Imperial College London

Henry Rzepa

[Ribulose-1,5-bisphosphate](http://en.wikipedia.org/wiki/Ribulose-1,5-bisphosphate){target="_blank"
rel="noopener"} 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](http://en.wikipedia.org/wiki/RuBisCO){target="_blank"
rel="noopener"}) 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^‡^.

[![carbox](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2014/04/carbox.svg){.aligncenter
.size-full .wp-image-12400 decoding="async"
width="250"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2014/04/carbox.svg)Firstly,
I will hypothesize that since C3 needs to lose a hydrogen, the easiest
way of doing so is to form the
**[enol](http://www.ch.imperial.ac.uk/rzepa/blog/?p=8246){target="_blank"
rel="noopener"}** 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.\[cite\]10.6084/m9.figshare.1004015\[/cite\],\[cite\]10.6084/m9.figshare.1004023\[/cite\]
This species can then react with CO~2~ (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\[cite\]10.6084/m9.figshare.1004011\[/cite\] has an IRC (intrinsic
reaction coordinate)\[cite\]10.6084/m9.figshare.1004037\[/cite\] that
reveals the activation barrier is \~17 kcal/mol with respect to the enol
(19.5 in ΔG~298~), with the overall
reaction\[cite\]10.6084/m9.figshare.1004038\[/cite\] 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](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2014/04/carbox.gif){.aligncenter
.size-full .wp-image-12427 decoding="async"
width="400"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2014/04/carbox.gif)  
[![carboxE](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2014/04/carboxE.svg){.aligncenter
.size-full .wp-image-12430 decoding="async"
width="350"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2014/04/carboxE.svg)  
[![carboxG](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2014/04/carboxG.svg){.aligncenter
.size-full .wp-image-12429 decoding="async"
width="350"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2014/04/carboxG.svg)  
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 + CO~2~           |  0.0 | \[cite\]10.6084/m9.figshare.1004086\[/cite\] |
| Ribulose-1,5-bisphosphate as enol + CO~2~           | 13.0 | \[cite\]10.6084/m9.figshare.1004066\[/cite\] |
| Transition state                                    | 34.8 | \[cite\]10.6084/m9.figshare.1004112\[/cite\] |
| Acyclic 3-keto-2-carboxyarabinitol 1,5-bisphosphate | 11.5 | \[cite\]10.6084/m9.figshare.1004085\[/cite\] |
| Cyclic 3-keto-2-carboxyarabinitol 1,5-bisphosphate  | -7.3 | \[cite\]10.6084/m9.figshare.1004111\[/cite\] |

Note the network of hydrogen bonds formed at the transition state
geometry (below) and the various [gauche stereo-electronic
alignments](http://www.ch.imperial.ac.uk/rzepa/blog/?p=12276){target="_blank"
rel="noopener"}\[cite\]10.6084/m9.figshare.1004026\[/cite\] which you
should really explore in the Jmol 3D model invoked by clicking below.

::: {#attachment_12444 .wp-caption .aligncenter style="width: 450px"}
![carbox-TS](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2014/04/carbox-TS.jpg){.aligncenter
.size-full .wp-image-12444 decoding="async"
aria-describedby="caption-attachment-12444"
onclick="jmolInitialize('../Jmol/','JmolAppletSigned.jar');jmolSetAppletColor('white');jmolApplet([450,450],'load wp-content/uploads/2014/04/carbox-1894.614105.log;vectors on;frame 12;vectors 40;vectors scale 8.0;color vectors green;vibration 6;animation mode loop;');"
width="440"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2014/04/carbox-TS.jpg 617w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2014/04/carbox-TS-300x120.jpg 300w"
sizes="(max-width: 617px) 100vw, 617px"}

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 + CO~2~ ***exo-energic*** by
    -7.3 kcal/mol. Thus the phosphates provide the overall thermodynamic
    driving force for the carbon fixation.

    ::: {#attachment_12448 .wp-caption .aligncenter style="width: 410px"}
    ![Click for
    3D](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2014/04/carbox-prod-cyclic.jpg){.size-full
    .wp-image-12448 decoding="async"
    aria-describedby="caption-attachment-12448"
    onclick="jmolInitialize('../Jmol/','JmolAppletSigned.jar');jmolSetAppletColor('white');jmolApplet([450,450],'load wp-content/uploads/2014/04/carbox-prod-chair-1894.680740.log;vectors on;frame 12;vectors 62;vectors scale 8.0;color vectors green;vibration 6;animation mode loop;');"
    width="400"
    srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2014/04/carbox-prod-cyclic.jpg 481w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2014/04/carbox-prod-cyclic-300x155.jpg 300w"
    sizes="(max-width: 481px) 100vw, 481px"}
    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 + CO~2~. 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.\[cite\]10.6084/m9.figshare.1004557\[/cite\] 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\[cite\]10.6084/m9.figshare.1004614\[/cite\] 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](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2014/04/carbox-prod1E.svg){.aligncenter
.size-full .wp-image-12464 decoding="async"
width="400"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2014/04/carbox-prod1E.svg)  
[![carbox-prod1G](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2014/04/carbox-prod1G.svg){.aligncenter
.size-full .wp-image-12463 decoding="async"
width="400"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2014/04/carbox-prod1G.svg)

**Postscript 1**. Yet another lower energy isomer of the product has
popped out\[cite\]10.6084/m9.figshare.1004778\[/cite\] 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](http://en.wikipedia.org/wiki/Light-independent_reactions){target="_blank"
rel="noopener"} 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.\[cite\]10.1039/C3SC53416B\[/cite\] 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\[cite\]10.1002/embr.201338302\[/cite\]. 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).

------------------------------------------------------------------------

#### Acknowledgments

This post has been cross-posted in PDF format at
[Authorea](https://doi.org/10.15200/winn.142795.56461){rel="noopener"
target="_blank"}.

::: {.wp_orcid_field}
[https://orcid.org/0000-0002-8635-8390](https://orcid.org/0000-0002-8635-8390){target="_blank"
rel="author"}
:::


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.

Messaggi di Rogue Scholar

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