Microscopic Insights into the NMR Relaxation-Based Protein Conformational Entropy Meter

Vignesh Kasinath, Kim A. Sharp, and A. Joshua Wand Journal of the American Chemical Society 2013, 135, 15092
Contributed by +Jan Jensen

Order parameters measured by NMR report on the local fluctuations of protein structures and should therefore be related to entropy. This study uses molecular dynamics (MD) simulations to obtain a quantitative relationship between conformational side chain entropy ($S_{sc}$) and Lipari-Szabo methyl group squared generalized order parameters ($O^2$).

First the authors demonstrate that MD simulations can reproduce experimentally measured $O^2$ values for 7 different proteins, with an $R^2$ of 0.92.

Second the authors demonstrate a linear correlation between the total $S_{sc}$ and computed $O^2$ values, both for methyl containing side chains ($R^2$ = 0.90) and for all side chains ($R^2$ = 0.91).

Based on these finding the authors re-analyzed data from two previously published studies, and extracted a similarly quantitative linear correlation ($R^2$ = 0.95) between the molecular entropy change ($\Delta S_{tot}-\Delta S_{solv}$) and the measured change in $O^2$ values for protein-protein and protein-DNA binding.  This suggest that both entropy changes are dominated by the changes in conformational side-chain entropy.

The method looks like a very powerful tool for obtaining detailed quantitative structural understanding of entropy changes in biomolecular processes.

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Popular highlights of 2013

Computational Chemistry Highlights received 28,762 pageviews in 2013.

A total of 48 highlights were published in 2013 and the five most viewed highlights are

1. Are Protein Force Fields Getting Better? A Systematic Benchmark on 524 Diverse NMR Measurements highlighted by Ric Baron in March

2. Will molecular dynamics simulations of proteins ever reach equilibrium? highlighted by Gerald Monard in July

3. Molecularspace.org highlighted by Jan Jensen in June

4. A geometrical correction for the inter- and intra-molecular basis set superposition error in Hartree-Fock and density functional theory calculations for large systems highlighted by Steven Bachrach in January

5. Intrinsic Atomic Orbitals: An Unbiased Bridge between Quantum Theory and Chemical Concepts highlighted by Grant Hill in October

However, the most viewed post in 2013 was Chemical Networks (Triple header!) highlighted by Rob Paton in July 2012.

The most popular entries within the last 30 days can as always be found on the right hand side of this page.

The are many ways to stay updated on the latest CCH highlights and CCH currently has 119 subscribers on Feedly, 130 twitter followers, 476 Google+ followers, 43 Facebook followers, and 90 followers on Linkedin.


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Six Pyranoside Forms of Free 2-Deoxy-D-ribose

Peña, I.; Cocinero, E. J.; Cabezas, C.; Lesarri, A.; Mata, S.; Écija, P.; Daly, A. M.; Cimas, Á.; Bermúdez, C.; Basterretxea, F. J.; Blanco, S.; Fernández, J. A.; López, J. C.; Castaño, F.; Alonso, J. L.  Angew. Chem. Int. Ed. 2013, 52, 11840-11845
Contributed by Steven Bachrach.
Reposted from Computational Organic Chemistry with permission

2-deoxyribose 1 is undoubtedly one of the most important sugars as it is incorporated into the backbone of DNA. The conformational landscape of 1 is complicated: it can exist as an open chain, as a five-member ring (furanose), or a six-member ring (pyranose), and intramolecular hydrogen bonding can occur. This internal hydrogen bonding is in competition with hydrogen bonding to water in aqueous solution. Unraveling all this is of great interest in predicting structures of this and a whole host of sugar and sugar containing-molecules.

1

In order to get a firm starting point, the gas phase structures of the low energy conformers of 1 would constitute a great set of structures to use as a benchmark for gauging force fields and computational methods. Cocinero and Alonso¹ have performed a laser ablation molecular beam Fourier transform microwave (LA-MB-FTMW) experiment (see these posts for other studies using this technique) on 1 and identified the experimental conformations by comparison to structures obtained at MP2/6-311++G(d,p). Unfortunately the authors do not include these structures in their supporting materials, so I have optimized the low energy conformers of 1 at ωB97X-D/6-31G(d) and they are shown in Figure 1.

1a (0.0)	1b (4.7)
1c (3.3)	1d (5.6)
1e (8.9)	1f (9.4)

Figure 1. ωB97X-D/6-31G(d) optimized structures of the six lowest energy conformers of 1. Relative free energy in kJ mol^-1.

The computed spectroscopic parameters were used to identify the structures responsible for the six different ribose conformers observed in the microwave experiment. To give a sense of the agreement between the computed and experimental parameters, I show these values for the two lowest energy conformers in Table 1.

Table 1. MP2/6-311++G(d,p) computed and observed spectroscopic parameters for the two lowest energy conformers of 1.

	1a		1c
	Expt	Calc	Expt	Calc
A(MHz)	2484.4138	2492	2437.8239	2447
B (MHz)	1517.7653	1533	1510.7283	1527
C (MHz)	1238.9958	1250	1144.9804	1158
ΔG (kJ mol-1)		0.0		3.3

This is yet another excellent example of the symbiotic relationship between experiment and computation in structure identification.

References

(1) Peña, I.; Cocinero, E. J.; Cabezas, C.; Lesarri, A.; Mata, S.; Écija, P.; Daly, A. M.; Cimas, Á.; Bermúdez, C.; Basterretxea, F. J.; Blanco, S.; Fernández, J. A.; López, J. C.; Castaño, F.; Alonso, J. L. "Six Pyranoside Forms of Free 2-Deoxy-D-ribose," Angew. Chem. Int. Ed. 2013, 52, 11840-11845, DOI:10.1002/anie.201305589.

InChIs

1a: InChI=1S/C5H10O4/c6-3-1-5(8)9-2-4(3)7/h3-8H,1-2H2/t3-,4+,5-/m0/s1
InChIKey=ZVQAVWAHRUNNPG-LMVFSUKVSA-N

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Computation-aided structure determination

(1) Jahn, M. K.; Dewald, D.; Vallejo-López, M.; Cocinero, E. J.; Lesarri, A.; Grabow, J.-U. "Rotational Spectra of Bicyclic Decanes: The Trans Conformation of (-)-Lupinine," J. Phys. Chem. A 2013
(2) Shepherd, D. J.; Broadwith, P. A.; Dyson, B. S.; Paton, R. S.; Burton, J. W. "Structure Reassignment of Laurefurenynes A and B by Computation and Total Synthesis," Chem. Eur. J. 2013, 19, 12644-12648

Contributed by Steven Bachrach.
Reposted from Computational Organic Chemistry with permission

I have not discussed any papers that utilize computations to confirm chemical structure in a while, so here are two recent examples.

Grabow has utilized MP2 and M06-2x computations to confirm the lowest energy conformation of (-)-lupinine 1.¹ The interesting structural aspect of this compound is the possibility of an intramolecular hydrogen bond linking the hydroxyl group with the amine.

1

Using molecular mechanics, the authors identified 57 structures within 50 kJ mol^-1 of each other. These geometries were reoptimized at MP2/6-311++G(d,p) and M06-2x/6-311++G(d,p).

The lowest energy structures had the expected trans ring fusion, with a trans relationship between the hydrogen on the bridgehead carbon (C9) and the hydroxymethyl group. This corresponds to either the (R,R) or (S,S) isomer. The three lowest energy structures are shown in Figure 1. Unfortunately, the geometry for the lowest energy isomer provided in the Supporting Materials is wrong, and the authors did not supply the geometries of the other isomers. This situation is unacceptable! Reviewers and editors must do a better job in policing the Supporting Materials; there is no excuse for not including all of the optimized structures, and better yet, in a more usable format that what has been done here. I have reoptimized these structures at M06-2x/6-31G(d). The lowest energy conformer 1a does possess the expected internal hydrogen bond.

1a (0.0)
1b (10.4)	12 (11.5)

Figure 1. M06-2x/6-31G(d) optimized structures of the three lowest energy conformers of 1, with relative free energies in kJ mol^-1.

Table 1 provides a comparison of the MP2 computed values of important structural parameters along with the experimental values obtained from a microwave experiment. The agreement with the computed values for 1a provides strong evidence that this is the structure of (-)-lupinine.

Table 1. Comparison of MP2 and experimental structural parameters of 1.^a

	Expt. (1)	MP2 (1a)
A	1414.126	1425.8
B	811.672	815.1
C	671.530	677.1
ΔJ	0.0255	0.023
ΔJK	0.0639	0.065
ΔK	0.0037	0.0022
χaa	1.9973	2.0
χbb	1.062	1.1
χcc	-3.059	-3.1

^aRotational constants (A, B, C) in MHz, centrifugal distortion constants (Δ_J, Δ_JK, Δ_K) in kHz, and nuclear quadrupole coupling tensor elements (χ_aa, χ_bb, χ_cc) in MHz.

The second study utilizes computed NMR chemical shifts to discriminate potential diastereomeric structures. Laurefurenyne A was first assigned the structure 2 based on 1D and 2D NMR experiments. However, based on potential biochemical analogy to other compounds, Paton and Burton² had doubts about this structure. In addition to synthesizing the natural material, they performed an extensive computational study of the chemical shifts of the diastereomers. For each of the 32 possible diastereomers, they performed a Monte Carlo search of the conformational space using molecular mechanics. The structures of all isomers within 10 kJ mol^-1 of the lowest energy structure were reoptimized at ωB97X-D/6-31G(d) with PCM (CHCl₃) and chemical shifts obtained at mPW1PW91/6-311G(d,p). Final chemical shifts were obtained using a Boltzmann weighting. The computed values for 2were quite off from the experimental values, with a mean unsigned error of 1.5 ppm. A better assessment was provided with the DP4 method, which indicated that 3 has the highest probability of being the correct structure, a structure consistent with the likely biosynthetic pathway.

2

3

References

(1) Jahn, M. K.; Dewald, D.; Vallejo-López, M.; Cocinero, E. J.; Lesarri, A.; Grabow, J.-U. "Rotational Spectra of Bicyclic Decanes: The Trans Conformation of (-)-Lupinine," J. Phys. Chem. A 2013, DOI:10.1021/jp407671m.

(2) Shepherd, D. J.; Broadwith, P. A.; Dyson, B. S.; Paton, R. S.; Burton, J. W. "Structure Reassignment of Laurefurenynes A and B by Computation and Total Synthesis," Chem. Eur. J. 2013, 19, 12644-12648, DOI: 10.1002/chem.201302349.

InChIs

(-)-Lupinine 1: InChI=1S/C11H21NO/c1-11-6-2-3-7-12(11)8-4-5-10(11)9-13/h10,13H,2-9H2,1H3/t10-,11+/m0/s1
InChIKey=WVDUAOYJLFVEMW-WDEREUQCSA-N

Laurefurenyne A 3: InChI=1S/C14H20O4.C2H6/c1-3-4-5-6-12-11(16)8-14(18-12)13-7-10(15)9(2)17-13;1-2/h1,4-5,9-16H,6-8H2,2H3;1-2H3/b5-4-;/t9-,10-,11-,12+,13-,14+;/m1./s1
InChIKey=ZYESDGGYHKCHMJ-SKFGUVSTSA-N

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Comparison of Molecular Mechanics, Semi-Empirical Quantum Mechanical, and Density Functional Theory Methods for Scoring Protein−Ligand Interactions

Nusret D. Yilmazer and Martin Korth Journal of Physical Chemistry B 2013, 117, 8075
Contributed by +Jan Jensen

This paper provides an extremely thorough comparison of electronic protein-ligand interaction energies computed using MM force fields, semi-empirical methods, and DFT.

About 700 protein-ligand complexes were selected from the PDBbind2007 database and four model systems of increasing size (including atoms up to 10 Å from a ligand atom) are created for each. DFT calculations were only possible for around 500 complexes using a 5 Å cutoff, and MM calculations were only possible for 352 complexes due to parameterization problems. 

Single point energies for the protein-ligand complex and separated protein and ligand are then computed and used to compute interaction energies, which were then compared amongst each other.  For example, systems of different size and be compared to monitor convergence and different methods can be compared for a given cutoff.  

Some of the more interesting comparisons to me are PM6-DH+ vs BP86-D2/TZVP (R = 1.00) and MMFF94 vs BP86-D2/TZVP (R = 0.93).  (Interestingly, the former value decreases to 0.92 if COSMO is included - that is unexpected to me.)  While these R values are quite good the corresponding MAD values are quite bad: 14 and 57 kcal/mol, respectively!  I find the former quite surprising since the error in the PM6-DH+ hydrogen bond strengths computed for the underlying training set are on the order of 2 kcal/mol. It could be non-additivity or more interactions between charged groups in the present set.

Acknowledgement: thanks to +Jimmy Charnley Kromann for alerting me to this paper

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Predicting Kinetically Unstable C-C Bonds from the Ground-State Properties of a Molecule

Markopoulos, G.; Grunenberg, J. Angew. Chem. Int. Ed. 2013, 52, 10648
Contributed by Steven Bachrach.
Reposted from Computational Organic Chemistry with permission

Can one identify a labile bond in a molecule without computing activation barriers? Markopoulos and Grunenberg suggest that examination of the bond length and its associated relaxed force constant might provide some guidance.¹

The relaxed force constant comes from identifying the force constant for some coordinate while allowing for other coordinates to relax. Badger’s rule relates the (normal) force constant to bond distance (k = a/(r_eq – d)³). For a series of 36 molecules, covering 71 C-C single bonds, Badger’s rule fits the data well, except for a set of molecules which undergo rapid Cope rearrangements (like bullvalene and semibullvalene). For these molecules, the relaxed force constants are much lower than Badger’s rule predicts, and indicates a weakened bond. This gives rise to their low activation barriers.

Another example is provided with the highly strained polycyclic hydrocarbon 1. This compound is predicted (B3LYP/6-31G(d)) to undergo a [1,2]-shift to give the carbene 2 (see Figure 1), and this is extremely exothermic: -105.7 kcal mol^-1, reflecting the enormous strain of 1. The barrier, through TS1 (Figure 1), is only 6.7 kcal mol^-1. This rearrangement was predicted by examining the relaxed force constants which identified a very weak bond, despite a short bond distance of 1.404 Å. It is unlikely that without this guidance, one would have predicted that this short bond is likely to rupture and produce this particular product.

1	2
TS1

Figure 1. B3LYP/6-31G(d) optimized structures of 1, 2, and TS1.

References

(1) Markopoulos, G.; Grunenberg, J. "Predicting Kinetically Unstable C-C Bonds from the Ground-State Properties of a Molecule," Angew. Chem. Int. Ed. 2013, 52, 10648-10651, DOI: 10.1002/anie.20130382.

InChIs

1: InChI=1S/C14H12/c1-2-8-11-5-3-9-7(1)10(9)4-6-12(8,11)14(8,11)13(7,9)10/h1-6H2
InChIKey=LNBZAENQMFDBJW-UHFFFAOYSA-N

2: InChI=1S/C14H12/c1-3-11-12-4-2-9-7-8(1,9)10(9)5-6-13(11,12)14(10,11)12/h1-6H2
InChIKey=UKVODHRLGFPZPT-UHFFFAOYSA-N

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Tunneling control of chemical reactions: C-H insertion versus H-tunneling in tert-butylhydroxycarbene

Ley, D.; Gerbig, D.; Schreiner, P. R. Chem. Sci. 2013, 4, 677
Contributed by Steven Bachrach.
Reposted from Computational Organic Chemistry with permission

Sorry I missed this paper from much earlier this year – it’s from a journal that’s not on my normal reading list. Anyways, here is another fantastic work from the Schreiner lab demonstrating the concept of tunneling control (see this post).¹ They prepare the t-butylhydroxycarbene 1 at low temperature to look for evidence of formation of possible products arising from a [1,2]-hydrogen shift (2), a [1,2]-methyl shift (3) or a [1,3]-CH insertion (4).

Schreiner performed CCSD(T)/cc-pVDZ optimizations of these compounds along with the transition states for the three migrations. The optimized geometries and relative energies are shown in Figure 1. The thermodynamic product is the aldehyde 2 while the kinetic product is the cyclopropane 4, with a barrier of 23.8 kcal mol^-1 some 3.5 kcal mol^-1 lower than the barrier leading to 2.

1 (0.0)	TS2 (27.3)	2 (-53.5)
	TS3 (31.0)	3 (-41.0)
	TS4 (23.8)	4 (-28.3)

Figure 1. CCSD(T)/cc-pVDZ optimized structures of 1-4 and the transition states for the three reaction. Relative energies in kcal mol^-1.

At low temperature (11 K), 1 is found to slowly convert into 2 with a half-life of 1.7 h. No other product is observed. Rates for the three reactions were also computed using the Wentzel-Kramers-Brillouin (WKB) method (which Schreiner and Allen have used in all of their previous studies). The predicted rate for the conversion of 1 into 2, which takes place at 11 K solely through a tunneling process, is 0.4h, in quite reasonable agreement with experiment. The predicted rates for the other two potential reactions at 11 K are 10³¹ and 10⁴⁰ years.

This is clearly an example of tunneling control. The reaction occurs not across the lowest barrier, butthrough the narrowest barrier.

References

(1) Ley, D.; Gerbig, D.; Schreiner, P. R. "Tunneling control of chemical reactions: C-H insertion versus H-tunneling in tert-butylhydroxycarbene," Chem. Sci. 2013, 4, 677-684, DOI: 10.1039/C2SC21555A.

InChI

1: InChI=1S/C5H10O/c1-5(2,3)4-6/h6H,1-3H3
InChIKey=ZGFKBRGJTPEEOC-UHFFFAOYSA-N

2: InChI=1S/C5H10O/c1-5(2,3)4-6/h4H,1-3H3

3: InChI=1S/C5H10O/c1-4(2)5(3)6/h6H,1-3H3
InChIKey=BZAZNULYLRVMSW-UHFFFAOYSA-N

4: InChI=1S/C5H10O/c1-5(2)3-4(5)6/h4,6H,3H2,1-2H3
InChIKey=MWWQKEGWQLBJBJ-UHFFFAOYSA-N

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