{"id":12395,"date":"2014-04-20T17:04:53","date_gmt":"2014-04-20T16:04:53","guid":{"rendered":"http:\/\/www.ch.imperial.ac.uk\/rzepa\/blog\/?p=12395"},"modified":"2023-09-16T18:15:30","modified_gmt":"2023-09-16T17:15:30","slug":"ribulose-15-bisphosphate-carbon-dioxide-%e2%86%92-carbon-fixation","status":"publish","type":"post","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=12395","title":{"rendered":"Ribulose-1,5-bisphosphate + carbon dioxide \u2192 carbon fixation!"},"content":{"rendered":"
\n

Ribulose-1,5-bisphosphate<\/a> 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<\/em>, or RuBisCO<\/a>) 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\u2021<\/sup>.<\/p>\n

\"carbox\"<\/a>Firstly, I will hypothesize that since C3 needs to lose a hydrogen, the easiest way of doing so is to form the enol<\/a><\/strong> 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]<\/a><\/span>,[2]<\/a><\/span> This species can then react with CO2<\/sub> (potentially with an accompanying proton transfer) to give 3-keto-2-carboxyarabinitol 1,5-bisphosphate directly. The transition state at the \u03c9B97XD\/6-311G(d,p)\/SCRF=water level[3]<\/a><\/span> has an IRC (intrinsic reaction coordinate)[4]<\/a><\/span> that reveals the activation barrier is ~17 kcal\/mol with respect to the enol (19.5 in \u0394G298<\/sub>), with the overall reaction[5]<\/a><\/span> being exo-energic by -2.6 kcal\/mol with respect to the enol, but endo-energic<\/em><\/strong> 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<\/em> 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.
\n\"carbox\"<\/a>
\n\"carboxE\"<\/a>
\n\"carboxG\"<\/a>
\nFor 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.<\/em> 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).<\/p>\n

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:<\/p>\n\n\n\n\n\n\n\n\n
System<\/th>\n\u0394\u0394G<\/th>\nData DOI<\/th>\n<\/tr>\n
Ribulose-1,5-bisphosphate\u00a0as keto + CO2<\/sub><\/td>\n\u00a00.0 <\/td>\n[6]<\/a><\/span><\/td>\n<\/tr>\n
Ribulose-1,5-bisphosphate\u00a0as enol + CO2<\/sub><\/td>\n13.0 <\/td>\n[7]<\/a><\/span><\/td>\n<\/tr>\n
Transition state<\/td>\n34.8 <\/td>\n[8]<\/a><\/span><\/td>\n<\/tr>\n
Acyclic\u00a03-keto-2-carboxyarabinitol 1,5-bisphosphate<\/td>\n11.5 <\/td>\n[9]<\/a><\/span><\/td>\n<\/tr>\n
Cyclic\u00a03-keto-2-carboxyarabinitol 1,5-bisphosphate<\/td>\n-7.3 <\/td>\n[10]<\/a><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

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

\"carbox-TS\"

Click for 3D<\/p><\/div>\n

    \n
  1. Addition of the phosphate groups has little effect on the energetics of the keto\/enol<\/em> equilibrium,<\/li>\n
  2. or on the barrier to reaction with \u00a0carbon dioxide.<\/li>\n
  3. But, they DO<\/strong> provide a new low energy sink I have not seen described before for the reaction (below), which makes the overall process from\u00a0Ribulose-1,5-bisphosphate + CO2<\/sub> exo-energic<\/em><\/strong> by -7.3 kcal\/mol. Thus the phosphates provide the overall thermodynamic driving force for the carbon fixation.\n

    \"Click

    Click for 3D. Cyclic low-energy cyclic chair isomer of\u00a03-keto-2-carboxyarabinitol 1,5-bisphosphate<\/p><\/div><\/li>\n

  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,\u00a0via<\/em> 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\u00a0functions can be listed:\n