## 9 Rubisco Kinetics  
From a bioenergetic point of view, the RuBP conversion into two 3 PGA molecules catalyzed by Rubisco is spontaneous as the Gibbs free energy change (\(\Delta\)G\({}^{\circ}\) as calculated by [PERSON] et al. [48] at about \(-\)30 kcal mol\({}^{-1}\)) allows the reaction to proceed without energy supply in the form of ATP, NAD(P)H or other reducing agents. Concerning the enzyme kinetics, experimental estimation of the activation free-energy barrier for the rate-limiting transition state is, as cited above, around 16 kcal/mol (at 298 K, for Rubisco from spinach). The corresponding maximal catalytic rate observed in vitro (\(K_{\text{cat,C}}\)) is 3-4 s\({}^{-1}\). However, the potential energy profile of the overall reaction appears quite complex (see Figure 15), therefore, over the last two decades, considerable effort has been made towards a complete description of the elementary steps and associated microscopic rate constants to assist in understanding enzyme kinetics. Very recently [PERSON] and [PERSON] [49] have described a detailed multistep mechanism for the Rubisco carboxylation and oxygenation reactions including microscopic rate constants associated with each elementary step (see Section S6, Figure S5). On the basis of the proposed mechanism the authors were able to derive equations that relate all measurable kinetic parameters such as S\({}_{\text{C/O}}\), \(k_{\text{cat,C}}\), K\({}_{\text{C}}\), \(k_{\text{cat,O}}\), and K\({}_{\text{O}}\) (defined in Table S3)  
Figure 15: Blue and orange traits depict the potential energy (kcal/mol) profiles along the Rubisco carboxylase reaction as calculated by the B3 LYP/6-31G\({}^{\ast}\) and the corresponding corrected B3 LYP-gCP-D3 functional. Relevant reaction steps along the reaction coordinate are: (1.) RuBP enolization; (2.) carboxylation of the 2,3-enol(ate) intermediate; (3.) hydration of the 2-carboxy-3-keto-arabinitol-1,5-bisphosphate intermediate followed by protonation (4. ); (5.) C2-C3 bond cleavage and (6.) protonation of C2. Black traits depict the potential energy (kcal/mol) profile indicated by experimental estimations of free-energy barriers. Figure 15 from ref. [43], used by permission of American Chemical Society (copyright © 2020)). to the microscopic rate constants. Moreover, the authors have calculated the expected values of dissociation rate constants for CO2 and O2 bound to the RuBP-enzyme complex. The kinetic model described by [PERSON] and [PERSON] has been used by [PERSON] et al., to draw important information about the variability of the S\({}_{\text{C/O}}\) selectivity factor among a large series of Rubisco enzymes (see later). Before describing recent advances achieved by the Grady and Milo Research Groups, it is worthwhile citing previous studies developed by [PERSON] [50] and [PERSON] [30], which started evidencing specific correlations between measurable kinetic parameters with the aim of finding specific adaptations during Rubisco evolution. In an interesting study, [PERSON] al. [50] have analyzed the \(k_{\text{cat,C}}\) value of diverse Rubisco enzymes (see Figure 16a), evidencing an inverse relationship between S\({}_{\text{C/O}}\) and \(k_{\text{cat,C}}\). This observation could be rationalized by proposing the qualitative energy profile along the reaction coordinate shown in Figure 16b.