Rubisco proton production can drive the elevation of CO2 within condensates and carboxysomes

Significance Rubisco is arguably the most abundant protein on Earth, and its catalytic action is responsible for the bulk of organic carbon in the biosphere. Its function has been the focus of study for many decades, but recent discoveries highlight that in a broad array of organisms, it undergoes liquid–liquid phase separation to form membraneless organelles, known as pyrenoids and carboxysomes, that enhance CO2 acquisition. We assess the benefit of these condensate compartments to Rubisco function using a mathematical model. Our model shows that proton production via Rubisco reactions, and those carried by protonated reaction species, can enable the elevation of condensate CO2 to enhance carboxylation. Application of this theory provides insights into pyrenoid and carboxysome evolution.


Which Rubisco catalytic parameters correlate with evolutionary fitness?
Applying the same evolutionary fitness analysis to the extant and extinct Rubiscos in our analysis (Table 2), we were able to estimate the Rubisco catalytic properties that would make the most competitive advances through condensation and encapsulation prior to evolution of mechanisms enabling HCO3accumulation. We determined correlation statistics for the average net carboxylation turnover rates (1/s) under different atmospheres, and each catalytic parameter (Table 2), for the most likely evolutionary steps determined from the initial analysis (Fig. 7). These analyses were modelled over a range of HCO3in the model at an [RuBP] of 5 mM, except for 'low light' simulations where we set RuBP to 50 µM. We draw the reader's attention to SI Appendix, SI datasets S1 and S2 and corresponding correlation plots in Fig. S16 to Fig. S21, where we present the data for the analysis presented in this section.
Competitive fitness analyses at the high CO2 range (1 -10 mM cytoplasmic HCO3 -; Fig. 8) indicated that the contemporary carboxysomal Rubisco from Synechococcus (characterized by low SC/O, high kcat C , high KMCO2, and high KMRuBP, Table 2) performed best in all proposed evolutionary stages, regardless of atmospheric O2, with the exception of free enzyme comparisons where it was outcompeted by the tobacco enzyme. At elevated O2 and low CO2, a condensate with an external CA (modelled by modification of the unstirred layer CA function) appeared to show similar dependencies on reduced kcat C and improved SC/O as the free enzyme. However, for condensates with internal CAs ('Condensate + int CA' and 'Condensate + int/ext CA'), net carboxylation correlated with increased SC/O and kcat C /KMCO2 (r = 0.83 -0.99, p < 0.05).
Like the free enzyme, there was no correlation between net carboxylation rates and any Rubisco catalytic parameter for any condensate type at high CO2, regardless of the O2 concentration. This implies no selective pressure to evolve the Rubisco catalytic parameters analyzed under a high CO2 environment for either free Rubisco or Rubisco condensates.
Comparative analysis of different Rubisco enzymes in large carboxysomes showed there was a strong correlation between kcat C /KMCO2 and net carboxylation rates at low CO2 (r = 0.89, p < 0.05), regardless of O2 concentration. At high CO2 concentrations (the likely cellular environment for contemporary carboxysomes in functional CCMs), kcat C was the only Rubisco catalytic parameter to correlate with net carboxylation rate in the model (r = 0.98, p < 0.05). For small carboxysomes, where a higher surface area/volume ratio means greater diffusional flux of substrates and products (Fig. S22), both kcat C /KMCO2 and SC/O correlated with net carboxylation rates at low CO2 (r = 0.88 -0.98, p < 0.05), suggesting that carboxysome size may correlate with catalytic efficiency and specificity, possibly due to lower CO2 availability in smaller carboxysomes (Fig. S22). Unlike their larger counterparts, small carboxysomes appear unconstrained by any catalytic parameter when CO2 is high.

Rubisco function in the model
For the purpose of modelling the function of Rubisco enzymes in a condensate, we examine a compartment filled with Rubisco active sites as an isolated entity within a larger compartment supplied with the theoretical substrates and products of the enzyme (Fig. 1). Rubisco utilizes ribulose-1,5bisphosphate (RuBP) as its 5-carbon substrate which can either be carboxylated with CO2 to produce two molecules of the 3-carbon product 3-phosphoglycerate (PGA), or oxygenated with O2 to produce one molecule of PGA and one molecule of 2-phosphoglycolate (2PG). Notably, Rubisco carboxylation is competitively inhibited by O2 while the oxygenation reaction is competitively inhibited by CO2 (1). 4 In this study we include the net production of two protons with each reaction, as outlined below and in greater detail in Fig. S1. 2

Reaction species and protons in the model
In contrast with existing models which address carboxysome function within complex cellular scenarios within CCMs with active HCO3accumulation (4-7), here we assume no HCO3accumulation and modify reaction output by enabling two moles of H + to be produced as by-products of both the carboxylase and oxygenase reactions along with PGA (above). Proton balance within the system is maintained by setting the external pH to a constant value, while protons are allowed to interact with other chemical species by reversible reactions in each model compartment (Fig. 1). Specifically, we allow H + take part in the protonation and deprotonation of RuBP and PGA species within the model, driven by their pKa values (6.7 and 6.5 respectively), yielding variable quantities of RuBP 4-:RuBP 3and PGA 3-:PGA 2depending on the pH of each compartment, and driven by their respective rate constants as follows: The second order association constants used for RuBP 4and PGA 3were 5.01187 × 10 9 and 3.15 × 10 9 m 3 /(mol.s) respectively (corresponding to the pKa of each substrate), and the first order dissociation constants were 1 × 10 6 1/s for both RuBP 3and PGA 2-.
We also include the interconversion of HCO3and CO2 as a reaction which utilizes a proton ( Fig.   1), and we enable control of the rate of this interconversion by carbonic anhydrase (CA) using rate constants for the forward (k1; CO2 to HCO3 -) and backward (k2; HCO3to CO2) reactions.
The first order rate constants k1 (0.05/s) and k2 (100/s) allow attainment of HCO3 -:CO2 ratio of 100:1, which approximates the proportion, assuming the uncatalyzed interconversion of each species at chemical equilibrium when pH is 8.0. Notably this ratio is typically much higher in cells displaying functional CCMs where a disequilibrium favoring HCO3is maintained (8). Here we deliberately model a primordial condition with no CCM in these experiments (see below).
An additional multiplying 'CA factor' is used when modelling the presence of CA activity in specific model compartments, where a CA factor of 1 represents the absence of CA activity, assuming the attainment of chemical equilibrium at the uncatalyzed rate. Where CA is present in the model we use a value 1 × 10 5 for this parameter (Table 1), as used in the model of Reinhold, Kosloff and Kaplan (7).
Compartment pH is calculated from total H + concentration at any given scenario in the model, driven primarily by setting the 'external' compartment to pH 8.0 with an H + concentration of 10 nM.
This value approximates the pH of a typical cyanobacterial cellular environment which has been shown to vary between pH 7.3 in the dark and pH 8.3 in the light (5). This range represents a ten-fold variation in total proton concentration in the external compartment (from 5 -50 nM). The lower pH would seem to favor carboxylation as it would lead to a lower Rubisco compartment pH and greater CO2 production.
However, it is unlikely to lead to significant changes in Rubisco carboxylation rates inside the compartment, as it equates to a small decrease in compartment proton permeability where internal proton concentrations are maintained and maximum carboxylation rates are observed (Fig. 2). The higher pH value of 8.3 represents a halving of the proton concentration from 10 to 5 nM compared with our standard modelling scenarios, however proton flux will still be predominantly maintained by other reaction species (Fig. 5), and is therefore unlikely to make a substantial difference to model outputs. 6 We nonetheless make comparisons between scenarios with consistent pH for the purposes of demonstrating the role of protons in the system.

RuBP concentrations used in modelling
RuBP is typically found within cyanobacterial and microalgal cells within the range of 0 -50 mM, depending on external Ci supply and light-limited photosynthetic rate (9,10). Regardless of the catalytic requirements, most Rubisco enzymes experience RuBP concentrations well above their KMRuBP (which is typically in the µM range; Table 2), both in the modelling presented here and under most growth conditions, except for low light (11). For most modelling scenarios we adopt 5 mM RuBP as a saturating supply concentration.
The application of diminished permeability to RuBP access in both condensate and carboxysome modelling, we find that this results in an increase in the apparent KMRuBP (Fig. S6), an observation made for comparison of free Rubisco and carboxysomes isolated from Cyanobium (12). Since the apparent KMRuBP differs between each compartment type and size we model, this has the potential to confound compartment comparisons at a specific [RuBP]. To account for this, we arbitrarily chose the RuBP response of a modelled condensate at saturating HCO3 -(20 mM) and determined the relative carboxylation rate at 50 µM RuBP. This provided ≈63% of the maximum carboxylation rate (Fig. S6).
We then determined the concentration of RuBP which provided an equivalent relative rate for the free enzyme (35 µM), and both small and large carboxysomes (87 µM and 1.3 mM, respectively).

CO2 and HCO3concentrations in the 'external' compartment and carbonic anhydrase (CA) activity
In a cellular context, the role of the relatively membrane-impermeable and dominant inorganic carbon (Ci) species HCO3is of importance as a companion species to the Rubisco substrate (and more membrane-permeable) CO2. We therefore include both HCO3and CO2 as the Ci species within the model, and we set CO2:HCO3in this compartment to approximate chemical equilibrium at pH 8.0. (13) While other Ci species (H2CO3 and CO3 2− ) are important to consider in cellular modelling contexts (5), for simplicity here we consider HCO3as the major Ci source at ≈pH 8.0, and CO2 as the Rubisco substrate.
In considering the relative concentrations of HCO3and CO2 within the model, we simulate an environment which is not representative of a modern CO2 concentrating mechanism (14) where a disequilibrium toward HCO3is favored (13). Instead we assume the external compartment as a bulk volume at pH 8.0 and with a constant HCO3 -:CO2 ratio, unlikely to be affected by the fluxes of a small Rubisco compartment or fluctuations resulting from CA activity, and O2 in equilibrium with the prevailing atmospheric gas composition. Current hypotheses predict that active Ci uptake and intracellular HCO3accumulation likely evolved subsequent to the evolution of carboxysomes in cyanobacteria, for example (15). Evolutions leading to an elevation of intracellular HCO3would lead to the need to eliminate cytosolic CA (16) to maintain this pool of HCO3 -. By simulating a primordial system without Ci uptake, or overaccumulation of HCO3 -, we are able to address both; 1) Rubisco compartment behavior alone as a function of Ci supply, and 2) Rubisco compartment responses in predicted evolutionary contexts where we can manipulate the location and speed of CA enzymes, and compartment permeabilities to substrates.
We maintain the external compartment HCO3 -:CO2 ratio at 100:1 in most modelling scenarios, assuming negligible changes to this bulk compartment in response to relatively small fluxes from a single Rubisco condensate. Thus, examination of the effects of external CA activity on Rubisco compartment function are addressed by modifying CA activity in the unstirred layer (Table 1).

Model reaction compartments and their permeabilities
The model utilizes three separate reaction compartments termed 'external', 'unstirred' and 'condensate' (Fig. 1). These are analogous, respectively, to a fixed cell cytoplasm, an unstirred boundary layer around the condensate, and the condensate (or Rubisco compartment) itself . We envision the condensate as either a liquid-liquid phase separated protein droplet such a pyrenoid (17), or a carboxysome which is formed via similar structural rules (18) but encased in a protein layer with increased diffusional resistance to substrate passage. Rubisco carboxylation and oxygenation are confined to the 'condensate' compartment while the reversible reactions involving the protonation of RuBP, PGA and HCO3 -(above) are allowed to occur in all three compartments (Fig. 1).
As highlighted above, we assume that the external compartment, akin to a fixed cell cytoplasm, is not dependent on the function of Ci transporters to elevate [HCO3 -]. Instead we view the external compartment simply as a means to supply substrate to the Rubisco compartment and that it simulates a primordial cellular state prior to CCM evolution. The external compartment volume is set at 1 m 3 to enable sufficient substrate supply. Within the context of the analysis carried out here, this volume has little relevance but can be modified to consider alternative substrate supply scenarios.
In the absence of accurately known permeabilities of each substrate through unstirred cellular boundaries and either phase-separated protein matrices or complex protein shell layers, we apply simple assumptions in order to demonstrate the concepts presented. While molecular dynamic modelling suggests that carboxysome shell channel proteins may be selective permeable to substrates (19,20), actual permeabilities still remain elusive. We therefore assume equal permeabilities for all substrates except for protons (see below) at each diffusional boundary in the model, recognizing that differences may exist in reality, but remain unknown.
The permeability coefficient we have chosen for substrates (other than protons) crossing the unstirred boundary layer is consistent with those calculated for diffusion of small solutes associated with spherical bodies of various sizes (21). For example, a sphere of ≈10 -6 m radius (the size we assume for a Rubisco condensate here) is calculated to have an unstirred layer permeability around 10 -4 m/s (21). We also assume that a value of 10 -4 m/s approximates the upper bound of small molecule permeabilities where the viscosity of the crowded cytosol or stroma of the organism in which the aggregates are formed can lead to a slowing of diffusion of up to four times that in water (22). For the same reason, we also consider the protein aggregated Rubisco condensate as having a similar resistance to small molecule flux and assign permeabilities of 10 -4 m/s for all substrates except for protons (below).
For carboxysomes, we assume the shell to have permeability some 100-fold lower than the unstirred layer and Rubisco condensate. Mangan, Flamholz, Hood, Milo and Savage (5) provide a detailed analysis of likely carboxysome shell permeabilities to relevant reaction species and conclude that significant hindrance to passage across the shell is likely. A relatively wide range of permeabilities are consistent with function in their model and ours (e.g. Fig. 2), without application of selectivity to particular species. We use a permeability of 10 -6 m/s for all substrates, except for protons, at the carboxysome shell, which brings each species within the functional range described previously (5), acknowledging an absence of real data to support the specific permeability of each species. Nonetheless, the prime outcome here is that, within carboxysome modelled scenarios, the shell resistance dominates the calculation of diffusion processes into and out of the carboxysome.
We treat the permeability of the unstirred layer and condensate/carboxysome to protons differently in the model. Proton movement is rapid in aqueous environments due to their ability to jump between hydrogen bonds via a water-based 'proton wires' mechanism (23). Based on this we have assumed a 100-fold greater permeability for protons than other solutes. We therefore apply a proton permeability of 10 -2 m/s at the unstirred layer boundary and the condensate, and 10 -4 m/s at the carboxysome. This implies some barrier to proton diffusion, however, and is perhaps counter to evidence that proton movement across the shell rapid and unimpeded (24). We highlight within the manuscript that there are a number of issues with this conclusion, and can model the same outcomes of the experiment by Menon, Heinhorst, Shively and Cannon (24) to show that they are not inconsistent with relatively low proton permeability (Fig. S3). In viral capsid systems, which are structurally analogous to carboxysomes, the compartment shell layer forms a significant barrier to proton diffusion (25,26), and it is assumed that specific proton pores may be needed to admit protons at significant rates to the inside of the virus. It is both feasible and consistent with existing evidence that complex and specific restriction to proton passage across the shell exists. 9 We apply a simple multiplication function for the thickness of the unstirred layer based on the radius of the Rubisco compartment (Table 1). This generates an unstirred layer of thickness 5 × 10 -7 m for condensates of 1 × 10 -6 m radius, and is consistent with vesicles of a similar size range (27).
However, the thickness of the unstirred layer is of little consequence in the model. Rather, it is the permeability coefficient which determines the rate limiting nature of the unstirred layer compartment.
The compartment acts only as a volume which can come to steady state equilibrium with the external and condensate volumes either side.

Rubisco compartment size
When considering appropriate sizes for the modelling of Rubisco compartments, we initially considered a pyrenoid as a canonical Rubisco condensate. These condensates are found in a wide variety of microalgae and hornwort species (28)(29)(30), and range widely in size and structure. In some hornworts, for example, pyrenoids can be highly dissected to form many disc-shaped 'subunits' as small as ≈25 × 200 nm (31), while the more regular spheroid pyrenoid of Chlamydomonas reinhardtii has been observed at 2 µm in diameter (32). For most scenarios, Rubisco condensates were assumed as spheres with radius 1 × 10 -6 m, approximating that of a pyrenoid from C. reinhardtii.
We recognize that carboxysome sizes also vary considerably across genera, and are often quite large in β-cyanobacteria (up to ≈6 × 10 -7 m in diameter; 33, 34) and as small as ≈9 × 10 -8 m wide in some α-cyanobacteria (35). Indeed, β-carboxysome size appears highly variable within the same species and is likely dependent upon growth conditions and stoichiometry of protein components (33,34). For the purpose of considering a possible evolutionary adaptation of a condensate into a carboxysome, and for simple comparisons between compartment types in the model, we consider both condensates and carboxysomes as spheres with the same radius (1 × 10 -6 m).
The size of a condensate or carboxysome will affect both its surface area and internal volume, therefore the diffusional flux, both across its boundary and within it. Compartment size will therefore have a supply-rate effect on Rubisco substrates, and therefore affect Rubisco function in the model.
Smaller carboxysomes in the model have less dramatic responses than larger structures with respect to elevation of internal [CO2], due to an increase in internal pH as carboxysome size decreases (Fig. S22).
These responses are also driven by substrate concentrations in the external medium, however, with greater decreases in compartment pH (and therefore increases in CO2) apparent at limited substrate concentrations. (Fig. S4, Fig. S22).
Large carboxysomes are capable of greater internal [CO2], leading to carboxylation turnover rates which are approximately 4% higher than the smallest of carboxysomes, and a concomitant decrease in internal [RuBP] (Fig. S22). A similar result is apparent for condensates, although the ability to generate very high internal [CO2] is diminished and the variation in carboxylation turnover is only 2% across the entire size range considered. This also means that the analysis of evolutionary progressions from condensates to carboxysomes may be marginally affected by the size of a carboxysome compared with its progenitor condensate, although notably the carboxylation turnover of even the smallest carboxysome is faster than that of the largest condensate (Fig. S22).

Rubisco active site concentration
Rubisco active site concentrations in pyrenoids have been measured at ≈4.8 mM (17), while estimates for carboxysomes are as high as ≈15 mM for tightly packed spherical Rubisco L8S8 holoenzymes of 11 nm diameter in a crystalline array in both C3 chloroplast stromae (36) and carboxysomes (9), and values around 10 mM calculated from stoichiometries and estimated packing in α-carboxysomes (9,37). In the absence of more definite data which presents a consolidated value for both pyrenoids and carboxysomes, we therefore set a value of 10 mM active sites as an upper bound of likely concentrations in our simulated Rubisco condensates and carboxysomes, which would allow for movement of holoenzymes within the compartment, and both small molecule and activation chaperone passage. We maintain this value between compartments types in the model for simple comparisons.
Given the relative increase in Rubisco carboxylation turnover in carboxysome scenarios in our model, we would expect carboxysomes specifically to show an upper limit in Rubisco active site concentrations since excessive enzyme amounts will lead to decrease in net carboxylation due to consumption of either RuBP or CO2, depending on which is limiting. This too may be dependent on carboxysome size as this will affect diffusional supply rates (above).    Experimental data were obtained for Rubisco turnover of the free Cyanobium Rubisco enzyme ('Free Rubisco experimental data'pink circles) and the same enzyme in intact carboxysomes ('Intact carboxysomes experimental data'purple circles) over a range of RuBP concentrationsdata from a previous report (see Supplementary materials in reference 12). Typical free enzyme and carboxysome comparisons give rise to an increase in the apparent KMRuBP and kcat C for intact carboxysomes compared with the naked enzyme in our hands. These shifts in Rubisco catalytic parameters observed in the experimental data are also apparent in the model, suggesting that catalytic parameters determined for the free enzyme are maintained within a carboxysome. Model output was generated using the kinetic properties of the free Cyanobium Rubisco enzyme ( Table 2) with an initial [HCO3 -] of 20 mM and pH 8.0 (as used in the experimental regime in 12), and the conditions for either the free enzyme or a carboxysome as outlined in Table 1. Carbonic anhydrase (CA) enzyme was absent from free Rubisco modelling, as was the case in experiments. For carboxysomes, CA was confined to the Rubisco compartment for modelling. Carboxysome size in the model was set to a radius of 5 × 10 -8 m, to represent the size of carboxysomes from Cyanobium (12). Solid pink and purple lines are the model output for the free enzyme and carboxysomes respectively, using an HCO3 -: CO2 ratio of 50:1 in the model. Permeability to protons (m/s)

Fig. S3 Time course of internal carboxysome pH response to changes in external pH
Modelled equilibration of carboxysome internal pH upon exposure to relatively acidic or basic external environments. This experiment attempts to replicate that of Menon, Heinhorst, Shively and Cannon (24) in which purified carboxysomes of the proteobacterium Halothiobacillus neapolitanus were first equilibrated overnight in buffer at pH 7.5, then exposed to external buffer conditions of pH 7.0 or 8.0 in the absence of substrates (RuBP or HCO3 -). In their experiments both broken and intact carboxysomes achieved stable pH values (as measured by the response of a carboxysomal pH-sensitive GFP-tagged Rubisco) within 20 milliseconds, implying free proton movement across the carboxysome shell. Here we simulate this experiment, modelling a 100 nm diameter carboxysome supplied with no substrates (eliminating internal proton production by Rubisco) and an initial internal pH of 7.5 (31.6 nM H + ). We m/s and greater. In the modelling experiments presented here we use a proton permeability of 10 -4 m/s for the carboxysome and assume a higher value of 10 -2 m/s for Rubisco condensates (see SI Appendix, SI Methods).

Fig. S4. Condensates and carboxysomes display low pH and elevated CO2 at low substrate concentrations
Condensate (top) and carboxysome (bottom) relative CO2 concentrations (blue shaded surface) and internal compartment pH (yellow shaded surface) as a function of both external HCO3and RuBP concentrations in the model. Compartment CO2 is presented as the ratio of CO2 inside the compartment to that outside (calculated as external HCO3concentration/100, see Methods). To place both CO2 and pH on the same z-axis, in the top 3D-surface plot pH is the scale value +4 and for the lower plot pH is the scale value divided by 5.

Fig. S7. Maximum Rubisco carboxylation turnover rate as a function of net proton production
Maximum Rubisco turnover rates calculated for free Rubisco, a Rubisco condensate and carboxysomes as a function of net proton production via the carboxylation reaction using the described model. Rates are calculated for saturating substrate conditions (5 mM RuBP, 20 mM HCO3 -) with 0, 1, 2, or 3 protons produced as products of the carboxylation reaction. In each case carbonic anhydrase (CA) activity is confined only to the Rubisco compartment. Conditions describing the free enzyme, condensate or carboxysome are indicated in Table 1. Correct stoichiometry produces two protons as products of the carboxylation reaction. Note a net increase in maximum turnover rates in the condensate and carboxysome over the free enzyme when one or more protons are produced. In the absence of proton production, carboxysomal Rubisco function is limited by reduced CO2 production via CA, dependent on proton diffusion into the compartment from the external volume. Maximum turnover rate of the tobacco Rubisco used in this modelling (3.4 1/s) is indicated by the black dashed line. Maximum turnover rate achieved for the condensate scenario at when 3 protons are produced (3.18 1/s) is indicated by the blue dashed line. Proton number was manufactured in the model by modifying the Rubisco carboxylation reaction stoichiometry to produce 0, 1, 2, or 3 protons. Data presented are for the tobacco Rubisco with parameters listed in Table 2 using typical modelling parameters as set out in Table 1

Fig. S8. Protons derived from the Rubisco oxygenation reaction support carboxylation in a carboxysome
Protons resulting from the oxygenation of RuBP within the model contribute to an improvement in carboxylation turnover (top panels) in a carboxysome (right panels) but less so in a condensate (left panels), especially at low HCO3supply. This improvement is diminished at higher HCO3concentrations as oxygenase is suppressed by increasing CO2 supply. Protons arising from the oxygenation reaction result in additional carboxysome CO2 production (bottom panels) via the internalized carbonic anhydrase (CA). Here we have run the model using the tobacco Rubisco (Table 2) with either zero or two protons arising from the oxygenation reaction in either a condensate or carboxysome using the parameters in Table 1. The COPASI (39) model was run in parameter scan mode, achieving steadystate values over the range of HCO3concentrations indicated.   (Table 1) allow for the production of 2 protons (pink line) from the Rubisco carboxylation reaction. This results in a net generation of free protons within the carboxysome, leading to enhanced dehydration of HCO3by carbonic anhydrase, production of CO2 and higher rates of carboxylation by Rubisco. While CO2 efflux from the carboxysome helps maintain moderate internal pH (Fig. 4), proton buffering by RuBP and PGA, and relative CA rate also contribute. Buffer capacity of RuBP and PGA is facilitated through protonation and deprotonation of functional groups with pKa values of 6.7 and 6.5 respectively (Fig. S1, Table S3). Manipulating these values within the model to pKa's of 5 (dashed blue line; kr1prot and kp1prot set to 1 × 10 8 ) and 8 (solid blue line; kr1prot and kp1prot set to 1 × 10 11 ) for both molecules reveals that their buffering capacity is a major contributor to pH stability. While our typical model scenarios have carboxysomal CA activity at 10 5 -fold the background rate of conversion, modifying this to a lower rate (500-fold; dot-dashed orange line) contributes to lower internal free proton concentrations at low external HCO3 -, yet still enables high carboxylation rates at saturating substrate concentrations (Fig. S11). This is due to the relative rates of proton production by the carboxylation and consumption by CA at low external HCO3 -. The COPASI (39) model was run in parameter scan mode, achieving steady-state values over the indicated range of HCO3concentrations at 5 mM RuBP. Data presented are for the tobacco Rubisco (Table 2).   Condensate + ext CA

Fig. S12 High external HCO3 -CO2 ratios enhance Rubisco compartment function
Variation in the ratio of HCO3 -:CO2 in the external compartment (here analogous to a fixed cellular cytoplasm) results in changes in relative Rubisco compartment CO2 (left panels, plotted over a range of cellular [HCO3 -]) and carboxylation turnover rates (right panels, plotted on a log scale over a range of cellular [CO2]). In the presence of either an internal carbonic anhydrase (CA; top panels -Condensate + int CA) or an external CA (bottom panels -Condensate + ext CAmodelled in the unstirred layer [ Table 1]) associated with a Rubisco condensate, elevation of the relative cytoplasmic ratio of HCO3 -:CO2 leads to both enhanced relative CO2 within the condensate and higher Rubisco turnover rates relative to the cellular [CO2]. This is because Rubisco condensation, in the presence of an internal or external CA, can lead to enhanced conversion of HCO3to CO2 in the Rubisco compartment. A decrease in the ratio of HCO3 -:CO2 in the cytoplasm (e.g. HCO3 -:CO2 = 10) diminishes the supply of HCO3to the Rubisco compartment and less CO2 is therefore generated at the site of fixation. A cell with no CA, either in the cytoplasm or in the condensate (middle panels -Condensate -int/ext CA) cannot generate additional CO2 within the condensate, such that Rubisco turnover rates are entirely dependent on CO2 supply from the cytoplasm. This is the prime reason that condensation is unlikely to have evolved in the absence of a cellular CA (Fig. 6). Modelled scenarios in this report utilize a HCO3 -:CO2 ratio of 100 (pink lines). Values approaching a ratio of 10 (blue lines) may occur in the absence of cytoplasmic CA in combination with the preferential diffusion of CO2 across the cell membrane. Values approaching a ratio of 1000 (orange lines) may occur in the advent of active HCO3transport and subsequent loss of CA from the cytoplasm and/or movement to the condensate. Modelled here are Rubisco compartment CO2/external compartment CO2 ratios and Rubisco carboxylation turnover rates for a condensate using the parameters in Table 1. The 'external' compartment HCO3 -:CO2 ratio (colored lines) was varied for each scenario. The COPASI (39) model was run in parameter scan mode, achieving steady-state values over the indicated range of HCO3concentrations at 5 mM RuBP. CO2 in the external compartment (cellular CO2) was determined from the HCO3 -:CO2 ratio in each scenario at each [HCO3 -]. Data presented are for the tobacco Rubisco (Table 2).

Fig. S13. Carboxysome CA activity is dependent on Rubisco activity
Carbonic anhydrase flux rates are closely coupled to Rubisco activity through the provision of internal protons by the Rubisco reaction. This is demonstrated by the response of both CA and Rubisco to RuBP. Here the COPASI (39) model was run in parameter scan mode, achieving steady-state values over the indicated range of [RuBP] in the carboxysome at either sub-saturating (1 mM) or saturating (20 mM) HCO3 -. CA activity was confined to the carboxysome for this modelling. Data presented are for the tobacco Rubisco (Table 2). Net carboxylation rates for potential evolutionary intermediates were calculated as the Rubisco carboxylation turnover minus ½ oxygenation turnover (1/s) over a range of HCO3concentrations in the model, assuming the same photorespiratory cost in all systems. In order to determine relative fitness of one evolutionary intermediate over another at high or low CO2, net carboxylation rates were averaged for each intermediate over the range 0.01 -1 mM HCO3 -(for low CO2) and 1 -10 mM HCO3 -(for high CO2). The average net carboxylation rates for each intermediate at different CO2 ranges are then compared to assess relative fitness under those conditions. In this example, relative rates of the free tobacco enzyme, a tobacco Rubisco condensate with an external carbonic anhydrase (Condensate + ext CA), or the tobacco Rubisco condensate with an internal CA (Condensate + int CA), are compared.  carboxylation minus ½ oxygenation turnover, assuming the same photorespiratory cost to carboxylation each case. Presented here are net carboxylation turnover rates for the tobacco enzyme (Table 2), modelled using the parameters for each scenario as in Table 1. Note that the condensate scenario here performs better than the free enzyme at low HCO3supply within the model, while the large carboxysome (which outperforms both the free enzyme and condensate under saturating conditions; Fig. S7) performs poorly. Very small carboxysomes have an additional performance benefit. This result supports the notion that Rubisco condensates and small carboxysomes have a performance advantage under light-limited and low Ci conditions, whereas a large carboxysome system is unlikely to be successful. Smaller carboxysomes may have a net advantage over larger carboxysomes, driven by relatively lower RuBP diffusional limitations, but improved CO2 fixation rates compared with condensates. Model conditions assume carbonic anhydrase (CA) is present in only the Rubisco compartment.

Fig. S16. Correlation plotsfree Rubisco under simulated varied atmospheres
Correlation plots of average net carboxylation turnover rates (1/s) of different Rubisco enzymes and their catalytic parameters simulated as the free enzyme in the model. Here, the catalytic parameters of each enzyme have been normalized to the maximum value for that parameter across the enzymes analyzed (Table 2) for simplicity. Pearson correlations were calculated between average net carboxylation rates over the ranges of CO2 and O2 indicated (Fig. S14), and the value of each Rubisco catalytic parameter (SI Appendix, SI dataset S1

Fig. S17. Correlation plots -Rubisco condensate with an external CA under simulated varied atmospheres
Correlation plots of average net carboxylation turnover rates (1/s) of different Rubisco enzymes and their catalytic parameters simulated as a Rubisco condensate with an external CA in the model. Here, the catalytic parameters of each enzyme have been normalized to the maximum value for that parameter across the enzymes analyzed (Table 2) for simplicity. Pearson correlations were calculated between average net carboxylation rates over the ranges of CO2 and O2 indicated (Fig. S14), and the value of each Rubisco catalytic parameter (SI Appendix, SI dataset S1

Fig. S20. Correlation plots -Large contemporary carboxysome under simulated varied atmospheres
Correlation plots of average net carboxylation turnover rates (1/s) of different Rubisco enzymes and their catalytic parameters simulated as a contemporary carboxysome (encapsulated Rubisco with an internal CA, , radius 1 × 10 -6 m) in the model. Here, the catalytic parameters of each enzyme have been normalized to the maximum value for that parameter across the enzymes analyzed (Table 2) for simplicity. Pearson correlations were calculated between average net carboxylation rates over the ranges of CO2 and O2 indicated (Fig. S14), and the value of each Rubisco catalytic parameter (SI Appendix, SI dataset S1

Fig. S21 Correlation plots -Small contemporary carboxysome under simulated varied atmospheres
Correlation plots of average net carboxylation turnover rates (1/s) of different Rubisco enzymes and their catalytic parameters simulated as a small contemporary carboxysome (encapsulated Rubisco with an internal CA, radius 5 × 10 -8 m) in the model. Here, the catalytic parameters of each enzyme have been normalized to the maximum value for that parameter across the enzymes analyzed (Table 2) for simplicity. Pearson correlations were calculated between average net carboxylation rates over the ranges of CO2 and O2 indicated (Fig. S14)

Fig. S22 Model responses to condensate and carboxysome size
Rubisco carboxylation turnover rate (A) increases by ≈4% for a carboxysome (purple lines) and ≈2% for a condensate (blue lines) over a broad range of compartment sizes ranging from very small carboxysomes (~5 x 10 -8 m; left-most hatched region of plots) to large pyrenoids (~1 x 10 -6 m; rightmost hatched region of plots). Carboxysomes and pyrenoids exist in a wide size range with some overlap (cross-hatched region of plots). Assuming each compartment type as a sphere, the surface area/volume (dashed black line) decreases significantly with increasing size (B), leading to changes in relative diffusional flux of substrates to Rubisco. Under the conditions modelled here, the ratio of Rubisco compartment CO2 to external CO2 is roughly three times greater in large carboxysomes compared with small carboxysomes, while the differences are not as pronounced for variable condensate sizes (C). The high CO2 in large carboxysomes leads to a decrease in compartment [RuBP] due to greater consumption rates by Rubisco (D). Modelling conditions are at saturating HCO3 -(20 mM) and RuBP (5 mM), using the tobacco Rubisco ( Table 2). The free enzyme (pink lines), which is unaffected by size, is shown as a reference. Responses at each size, for each compartment type, is also dependent upon substrate concentration (Fig. S4).

Legend for Dataset S1
This dataset contains: 1) net carboxylation turnover numbers for various Rubisco enzymes (Table 2) over the range 0.01 -25 mM HCO3at 20% and 30% (v/v) O2 in the external compartment (analogous to a fixed cell cytoplasm) in the COPASI model; 2) a set of evolution matrices for each of the Rubisco enzymes where each is modelled as potential intermediate evolutionary states from the free enzyme to contemporary carboxysomes at high and low CO2 and O2; 3) summary matrices in which the catalytic parameters of each Rubisco enzyme are compared to enable correlations between relative enzyme fitness at different potential intermediate evolutionary states from the free enzyme to large contemporary carboxysomes (radius 1 × 10 -6 m) at high and low CO2 and O2.
For the net carboxylation turnover numbers, these values are the sum of Rubisco carboxylation turnover numbers minus ½ Rubisco oxygenase turnover at each HCO3concentration in the range analyzed. Net rates are presented for 20% and 30% (v/v) O2 atmospheres.
Evolution matrix data are calculated as % changes, between potential evolutionary states, in average net carboxylation rates over high or low CO2 ranges at either 20% or 30% (v/v) O2 (see Fig. 6). An additional set of evolution matrix data are supplied for the tobacco enzyme modelled at 50 µM RuBP in the model at 20% (v/v) O2 as described in Fig. S15.
Summary matrix data for specific evolutionary intermediates are comparisons of net carboxylation rates, at high and low CO2 and O2, for each Rubisco enzyme used in the model. These tables also contain Pearson statistics for correlations between average net carboxylation (under each CO2 range and O2 concentration), and the catalytic parameters of each Rubisco analyzed ( Table 2).

Legend for Dataset S2
This dataset contains: 1) net carboxylation turnover numbers for various Rubisco enzymes (Table 2) over the range 0.01 -25 mM HCO3at 20% and 30% (v/v) O2 in the external compartment (analogous to a fixed cell cytoplasm) in the COPASI model; 2) a set of evolution matrices for each of the Rubisco enzymes where each is modelled as potential intermediate evolutionary states from the free enzyme to contemporary carboxysomes at high and low CO2 and O2; 3) summary matrices in which the catalytic parameters of each Rubisco enzyme are compared to enable correlations between relative enzyme fitness at different potential intermediate evolutionary states from the free enzyme to small contemporary carboxysomes (radius 5 × 10 -8 m) at high and low CO2 and O2.
For the net carboxylation turnover numbers, these values are the sum of Rubisco carboxylation turnover numbers minus ½ Rubisco oxygenase turnover at each HCO3concentration in the range analyzed. Net rates are presented for 20% and 30% (v/v) O2 atmospheres.
Evolution matrix data are calculated as % changes, between potential evolutionary states, in average net carboxylation rates over high or low CO2 ranges at either 20% or 30% (v/v) O2 (see Fig. 6). An additional set of evolution matrix data are supplied for the tobacco enzyme modelled at 50 µM RuBP in the model at 20% (v/v) O2 as described in Fig. S15.
Summary matrix data for specific evolutionary intermediates are comparisons of net carboxylation rates, at high and low CO2 and O2, for each Rubisco enzyme used in the model. These tables also contain Pearson statistics for correlations between average net carboxylation (under each CO2 range and O2 concentration), and the catalytic parameters of each Rubisco analyzed ( Table 2).