AREQUIPA – PERÚ
C. Síndrome del Túnel Carpiano
2.2. PAUSAS ACTIVAS: MEDIDA DE CONTROL 1 Conceptualizaciones
Modelling of intramolecular protein reactions such as isopeptide bond formation is made convenient by the QM/MM methodology. In order to gauge the effect of the protein environment, gas-‐phase modelling of the basic reaction was undertaken.
Specifically we were interested if an amidation reaction calculated using a part of the previously employed QM region in the gas-‐phase, would be favourable.
The reaction profile was calculated at the B3LYP/6-‐31+G(d,p) level with single-‐point energy calculations at the M06-‐2X/6-‐311+G(3df,3pd) level, i.e. the same level of theory as in the QM/MM calculations. The Synchronous Transit and Quasi-‐Newton method (STQN)343 in Gaussian was used to locate transition states (QST2 and QST3
keywords) all of which were confirmed by frequency calculations which were also used to calculate the thermal correction to enthalpy and free energy.
The computed potential energy profile ΔE (0K, no ZPVE), enthalpy profile ΔH (298 K) and free energy profile ΔG (298 K) are shown in Figure 55.
The gas-‐phase mechanism is slightly different than the QM/MM calculated
mechanism. First of all, an NH3+ group on the lysine-‐like residue is not stable and
leads to spontaneous proton transfer to the carboxylic acid groups and no zwitterionic intermediates are found on the reaction profile unlike the QM/MM profile. Apart from these differences, a very similar reaction profile is predicted, a similar nucleophilic attack step, proton shuttling involving the glutamate-‐model and water dissociation. Transition states between GAS1 & GAS3 and GAS6 & GAS7 were troublesome to locate with STQN algorithms (subtle conformational changes of the reactant and product states) and were eventually abandoned as they are not very important for the mechanism.
Figure 55 The gas-‐phase reaction profile calculated at the M06-‐2X/6-‐311+G(3df,3pd)//B3LYP/6-‐31+G(d,p) level. Potential energy profile and free energy profile shown (free energy corrections at the B3LYP/6-‐31+G(d,p) level. The numbering of minima was deliberately made similar as the numbering in the QM/MM profile.
The energetics of the 0 K potential energy pathway are very similar to the original QM/MM pathway shown in Figure 45 and 48. Interestingly, the ΔH pathway is for the most part very similar as the ΔE pathway, but the energies of the two main barriers are lowered, presumably due to favourable loss of vibrational energy of the bonds being broken in the transition states. However, the 298 K free energy pathway raises the barriers substantially, due to unfavourable entropy effects, which would
presumably prevent reactions of this kind from occurring spontaneously in the gas-‐ phase or solution. We do note, however, that the accuracy of the free energy
correction is unknown. Due to the many low-‐frequency vibrations of this system, harmonic vibrational frequencies may be inaccurate for the entropy contribution.1
Free energy simulations of the QM/MM isopeptide bond pathway were not attempted as they require lengthy MD simulations so it is currently not known whether a
calculated QM/MM free energy profile of the mechanism would raise the barriers considerably. It may be that isopeptide bond formation occurs primarily because the entropy penalty has already been paid by how the residues are positioned inside the protein, i.e. it is the folding of the peptide that brings the residues together and allows the reaction to occur in the first place. Recent studies of free-‐energy effects in
enzymatic reactions suggest that for the most part, entropy effects are low and that free-‐energy profiles compare well to potential energy profiles as the entropy penalty of binding and pre-‐organisation of the substrates has already been paid.344,345
However, it may also be that calculation of the ZPVE and thermal corrections to enthalpy would lower the barriers in our QM/MM mechanisms of isopeptide bond formation. !"#$% $#$% "#$% &$#$% &"#$% '$#$% '"#$% ($#$% )*+,-%.% )*+,-%/% )*+,-%0% 1.2*+3%45-+678+9% !"#$% !"#&% !"#'% !"#(% !"#)% !"#*% !"#*+% ,#% ,#% ,#% ,#% -!" -#" -$"
Finally, we note that our computed mechanism of amide bond formation in the gas-‐ phase is intriguing, despite the high free energy barriers. Amide bond formation has been described as one of the most important reactions in organic chemistry and amide bonds are common in drug molecules and biologically relevant compounds. Current synthetic methods to create amide bonds have come under scrutiny due to waste and expense and it is clear that new and better methods to create amide bonds are needed, especially for the growing area of synthesis and modification of
peptides.346 The gas-‐phase mechanism in Figure 55 would only be applicable as a
catalytic strategy if it is favourable to bring the 3 molecules together in solution, i.e. if the intermolecular forces of the GAS1 structure in solution (or a similar complex) are stronger than the associated entropic penalty. Calculations suggest this to be the case in the gas-‐phase by ~ 3 kcal/mol (corrected for basis set superposition error) but this may not be the case in solution. Some kind of supramolecular complex might be required to accomplish this in practice (by somehow trapping the substrates and bringing them close together).347
5.7 Summary
A mechanism of the recently discovered Lys-‐Asp isopeptide bond in a surface bacterial protein has been computed by QM/MM calculations. The mechanism explains some key experimental observations such as the catalytic role of the
glutamate residue and the reason for the experimental observation that no isopeptide bond is formed in mutants with no glutamate.
There are still a number of open questions for spontaneous formation of isopeptide bonds in bacterial proteins, such as whether Lys-‐Asn and Lys-‐Asp isopeptide bonds are formed by a common mechanism, why the Lys-‐Asp bond is formed more rapidly than the Lys-‐Asn bond in the CnaB2 mutant, the preference for cis vs. trans isopeptide bonds and many others.
We suggest future computational studies of isopeptide bond formation to utilise molecular dynamics and free energy simulations in a QM/MM scheme. Molecular dynamics simulation should enable one to better understand the importance of the environment on the mechanism (our calculations already suggest that such effects could stabilise the water dissociation step considerably), check for the flexibility of the protein and interaction of the reaction site with the nearby bulk solvent as well as giving a clearer picture of how entropy affects the kinetics of the reaction. Such MD simulations would most likely require the use of semi-‐empirical methods due to computational cost and we note the successful use of the PM3 method in the 3F-‐GABA study. The recent OMX methods have also been shown to be remarkably successful in a recent benchmark study of organic thermochemistry, kinetics and weak
interactions.321 OMX/MM free energy simulations could be performed either using
thermodynamic integration or umbrella sampling to yield a free energy profile and could possibly be corrected to a DFT/MM energy profile by using a thermodynamic cycle as in the 3F-‐GABA study. The recent use of QM/MM FEP methods on frozen NEB pathways also looks promising.344,345
Finally we note that nature has of course already come up with an elegant way of creating amide bonds in the peptidyltransferase centre in the ribosome where the
peptidyl-‐tRNA residue is transferred to the aminoacyl-‐tRNA residue and the peptide bond is created. The mechanism of peptide bond mechanism is still under debate.348-‐ 355 The main rate-‐enhancing effect of peptide bond formation in the ribosome has
been suggested to be entropic in origin,348 that is achieved by desolvation and
positioning of the substrates, leading to a small TΔS factor. However, such observations do not explain the mechanism (whether catalytic or not). Several studies have suggested that the peptidyl-‐tRNA 2’-‐OH is involved and acts as a proton shuttle leading to possible 6-‐ to 8-‐membered transition states349-‐352 and tetrahedral
intermediates, but the importance of the 2’-‐OH group has been challenged as well.353
Most recently, kinetic isotope analyses354 have ruled out a completely concerted
mechanism and suggest instead a stepwise mechanism where the C-‐N bond formation (nucleophilic attack by the aminoacyl group) leading to a tetrahedral intermediate is rate-‐limiting. A proton-‐shuttle role by peptidyl-‐tRNA 2’-‐OH is still conceivable but its role might also just be that of a stabilising hydrogen bond (possibly involved in the orientation of the substrate for subsequent nucleophilic attack) while nearby water molecules are responsible for the necessary proton transfers (deprotonation of the aminoacyl-‐tRNA amine group and protonation of the peptidyl-‐tRNA 3’O leaving group).
The currently proposed ideas for peptide bond formation in the ribosome are thus not too dissimilar to the proposed mechanisms discussed in our work on isopeptide bond formation where orientation of the residues for nucleophilic attack, stabilisation of a tetrahedral intermediate and low barrier proton transfers are all key points and may well be nature’s efficient way of making amide bonds.