disappearance of two bending vibrations is also included, k H / k D values as large as 15-20 can be predicted. Bending frequencies are very unlikely to vanish in the transition state, however, and there are only a few cases in which k H / k D values exceed 7-8 near room temperature. Furthermore, it

3162-524: Is ~30 kcal/mol more stable than the ionic intermediate from the Phillips mechanism. These calculations demonstrate that the ionic intermediate is extremely energetically unfavorable and the covalent intermediates observed from experiments using less active mutant or non-native substrates provide useful insight into the mechanism of wild-type HEWL. Imidazole derivatives can form a charge-transfer complex with some residues (in or outside active center) to achieve

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3264-538: The Arrhenius equation , which includes the addition of a tunneling factor, Q: where A is the Arrhenius parameter, E is the barrier height and where α = E R T {\displaystyle \alpha ={\frac {E}{RT}}} and β = 2 a π 2 ( 2 m E ) 1 / 2 h {\displaystyle \beta ={\frac {2a\pi ^{2}(2mE)^{1/2}}{h}}} Examination of

3366-474: The Born–Oppenheimer approximation , the potential energy surface is the same for both isotopic species. However, a quantum treatment of the energy introduces discrete vibrational levels onto this curve, and the lowest possible energy state of a molecule corresponds to the lowest vibrational energy level, which is slightly higher in energy than the minimum of the potential energy curve. This difference, known as

3468-562: The EMBL-EBI Enzyme Portal). Before the development of the EC number system, enzymes were named in an arbitrary fashion, and names like old yellow enzyme and malic enzyme that give little or no clue as to what reaction was catalyzed were in common use. Most of these names have fallen into disuse, though a few, especially proteolyic enzymes with very low specificity, such as pepsin and papain , are still used, as rational classification on

3570-488: The conjunctiva (membrane covering the eye) is, instead, protected by secreted enzymes, mainly lysozyme and defensin . However, when these protective barriers fail, conjunctivitis results. In certain cancers (especially myelomonocytic leukemia) excessive production of lysozyme by cancer cells can lead to toxic levels of lysozyme in the blood. High lysozyme blood levels can lead to kidney failure and low blood potassium, conditions that may improve or resolve with treatment of

3672-449: The reactants is replaced by one of its isotopes . Formally, it is the ratio of rate constants for the reactions involving the light ( k L ) and the heavy ( k H ) isotopically substituted reactants ( isotopologues ): KIE = k L /k H . This change in reaction rate is a quantum effect that occurs mainly because heavier isotopologues have lower vibrational frequencies than their lighter counterparts. In most cases, this implies

3774-452: The tripeptide aminopeptidases have the code "EC 3.4.11.4", whose components indicate the following groups of enzymes: NB:The enzyme classification number is different from the 'FORMAT NUMBER' Oxidation /reduction reactions; transfer of H and O atoms or electrons from one substance to another Similarity between enzymatic reactions can be calculated by using bond changes, reaction centres or substructure metrics (formerly EC-BLAST], now

3876-505: The β term shows exponential dependence on the particle's mass. As a result, tunneling is much more likely for a lighter particle such as hydrogen. Simply doubling the mass of a tunneling proton by replacing it with a deuteron drastically reduces the rate of such reactions. As a result, very large KIEs are observed that can not be accounted for by differences in ZPEs. Also, the β term depends linearly with barrier width, 2a. As with mass, tunneling

3978-533: The Enzyme Commission was dissolved at that time, though its name lives on in the term EC Number . The current sixth edition, published by the International Union of Biochemistry and Molecular Biology in 1992 as the last version published as a printed book, contains 3196 different enzymes. Supplements 1-4 were published 1993–1999. Subsequent supplements have been published electronically, at the website of

4080-497: The GEBIK and GEBIF equations. Simmons and Hartwig refer to the following three cases as the main types of KIE experiments involving C-H bond functionalization: In this experiment, the rate constants for the normal substrate and its isotopically labeled analogue are determined independently, and the KIE is obtained as a ratio of the two. The accuracy of the measured KIE is severely limited by

4182-458: The KIE caused by the reactions of vibrationally excited molecules. The fraction of molecules with enough energy to have excited state A–H/D bond vibrations is generally small for reactions at or near room temperature (bonds to hydrogen usually vibrate at 1000 cm or higher, so exp(- u i ) = exp(- hν i / k B T ) < 0.01 at 298 K, resulting in negligible contributions from the 1–exp(- u i ) factors). Hence, for hydrogen/deuterium KIEs,

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4284-401: The KIE, but stretching vibrational contributions are of more comparable magnitude, and the resulting KIE may be normal or inverse depending on the specific contributions of the respective vibrations. The theoretical treatment of isotope effects relies heavily on transition state theory , which assumes a single potential energy surface for the reaction, and a barrier between the reactants and

4386-574: The Nomenclature Committee of the International Union of Biochemistry and Molecular Biology. In August 2018, the IUBMB modified the system by adding the top-level EC 7 category containing translocases. Kinetic isotope effect In physical organic chemistry , a kinetic isotope effect ( KIE ) is the change in the reaction rate of a chemical reaction when one of the atoms in

4488-441: The T7-RNA-polymerase. Newly invented strains, containing a helper plasmid (pLysS), constitutively co-express low levels of T7 lysozyme, providing high stringency and consistent expression of the toxic recombinant protein. The antibacterial property of hen egg white, due to the lysozyme it contains, was first observed by Laschtschenko in 1909. The bacteria-killing activity of nasal mucus was demonstrated in 1922 by Alexander Fleming ,

4590-446: The ZPE, is a manifestation of the uncertainty principle that necessitates an uncertainty in the C-H or C-D bond length. Since the heavier (in this case the deuterated) species behaves more "classically", its vibrational energy levels are closer to the classical potential energy curve, and it has a lower ZPE. The ZPE differences between the two isotopic species, at least in most cases, diminish in

4692-407: The accuracy with which each of these rate constants can be measured. Furthermore, reproducing the exact conditions in the two parallel reactions can be very challenging. Nevertheless, a measurement of a large kinetic isotope effect through direct comparison of rate constants is indicative that C-H bond cleavage occurs at the rate-determining step. (A smaller value could indicate an isotope effect due to

4794-415: The active site (52- Asp -> 52- Ser ) does not eliminate its antimicrobial activity. The lectin-like ability of lysozyme to recognize bacterial carbohydrate antigen without lytic activity was reported for tetrasaccharide related to lipopolysaccharide of Klebsiella pneumoniae . Also, lysozyme interacts with antibodies and T-cell receptors . Lysozyme exhibits two conformations: an open active state and

4896-584: The basis of specificity has been very difficult. By the 1950s the chaos was becoming intolerable, and after Hoffman-Ostenhof and Dixon and Webb had proposed somewhat similar schemes for classifying enzyme-catalyzed reactions, the International Congress of Biochemistry in Brussels set up the Commission on Enzymes under the chairmanship of Malcolm Dixon in 1955. The first version was published in 1961, and

4998-436: The bound substrate and electrostatic stabilization of an oxo-carbenium intermediate. From X-ray crystallographic data, Phillips proposed the active site of the enzyme, where a hexasaccharide binds. The lysozyme distorts the fourth sugar (in the D or -1 subsite) in the hexasaccharide into a half-chair conformation. In this stressed state, the glycosidic bond is more easily broken. An ionic intermediate containing an oxo-carbenium

5100-410: The breakdown of that intermediate. In an early debate in 1969, Dahlquist proposed a covalent mechanism for lysozyme based on kinetic isotope effect , but for a long time the ionic mechanism was more accepted. In 2001, a revised mechanism was proposed by Vocadlo via a covalent but not ionic intermediate. Evidence from ESI - MS analysis indicated a covalent intermediate. A 2-fluoro substituted substrate

5202-446: The case of an inverse isotope effect) of bending modes from the reactant ground state to the transition state are largely responsible for observed isotope effects. These changes are attributed to a change in steric environment when the carbon bound to the H/D undergoes rehybridization from sp to sp or vice versa (an α SKIE), or bond weakening due to hyperconjugation in cases where a carbocation

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5304-429: The cell by suddenly changing solute concentration around the cell and thus the osmotic pressure ), lysozyme is commonly used in lab setting to release proteins from bacterium periplasm while the inner membrane remains sealed as vesicles called the spheroplast . For example, E. coli can be lysed using lysozyme to free the contents of the periplasmic space. It is especially useful in lab setting for trying to collect

5406-2083: The chitosanase GH46 families. The lysozyme-type nomenclature only reflects the source a type is originally isolated from and does not fully reflect the taxonomic distribution. For example, humans and many other mammals have two G-type lysozyme genes, LYG1 and LYG2 . 133L , 134L , 1B5U , 1B5V , 1B5W , 1B5X , 1B5Y , 1B5Z , 1B7L , 1B7M , 1B7N , 1B7O , 1B7P , 1B7Q , 1B7R , 1B7S , 1BB3 , 1BB4 , 1BB5 , 1C43 , 1C45 , 1C46 , 1C7P , 1CJ6 , 1CJ7 , 1CJ8 , 1CJ9 , 1CKC , 1CKD , 1CKF , 1CKG , 1CKH , 1D6P , 1D6Q , 1DI3 , 1DI4 , 1DI5 , 1EQ4 , 1EQ5 , 1EQE , 1GAY , 1GAZ , 1GB0 , 1GB2 , 1GB3 , 1GB5 , 1GB6 , 1GB7 , 1GB8 , 1GB9 , 1GBO , 1GBW , 1GBX , 1GBY , 1GBZ , 1GDW , 1GDX , 1GE0 , 1GE1 , 1GE2 , 1GE3 , 1GE4 , 1GEV , 1GEZ , 1GF0 , 1GF3 , 1GF4 , 1GF5 , 1GF6 , 1GF7 , 1GF8 , 1GF9 , 1GFA , 1GFE , 1GFG , 1GFH , 1GFJ , 1GFK , 1GFR , 1GFT , 1GFU , 1GFV , 1HNL , 1I1Z , 1I20 , 1I22 , 1INU , 1IOC , 1IP1 , 1IP2 , 1IP3 , 1IP4 , 1IP5 , 1IP6 , 1IP7 , 1IWT , 1IWU , 1IWV , 1IWW , 1IWX , 1IWY , 1IWZ , 1IX0 , 1IY3 , 1IY4 , 1JKA , 1JKB , 1JKC , 1JKD , 1JSF , 1JWR , 1LAA , 1LHH , 1LHI , 1LHJ , 1LHK , 1LHL , 1LHM , 1LMT , 1LOZ , 1LYY , 1LZ1 , 1LZ4 , 1LZ5 , 1LZ6 , 1LZR , 1LZS , 1OP9 , 1OUA , 1OUB , 1OUC , 1OUD , 1OUE , 1OUF , 1OUG , 1OUH , 1OUI , 1OUJ , 1QSW , 1RE2 , 1REM , 1REX , 1REY , 1REZ , 1TAY , 1TBY , 1TCY , 1TDY , 1UBZ , 1W08 , 1WQM , 1WQN , 1WQO , 1WQP , 1WQQ , 1WQR , 1YAM , 1YAN , 1YAO , 1YAP , 1YAQ , 207L , 208L , 2BQA , 2BQB , 2BQC , 2BQD , 2BQE , 2BQF , 2BQG , 2BQH , 2BQI , 2BQJ , 2BQK , 2BQL , 2BQM , 2BQN , 2BQO , 2HEA , 2HEB , 2HEC , 2HED , 2HEE , 2HEF , 2LHM , 2MEA , 2MEB , 2MEC , 2MED , 2MEE , 2MEF , 2MEG , 2MEH , 2MEI , 2NWD , 2ZIJ , 2ZIK , 2ZIL , 2ZWB , 3EBA , 3FE0 , 3LHM , 3LN2 , 4I0C , 4ML7 , 4R0P 4069 17110 ENSG00000090382 ENSMUSG00000069515 P61626 P17897 NM_000239 NM_013590 NP_000230 NP_038618 Lysozyme

5508-435: The contents of the periplasm. Lysozyme treatment is optimal at particular temperatures, pH ranges, and salt concentrations. Lysozyme activity increases with increasing temperatures, up to 60 degrees Celsius, with a pH range of 6.0-7.0. The salts present also affect lysozyme treatment, where some assert inhibitory effects, and others promote lysis via lysozyme treatment. Sodium chloride induces lysis, but at high concentrations, it

5610-412: The context of isotope effects, hydrogen often means the light isotope, protium ( H), specifically. In the rest of this article, reference to hydrogen and deuterium in parallel grammatical constructions or direct comparisons between them should be interpreted as meaning H and H. The theory of KIEs was first formulated by Jacob Bigeleisen in 1949. Bigeleisen's general formula for H KIEs (which

5712-407: The discoverer of penicillin , who coined the term "lysozyme". He is reported as saying: "As this substance has properties akin to those of ferments I have called it a 'Lysozyme'." Fleming went on to show that an enzymic substance was present in a wide variety of secretions and was capable of rapidly lysing (i.e. dissolving) different bacteria, particularly a yellow "coccus" that he studied". Lysozyme

5814-418: The donor and acceptor atom close to the optimal tunneling distance, where the amino acid side chains can "force" the donor and acceptor atom closer together by electrostatic and noncovalent interactions. It is also possible that the enzyme and its unusual hydrophobic environment inside a reaction site provides tunneling-promoting vibration. Studies on ketosteroid isomerase have provided experimental evidence that

5916-445: The energy barrier, quantum tunnelling may also make a large contribution to an observed kinetic isotope effect and may need to be separately considered, in addition to the "semi-classical" transition state theory model. The deuterium kinetic isotope effect ( H KIE) is by far the most common, useful, and well-understood type of KIE. The accurate prediction of the numerical value of a H KIE using density functional theory calculations

6018-562: The energy surface of a reaction but can "leak out" into the next energy minimum. In light of this, tunneling should be temperature independent. For the hydrogen abstraction from gaseous n-alkanes and cycloalkanes by hydrogen atoms over the temperature range 363–463 K, the H/D KIE data were characterized by small preexponential factor ratios A H / A D ranging from 0.43 to 0.54 and large activation energy differences from 9.0 to 9.7 kJ/mol. Basing their arguments on transition state theory ,

6120-507: The enzyme actually enhances the coupled motion/hydrogen tunneling by comparing primary and secondary KIEs of the reaction under enzyme-catalyzed and non-enzyme-catalyzed conditions. Many examples exist for proton tunneling in enzyme-catalyzed reactions that were discovered by KIE. A well-studied example is methylamine dehydrogenase, where large primary KIEs of 5–55 have been observed for the proton transfer step. Another example of tunneling contribution to proton transfer in enzymatic reactions

6222-571: The extent to which a primary H isotope effect approaches this maximum, varies. A model developed by Westheimer predicted that symmetrical (thermoneutral, by Hammond's postulate ), linear transition states have the largest isotope effects, while transition states that are "early" or "late" (for exothermic or endothermic reactions, respectively), or nonlinear (e.g. cyclic) exhibit smaller effects. These predictions have since received extensive experimental support. For secondary H isotope effects, Streitwieser proposed that weakening (or strengthening, in

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6324-410: The factor of ⁠ 1 / 2 ⁠ and the sums of u i = h ν i / k B T {\displaystyle u_{i}=h\nu _{i}/k_{\mathrm {B} }T} terms over ground state and transition state vibrational modes in the exponent of the simplified formula above. For a harmonic oscillator, vibrational frequency is inversely proportional to

6426-441: The first enzyme to be fully sequenced that contains all twenty common amino acids. As a result of Phillips' elucidation of the structure of lysozyme, it was also the first enzyme to have a detailed, specific mechanism suggested for its method of catalytic action. This work led Phillips to provide an explanation for how enzymes speed up a chemical reaction in terms of its physical structures. The original mechanism proposed by Phillips

6528-415: The fourth carbon atom of N-acetylglucosamine (NAG). Shorter saccharides like tetrasaccharide have also shown to be viable substrates but via an intermediate with a longer chain. Chitin has also been shown to be a viable lysozyme substrate. Artificial substrates have also been developed and used in lysozyme. The Phillips mechanism proposed that the enzyme's catalytic power came from both steric strain on

6630-756: The general expression given above using some simplifications: i.e., In deriving these expressions, the reasonable approximation that reduced mass roughly equals the mass of the H, H, or H, was used. Also, the vibrational motion was assumed to be approximated by a harmonic oscillator, so that u i X ∝ μ X − 1 / 2 ≅ m X − 1 / 2 {\displaystyle u_{i\mathrm {X} }\propto \mu _{\mathrm {X} }^{-1/2}\cong m_{\mathrm {X} }^{-1/2}} ; X = H. The subscript " s " refers to these "semi-classical" KIEs, which disregard quantum tunneling. Tunneling contributions must be treated separately as

6732-437: The integrity of bacterial cell walls causing lysis of the bacteria. Lysozyme is abundant in secretions including tears , saliva , human milk , and mucus . It is also present in cytoplasmic granules of the macrophages and the polymorphonuclear neutrophils (PMNs). Large amounts of lysozyme can be found in egg white . C-type lysozymes are closely related to α-lactalbumin in sequence and structure, making them part of

6834-403: The knowledge of which allows improvement of the desirable qualities of said reactions. For example, KIEs can be used to reveal whether a nucleophilic substitution reaction follows a unimolecular (S N 1) or bimolecular (S N 2) pathway. In the reaction of methyl bromide and cyanide (shown in the introduction), the observed methyl carbon KIE indicates an S N 2 mechanism. Depending on

6936-486: The large relative difference in the mass of H and H and the attendant differences in vibrational frequency, the isotope effect is larger than for any other pair of isotopes except H and H, allowing both primary and secondary isotope effects to be easily measured and interpreted. In contrast, secondary effects are generally very small for heavier elements and close in magnitude to the experimental uncertainty, which complicates their interpretation and limits their utility. In

7038-512: The leaving groups, the nucleophiles, and the α-carbon at which the substitution occurs. Interpretation of the leaving group KIEs was difficult at first due to significant contributions from temperature independent factors. KIEs at the α-carbon can be used to develop some understanding into the symmetry of the transition state in S N 2 reactions, though this KIE is less sensitive than what would be ideal, also due to contribution from non-vibrational factors. A secondary kinetic isotope effect (SKIE)

7140-409: The mass; whereas in replacing carbon-12 with carbon-13 , the mass increases by only 8%. The rate of a reaction involving a C– H bond is typically 6–10x faster than with a C– H bond, whereas a C reaction is only 4% faster than the corresponding C reaction; even though, in both cases, the isotope is one atomic mass unit (amu) ( dalton ) heavier. Isotopic substitution can modify the reaction rate in

7242-435: The maximum possible value for a non-tunneling H KIE, we consider the case where the ZPE difference between the stretching vibrations of a C- H bond (3000 cm ) and C- H bond (2200 cm ) disappears in the transition state (an energy difference of [3000 – 2200 cm ]/2 = 400 cm ≈ 1.15 kcal/mol), without any compensation from a ZPE difference at the transition state (e.g., from the symmetric A···H···B stretch, which

7344-405: The number of atoms in the reactants and the transition states, respectively. The complicated expression given above can be represented as the product of four separate factors: For the special case of H isotope effects, we will argue that the first three terms can be treated as equal to or well approximated by unity. The first factor S (containing σ X ) is the ratio of the symmetry numbers for

7446-463: The observation of a PKIE is indicative of breaking/forming a bond to the isotope at the rate-limiting step, or subsequent product-determining step(s). (The misconception that a PKIE must reflect bond cleavage/formation to the isotope at the rate-limiting step is often repeated in textbooks and the primary literature: see the section on experiments below. ) For the aforementioned nucleophilic substitution reactions, PKIEs have been investigated for both

7548-517: The observed isotope effect is often the result of several H/D's at the β position acting in concert. In these cases, the effect of each isotopically labeled atom is multiplicative, and cases where k H / k D > 2 are not uncommon. The following simple expressions relating H and H KIEs, which are also known as the Swain equation (or the Swain-Schaad-Stivers equations), can be derived from

7650-421: The observed values are typically dominated by the last factor, ZPE (an exponential function of vibrational ZPE differences), consisting of contributions from the ZPE differences for each of the vibrational modes of the reactants and transition state, which can be represented as follows: where we define The sums in the exponent of the second expression can be interpreted as running over all vibrational modes of

7752-538: The one corresponding to the reaction coordinate, is missing at the transition state, since a bond breaks and there is no restorative force against the motion). The harmonic oscillator is a good approximation for a vibrating bond, at least for low-energy vibrational states. Quantum mechanics gives the vibrational ZPE as ϵ i ( 0 ) = 1 2 h ν i {\displaystyle \epsilon _{i}^{(0)}={\frac {1}{2}}h\nu _{i}} . Thus, we can readily interpret

7854-480: The pathway, different strategies may be used to stabilize the transition state of the rate-determining step of the reaction and improve the reaction rate and selectivity, which are important for industrial applications. Isotopic rate changes are most pronounced when the relative mass change is greatest, since the effect is related to vibrational frequencies of the affected bonds. Thus, replacing normal hydrogen ( H) with its isotope deuterium (D or H), doubles

7956-539: The primary malignancy. Serum lysozyme is much less specific for diagnosis of sarcoidosis than serum angiotensin converting enzyme; however, since it is more sensitive, it is used as a marker of sarcoidosis disease activity and is suitable for disease monitoring in proven cases. The first chemical synthesis of a lysozyme protein was attempted by Prof. George W. Kenner and his group at the University of Liverpool in England. This

8058-440: The products on this surface, on top of which resides the transition state. The KIE arises largely from the changes to vibrational ground states produced by the isotopic perturbation along the minimum energy pathway of the potential energy surface, which may only be accounted for with quantum mechanical treatments of the system. Depending on the mass of the atom that moves along the reaction coordinate and nature (width and height) of

8160-465: The ratio of the molecular masses and the moments of inertia. Since hydrogen and deuterium tend to be much lighter than most reactants and transition states, there is little difference in the molecular masses and moments of inertia between H and D containing molecules, so the MMI factor is usually also approximated as unity. The EXC factor (containing the product of vibrational partition functions ) corrects for

8262-571: The reactant ground state and the transition state. Or, one may interpret them as running over those modes unique to the reactant or the transition state or whose vibrational frequencies change substantially upon advancing along the reaction coordinate. The remaining pairs of reactant and transition state vibrational modes have very similar Δ u i {\displaystyle \Delta u_{i}} and Δ u i ‡ {\displaystyle \Delta u_{i}^{\ddagger }} , and cancellations occur when

8364-457: The relative amounts of unreacted starting materials). One must quench the reaction before it goes to completion to observe the KIE (see the Evaluation section below). Generally, the reaction is halted at low conversion (~5 to 10% conversion) or a large excess (> 5 equiv.) of the isotopic mixture is used. This experiment type ensures that both C-H and C-D bond functionalizations occur under exactly

8466-404: The ring expansion of 1-methylcyclobutylfluorocarbene to be 4.0 × 10 /s in nitrogen and 4.0 × 10 /s in argon at 8 kelvin. They calculated that at 8 kelvin, the reaction would proceed via a single quantum state of the reactant so that the reported rate constant is temperature independent and the tunneling contribution to the rate was 152 orders of magnitude greater than the contribution of passage over

8568-545: The same glycoside hydrolase family 22 . In humans, the C-type lysozyme enzyme is encoded by the LYZ gene. Hen egg white lysozyme is thermally stable, with a melting point reaching up to 72 °C at pH 5.0. However, lysozyme in human milk loses activity very quickly at that temperature. Hen egg white lysozyme maintains its activity in a large range of pH (6–9). Its isoelectric point is 11.35. The isoelectric point of human milk lysozyme

8670-401: The same EC number. By contrast, UniProt identifiers uniquely specify a protein by its amino acid sequence. Every enzyme code consists of the letters "EC" followed by four numbers separated by periods. Those numbers represent a progressively finer classification of the enzyme. Preliminary EC numbers exist and have an 'n' as part of the fourth (serial) digit (e.g. EC 3.5.1.n3). For example,

8772-427: The same conditions, and the ratio of products from C-H and C-D bond functionalizations can be measured with much greater precision than the rate constants in Experiment A. Moreover, only a single measurement of product concentrations from a single sample is required. However, an observed kinetic isotope effect from this experiment is more difficult to interpret, since it may either mean that C-H bond cleavage occurs during

8874-896: The slightly shorter C–D bond compared to a C–H bond. In the equation, subscript H or D refer to the species with H or H, respectively; quantities with or without the double-dagger, ‡, refer to transition state or reactant ground state, respectively. (Strictly speaking, a κ H / κ D {\displaystyle \kappa _{\mathrm {H} }/\kappa _{\mathrm {D} }} term resulting from an isotopic difference in transmission coefficients should also be included. ) where we define Here, h = Planck constant ; k B = Boltzmann constant ; ν ~ i {\displaystyle {\tilde {\nu }}_{i}} = frequency of vibration, expressed in wavenumber ; c = speed of light ; N A = Avogadro constant ; and R = universal gas constant . The σ X (X = H or D) are

8976-414: The small A factor ratios associated with the large activation energy differences (usually about 4.5 kJ/mol for C–H(D) bonds) provided strong evidence for tunneling. For the purpose of this discussion, it is important is that the A factor ratio for the various paraffins they used was roughly constant throughout the temperature range. To determine if tunneling is involved in KIE of a reaction with H or D,

9078-433: The square root of the reduced mass of the vibrating system: where k f is the force constant . Moreover, the reduced mass is approximated by the mass of the light atom of the system, X = H or D. Because m D ≈ 2 m H , In the case of homolytic C–H/D bond dissociation, the transition state term disappears; and neglecting other vibrational modes, k H / k D = exp( ⁠ 1 / 2 ⁠ Δ u i ). Thus,

9180-449: The sums in the exponent are calculated. Thus, in practice, H KIEs are often largely dependent on a handful of key vibrational modes because of this cancellation, making qualitative analyses of k H / k D possible. As mentioned, especially for H/ H substitution, most KIEs arise from the difference in ZPE between the reactants and the transition state of the isotopologues; this difference can be understood qualitatively as follows: in

9282-430: The symmetry numbers for the reactants and transition states. The M X are the molecular masses of the corresponding species, and the I q X ( q = x , y , or z ) terms are the moments of inertia about the three principal axes. The u i X are directly proportional to the corresponding vibrational frequencies, ν i , and the vibrational zero-point energy (ZPE) (see below). The integers N and N are

9384-409: The transition state are expected to yield a normal KIE, and larger force constants in the transition state are expected to yield an IKIE when stretching vibrational contributions dominate the KIE. The magnitudes of such SKIEs at the α-carbon atom are largely determined by the C α -H( H) vibrations. For an S N 1 reaction, since the carbon atom is converted into an sp hybridized carbenium ion during

9486-409: The transition state energy barrier. So even though conventional chemical reactions tend to slow down dramatically as the temperature is lowered, tunneling reactions rarely change at all. Particles that tunnel through an activation barrier are a direct result of the fact that the wave function of an intermediate species, reactant or product is not confined to the energy well of a particular trough along

9588-444: The transition state for the rate-determining step with an increase in C α -H( H) bond order, an IKIE would be expected if only the stretching vibrations were important. The observed large normal KIEs are found to be caused by significant out-of-plane bending vibrational contributions when going from the reactants to the transition state of carbenium ion formation. For S N 2 reactions, bending vibrations still play an important role for

9690-429: The transition state, since the bond force constant decreases during bond breaking. Hence, the lower ZPE of the deuterated species translates into a larger activation energy for its reaction, as shown in the following figure, leading to a normal KIE. This effect should, in principle, be taken into account all 3 N− 6 vibrational modes for the starting material and 3 N − 7 vibrational modes at the transition state (one mode,

9792-423: The various species. This will be a rational number (a ratio of integers) that depends on the number of molecular and bond rotations leading to the permutation of identical atoms or groups in the reactants and the transition state. For systems of low symmetry, all σ X (reactant and transition state) will be unity; thus S can often be neglected. The MMI factor (containing the M X and I q X ) refers to

9894-482: The α-carbon provide a direct means to distinguish between S N 1 and S N 2 reactions. It has been found that S N 1 reactions typically lead to large SKIEs, approaching to their theoretical maximum at about 1.22, while S N 2 reactions typically yield SKIEs that are very close to or less than 1. KIEs greater than 1 are called normal kinetic isotope effects , while KIEs less than 1 are called inverse kinetic isotope effects (IKIE). In general, smaller force constants in

9996-427: Was based on comparison to bulk water, the reorientation of water dipoles can cancel out the stabilizing energy of charge interaction. In Warshel's model, the enzyme acts as a super-solvent, which fixes the orientation of ion pairs and provides super- solvation (very good stabilization of ion pairs), and especially lower the energy when two ions are close to each other. The rate-determining step (RDS) in this mechanism

10098-490: Was finally achieved in 2007 by Thomas Durek in Steve Kent's lab at the University of Chicago who made a synthetic functional lysozyme molecule. Lysozyme crystals have been used to grow other functional materials for catalysis and biomedical applications. Lysozyme is a commonly used enzyme for lysing gram positive bacteria. Due to the unique function of lysozyme in which it can digest the cell wall and causes osmotic shock (burst

10200-468: Was first crystallised by Edward Abraham in 1937, enabling the three-dimensional structure of hen egg white lysozyme to be described by David Chilton Phillips in 1965, when he obtained the first 2- ångström (200 pm ) resolution model via X-ray crystallography . The structure was publicly presented at a Royal Institution lecture in 1965. Lysozyme was the second protein structure and the first enzyme structure to be solved via X-ray diffraction methods, and

10302-476: Was more recently revised. Enzyme Commission number EC numbers do not specify enzymes but enzyme-catalyzed reactions. If different enzymes (for instance from different organisms) catalyze the same reaction, then they receive the same EC number. Furthermore, through convergent evolution , completely different protein folds can catalyze an identical reaction (these are sometimes called non-homologous isofunctional enzymes ) and therefore would be assigned

10404-499: Was used to lower the reaction rate and accumulate an intermediate for characterization. The amino acid side-chains glutamic acid 35 (Glu35) and aspartate 52 (Asp52) have been found to be critical to the activity of this enzyme. Glu35 acts as a proton donor to the glycosidic bond, cleaving the C-O bond in the substrate, whereas Asp52 acts as a nucleophile to generate a glycosyl enzyme intermediate. The Glu35 reacts with water to form hydroxyl ion,

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