Posts Tagged ‘low energy’

Ribulose-1,5-bisphosphate + carbon dioxide → carbon fixation!

Sunday, April 20th, 2014

Ribulose-1,5-bisphosphate reacts with carbon dioxide to produce 3-keto-2-carboxyarabinitol 1,5-bisphosphate as the first step in the biochemical process of carbon fixation. It needs an enzyme to do this (Ribulose-1,5-bisphosphate carboxylase/oxygenase, or RuBisCO) and lots of ATP (adenosine triphosphate, produced by photosynthesis). Here I ask what the nature of the uncatalysed transition state is, and hence the task that might be facing the catalyst in reducing the activation barrier to that of a facile thermal reaction. I present my process in the order it was done‡.

carboxFirstly, I will hypothesize that since C3 needs to lose a hydrogen, the easiest way of doing so is to form the enol of Ribulose-1,5-bisphosphate. I am going to start by reducing the above model to its core; C1 and the attached phosphate is replaced by a methyl, and C4-5 likewise. In this model, it takes 13.1 kcal/mol of free energy to enolize.[1],[2] This species can then react with CO2 (potentially with an accompanying proton transfer) to give 3-keto-2-carboxyarabinitol 1,5-bisphosphate directly. The transition state at the ωB97XD/6-311G(d,p)/SCRF=water level[3] has an IRC (intrinsic reaction coordinate)[4] that reveals the activation barrier is ~17 kcal/mol with respect to the enol (19.5 in ΔG298), with the overall reaction[5] being exo-energic by -2.6 kcal/mol with respect to the enol, but endo-energic by +10.5 kcal/mol with respect to keto-Ribulose-1,5-bisphosphate + carbon dioxide. Note the characteristic feature at IRC -3.0 of a hidden zwitterionic intermediate, which marks a belated proton transfer occurring AFTER the transition state for C-C bond formation. The reaction is asynchronous for this basic model.
carbox
carboxE
carboxG
For this very basic (phosphate-free) model of Ribulose-1,5-bisphosphate, the total computed free energy barrier@298K is 32.6 kcal/mol (standard state of 0.041M; reduced by ~1.9 kcal/mol for more concentrated, e.g. 1M solutions). This is ~13 kcal/mol too high to correspond to a uncatalysed fast process at room temperatures, a gap that the phosphate end-groups and the enzyme have to address (a challenge typically enzymes do manage to achieve).

With a basic model in place, it is time to restore those truncated phosphate end-groups to see what their contribution might be (treated as dianions each for the time being, and stabilized by using a continuum solvent field for water). First, the energies:

System ΔΔG Data DOI
Ribulose-1,5-bisphosphate as keto + CO2  0.0 [6]
Ribulose-1,5-bisphosphate as enol + CO2 13.0 [7]
Transition state 34.8 [8]
Acyclic 3-keto-2-carboxyarabinitol 1,5-bisphosphate 11.5 [9]
Cyclic 3-keto-2-carboxyarabinitol 1,5-bisphosphate -7.3 [10]

Note the network of hydrogen bonds formed at the transition state geometry (below) and the various gauche stereo-electronic alignments[11] which you should really explore in the Jmol 3D model invoked by clicking below.

carbox-TS

Click for 3D

  1. Addition of the phosphate groups has little effect on the energetics of the keto/enol equilibrium,
  2. or on the barrier to reaction with  carbon dioxide.
  3. But, they DO provide a new low energy sink I have not seen described before for the reaction (below), which makes the overall process from Ribulose-1,5-bisphosphate + CO2 exo-energic by -7.3 kcal/mol. Thus the phosphates provide the overall thermodynamic driving force for the carbon fixation.

    Click for 3D

    Click for 3D. Cyclic low-energy cyclic chair isomer of 3-keto-2-carboxyarabinitol 1,5-bisphosphate

  4. Which leaves the role of the enzyme as one of reducing the overall activation barrier. The reaction MUST be enzymatically favoured, since the enzyme also needs to control when the cycle occurs, via a light-sensitive switch. If no enzyme-catalysis were needed, then carbon-fixation would occur in the dark, and consume all available ATP in the process. Inferred purely from the results in the table above, two functions can be listed:
    • The enzyme can help increase the effective molarity of the bimolecular reaction between Ribulose-1,5-bisphosphate + CO2. As noted above, increasing the concentration from e.g. 1 atmosphere (0.041M) to 1M reduces ΔG† by 1.9 kcal/mol.
    • The most influential role the enzyme could play is to bind the enol form of Ribulose-1,5-bisphosphate preferentially over the keto form. If most of the substrate is bound in this form, that would reduce the overall barrier by 13 kcal/mol, more than enough to enable a room temperature reaction.
    • There may of course be many other subtle effects in operation, such as preferential stabilisation of the transition state, which cannot be inferred here without a detailed knowledge of the enzyme. I have deliberately tried to avoid doing that, since I wanted to see what might be concluded purely from the energetics found above.

There is one final step required; a very rapid decomposition of the 3-keto-2-carboxyarabinitol 1,5-bisphosphate (cyclic or not) to produce two molecules of 3-phosphoglycerate. I will leave my computational-energetic analysis and mechanism of that step to another post.

Postscript. An IRC on the full phosphate model took three days to run and has only just finished.[12] The profile is similar to that obtained for the phosphate-free model, with the exception of the IRC feature at -13, where one phosphate group rotates and starts to H-bond to the 3-keto-2-carboxyarabinitol, resulting in a lower energy conformation than that reported above. The energy of this new conformation[13] relative to the starting point (labelled as 0.0 above) is +2.3 kcal/mol (c.f. +11.5 for the previous conformation). The phosphates clearly remain a strong driving force for the reaction. It is quite possible that even more stable forms of this product could be found (by varying where the acidic protons reside) but at least we now know that the product can be more stable than the reactant (by at least -7.3 kcal/mol), which is the important conclusion.
carbox-prod1E
carbox-prod1G

Postscript 1. Yet another lower energy isomer of the product has popped out[14] being -13.1 kcal/mol lower than the initial reactants.

‡I do not describe much molecular biology on this blog, but an urge to rectify this was inspired by a TV program I watched four days ago charting how the pathway chronologically known first as the Calvin, then the Calvin-Benson and now the Calvin-Benson-Bassham cycle for carbon fixation became known (and how it gradually gathered attribution). As a chemist who was trained to try to understand reaction mechanisms, my immediate question (unsurprisingly not addressed at all in the TV program) was: what is the key carbon-carbon bond forming step? Here, I simply wanted initially to answer that one simple question and perhaps the aspect of the relative timing of any C-C bond formation and associated proton transfer. This latter idea in turn was hovering in the background of my mind from association with our previous project in proline-catalysed aldol reactions, where a similar question can be posed and indeed has been answered.[15] The rest of what you see here led directly from trying to answer that initial question. Peter Medawar’s 1963 talk Is the scientific paper a fraud? presented the argument that scientific journal articles give a misleading idea of the actual process of scientific discovery[16]. I hope that perhaps as a blog post, the above does give a little insight into the scientific process I experienced for myself over a period of the last two days (and with conclusions which may of course turn out to be quite wrong).

References

  1. H.S. Rzepa, "Gaussian Job Archive for C5H8O4", 2014. https://doi.org/10.6084/m9.figshare.1004015
  2. H.S. Rzepa, "Gaussian Job Archive for C5H8O4", 2014. https://doi.org/10.6084/m9.figshare.1004023
  3. H.S. Rzepa, "Gaussian Job Archive for C5H8O4", 2014. https://doi.org/10.6084/m9.figshare.1004011
  4. H.S. Rzepa, "Gaussian Job Archive for C5H8O4", 2014. https://doi.org/10.6084/m9.figshare.1004037
  5. H.S. Rzepa, "Gaussian Job Archive for C5H8O4", 2014. https://doi.org/10.6084/m9.figshare.1004038
  6. H.S. Rzepa, "Gaussian Job Archive for C6H8O13P2(4-)", 2014. https://doi.org/10.6084/m9.figshare.1004086
  7. H.S. Rzepa, "Gaussian Job Archive for C6H8O13P2(4-)", 2014. https://doi.org/10.6084/m9.figshare.1004066
  8. H.S. Rzepa, "Gaussian Job Archive for C6H8O13P2(4-)", 2014. https://doi.org/10.6084/m9.figshare.1004112
  9. H.S. Rzepa, "Gaussian Job Archive for C6H8O13P2(4-)", 2014. https://doi.org/10.6084/m9.figshare.1004085
  10. H.S. Rzepa, "Gaussian Job Archive for C6H8O13P2(4-)", 2014. https://doi.org/10.6084/m9.figshare.1004111
  11. H.S. Rzepa, "Gaussian Job Archive for C6H8O13P2(4-)", 2014. https://doi.org/10.6084/m9.figshare.1004026
  12. H.S. Rzepa, "Gaussian Job Archive for C6H8O13P2(4-)", 2014. https://doi.org/10.6084/m9.figshare.1004557
  13. H.S. Rzepa, "Gaussian Job Archive for C6H8O13P2(4-)", 2014. https://doi.org/10.6084/m9.figshare.1004614
  14. H.S. Rzepa, "Gaussian Job Archive for C6H8O13P2(4-)", 2014. https://doi.org/10.6084/m9.figshare.1004778
  15. A. Armstrong, R.A. Boto, P. Dingwall, J. Contreras-García, M.J. Harvey, N.J. Mason, and H.S. Rzepa, "The Houk–List transition states for organocatalytic mechanisms revisited", Chem. Sci., vol. 5, pp. 2057-2071, 2014. https://doi.org/10.1039/c3sc53416b
  16. S.M. Howitt, and A.N. Wilson, "Revisiting “Is the scientific paper a fraud?”", EMBO reports, vol. 15, pp. 481-484, 2014. https://doi.org/10.1002/embr.201338302

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Six vs ten aromatic electrons?

Sunday, October 20th, 2013

Homoaromaticity is a special case of aromaticity in which π-conjugation is interrupted by a single sp3 hybridized carbon atom (it is sometimes referred to as a suspended π-bond with no underlying σ-foundation). But consider the carbene shown below. This example comes from a recently published article[1] which was highlighted on Steve Bachrach’s blog. Here aromaticity has resulted from a slightly different phenomenon, whereby a 4π-electron planar (and hence nominally anti-aromatic) molecule is elevated to aromatic peerage by promoting the two carbene σ-electrons to have π-status. 

B10

Normally, such electrons in a σ framework are considered to be more stable than in a p-π-framework,‡ because the s-character of the former does not have a node at the nucleus and hence the electrons are bound more strongly. In this case however, the transformation from anti-aromaticity to aromaticity provides more than enough stabilisation through resonance for the σ-to-π promotion to occur.

So here I ask a different question to that posed on the aforementioned blog or article; could you achieve the same result using ten electrons rather than six? On the left of the diagram above for the 10-case, we have a planar 8-ring with 8 p-π-electrons and two carbene electrons. Promoting the latter would produce a 10π-aromatic ring (for another example of such, see here). Indeed so![2] This 10π-system has five occupied π-MOs, a low energy delocalised σ-MO of interest (below; is it σ-aromatic?) and a LUMO corresponding to the vacated carbene orbital.

Click for 3D

Click for 3D

ELF analysis (below) also reveals no carbene lone pair (basins 20 and 21 have 0.44e each, and 18/19 2.70 each, giving that central carbon 6.28e, resembling the vinyl carbocation shown above in resonance). 

Click for 3D

Click for 3D

Not all is rosy however. This species is in fact not a stable minimum, but a transition state interconverting two buckled (and hence non-aromatic) conformations. It seems that the additional angular ring strain induced by an 8-membered ring has pushed it over the edge from aromatic royalty to non-aromatic commoness (remember this?). But that apart, we can see that 10 electrons can behave similarly to six in inducing a two-electron promotion from a carbene lone pair. Not quite homoaromaticity;  I think it should be given its own named aromatic type! Any suggestions? 

‡That is certainly largely true of carbon. But much less true for the more electropositive boron. Thus it is not unusual to find such promotions occurring for planar boron frameworks.

References

  1. B. Chen, A.Y. Rogachev, D.A. Hrovat, R. Hoffmann, and W.T. Borden, "How to Make the σ<sup>0</sup>π<sup>2</sup> Singlet the Ground State of Carbenes", Journal of the American Chemical Society, vol. 135, pp. 13954-13964, 2013. https://doi.org/10.1021/ja407116e
  2. "C 3 H 5 B 1 N 4", 2013. http://hdl.handle.net/10042/25837

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Mechanism of the Van Leusen reaction.

Wednesday, May 29th, 2013

This is a follow-up to comment posted by Ryan, who asked about isocyanide’s role (in the form of the anion of tosyl isocyanide, or TosMIC): “In Van Leusen, it (the isocyanide) acts as an electrophile”. The Wikipedia article (recently updated by myself) shows nucleophilic attack by an oxy-anion on the carbon of the C≡N group, with the isocyanide group acting as the acceptor of these electrons (in other words, the electrophile). In the form shown below, one negatively charged atom appears to be attacking another also carrying a negative charge. Surely this breaks the rules that like charges repel? So we shall investigate to see if this really happens.

VL1

I have extended the basic mechanistic scheme below to investigate other possibilities (with the aim of probing using the ωB97XD/6-311G(d,p)/scrf=methanol theory to see how realistic any of these routes might be). Starting from 1, the product 6 can now be formed by three routes from the common intermediate 3 (there may be other routes of course not considered here). The relative computed free energies of these various species, and some of the transition states leading to them are listed in the table below.VanLeusen

The path leading to 3 is very low energy which may in part also be due to my using formaldehyde for expediency rather than a substituted aldehyde (I have to confess to having taken another short-cut, which is to miss out any counter-ion to the TosMIC anion). The first step is defined by TS1, which forms a C-C bond, and results in the intermediate 2. TS2 corresponds to O…C bond formation to yield 3. Getting to 3 is thus a two-stage process, or a stepwise cycloaddition. The alternative would have been to regard TosMIC anion as a 1,3-dipole (isoelectronic with e.g.diazomethane) in which these two steps are conflated into a concerted cycloaddition across the carbonyl group.

TS2 is the interesting step from the point of view of the question raised above. It has a very low free-energy barrier from either 1 or 2, and therefore appears very facile. The angle of approach by the oxy-anion to the triple bond (we established it as being triple in the previous post) is 87°. This angle explains why a carbon bearing (a formal) negative charge easily accepts attack on itself by a nucleophile (i.e. acting as an electrophile). The formal negative charge originates from an electron lone pair located in an sp-hybrid orbital lying along the axis of the C≡N bond. But the nucleophilic attack is occurring at 87° to this axis, putting electrons into the empty π* orbital of the C≡N bond. So in effect the two apparent “negative charges” in the mechanistic schemes above are orthogonal to each-other, which in a simplistic way explains why the diagram is not actually contradictory. The reaction itself is an example of Baldwin’s rules in action; one of these is that a 5-endo-dig cyclisation is allowed. This angle of attack and Baldwin’s rules may of course be related.

System Relative free energy
1 0.0
TS1 1.2
2 -3.1
TS2 1.7
3 -14.4
4 -16.7
TS3 5.9
5 4.0
TS4 17.7
6 -51.1
TS5 -2.3
7 -3.1
TS6 57.0
“8” -37.4
“9” -36.2
10 -25.3

After 3, the mechanism can channel several ways. For example, a proton transfer can precede the departure of Ts to give 4 and thence 5. The final [1,2] shift to form the product 6 has a relatively high barrier however. More likely is the Ts group heterolysing off 3 via TS5 to form 7. All that is now needed is to shift a proton from 7 to form 6, and this also can take several routes. One would involve base/acid catalysed deprotonation/reprotonation. Alternatively, the hydrogen could migrate by a series of uncatalysed [1,5]sigmatropic hydrogen shifts via e.g. 8, 9 or 10. In fact, the calculated geometries of both 8 and 9 show that the C…O bond is broken, thus forming entirely different products. Thus the most probable route is indeed a simple catalysed proton transfer from 7.

This computational exploration of the mechanism has reinforced the accepted one, and hopefully cast some light on why an isocyanide can appear to act as an electrophile.

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Scalemic molecules: a cheminformatics challenge!

Wednesday, July 6th, 2011

A scalemic molecule is the term used by Eliel to describe any non-racemic chiral compound. Synthetic chemists imply it when they describe a synthetic product with an observable enantiomeric excess or ee (which can range from close to 0% to almost 100%). There are two cheminformatics questions of interest to me:

  1. How many non-trivial scalemic molecules have been reported in the literature (let’s assume their ee is significantly greater than 0%)?
    • The distribution function for the ee of these molecules would be most interesting!
  2. Of those, how many have the absolute configuration of the predominant enantiomer established with high confidence?
    • Or, to put this another way, how many may prove to be mis-assigned?

Note the careful qualification in the above questions. Thus by non-trivial, I mean compounds whose scalemic attributes persist in solution for a chemically useful duration. That could be taken to mean configurationally stable chiral molecules, rather than those that might be conformationally chiral (an example of a trivial scalemic molecule would be e.g. the twist-boat conformation of cyclohexane, which having D2 symmetry is dissymetric, but which would only retain its scalemic property for a trivially short timescale).

What are boundary values? These are some:

  • As I write this, CAS records 61,257,703 chemical substances. Needless to say (unless I missed it), the answer to my first question is not to be found there.
  • Beilstein (Reaxys) records 1,126,995 compounds as having one or more reported chiroptical properties (which is the most direct way of establishing a molecule is scalemic, although strictly, having say an optical rotation of 0° does not necessarily mean the molecule is not scalemic). We have no way of knowing how many molecules are scalemic for which no chiroptical measurement has been made (but one would hope its a small proportion). Perhaps that is a good answer to question 1?
    • of which 1,097,094 relate to optical rotatory power, 17,515 to optical rotatory dispersion and 62,248 to electronic circular dichroism.
    • it is more difficult to answer how many of these 1,126,995 substances have a firmly established absolute configuration. Measuring a chiroptical property per se does NOT in itself establish the absolute configuration. Doing so is a fascinating exercise in sequential logical argument, and how one does it has changed quite a lot over time. And what might I mean with high confidence? An older assignment (made say > 40 years ago) might be less confident than one established in 2011 (fortunately, we can probably trust the absolute configurations of the amino acids!). A bit of a can of worms, nevertheless. But it interests me because it is a good example of what the semantic web is supposed to be all about.
  • The Cambridge crystallographic database reports 560,307 entries, of which 72,340 are in chiral space groups (in which a chiral molecule can crystallise) and exhibit no disorder or other errors. We do not know how many of these are non-trivial, since all manner of small (and low energy) distortions can create a chiral species (in the solid state), but which would not persist  for a chemically useful duration in solution (i.e. it might for example immediately racemize and become non-scalemic).
  • The Flack parameter has been used since 1983 for enantiomorph estimation (a value of ~≤ 0.10(10) would be considered meaningful). This could in principle provide an answer of known confidence to my question 2 above (but would not address the issue of non-triviality).
    • The challenge now is to quantify how many compounds have a meaningful reported Flack parameter (presumably a sub-set of 72,340?)

Let me declare one personal interest. Over the last four years or so, we have been asked to confirm the absolute configuration of around eight scalemic molecules. After a detailed study, we concluded three were mis-assigned. Now this in no way implies anything about what the answer to question 2 above might be! But it does make one think!

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