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Optimal coordination and reorganization of photosynthetic properties in C4 grasses

C3 and C4 are major functional types in terrestrial biosphere models, with photosynthesis traits as important input parameters. The evolution of C4 required reorganizations of Calvin-Benson-cycle and coordination of C4-cycle enzymes, resulting in divergences of physiological traits between C3 and C4. In addition, photosynthesis further optimized after the evolution of C4 causing diversification within C4 lineages due to different evolutionary histories. We combined optimality modeling, physiological measurements and phylogenetic analysis to examine how various aspects of C4 photosynthetic machinery were reorganized and coordinated within C4 lineages and as compared to closely-related C3 in grasses. Optimality models and measurements indicated a higher maximal electron transport to maximal Rubisco carboxylation ratio (Jmax/Vcmax) in C4 than C3, consistent with the optimal prediction to maximize photosynthesis. The coordination between Calvin-Benson and C4 cycles (Vpmax/Vcmax), however, is in line with the optimal modeling results under 200 ppm, as opposed to current CO2. Such inconsistencies can be explained by a slowly declining assimilation rate beyond optimal Vpmax/Vcmax. Although rapid coordination occurred early in C4 evolution, C4 is still under optimizing processes and photosynthetic measures have continued to increase across time. Lastly, better understandings of Jmax/Vcmax, Vpmax/Vcmax and fluorescence-based-electron-transport proffer enhanced approaches to parameterize terrestrial biosphere models.

Introduction 57 C3 and C4 are major photosynthesis pathways and important functional types identified in the 58 cycle does have additional ATP costs for which C3 plants do not remunerate (Hatch, 1987). 84 In sum, the assembly of C4 photosynthesis broke the balance between CO2 carboxylation and 85 electron transport of the CB cycle, which existed in C3 ancestors: C4 photosynthesis elevates 86 the efficiency of CO2 carboxylation at the expense of using more energy from electron 87 transport (Sage, 2001(Sage, , 2004(Sage, , 2016 would also represent evolutionary trends between photosynthetic parameters and 97 evolutionary time/ages. In the current study, we examine how various aspects of C4 98 photosynthetic machinery-nitrogen allocation between Rubisco carboxylation and electron 99 transport, and CB and C4 cycle-were reorganized and coordinated within C4 lineage, as 100 well as compared to closely-related C3 species, and whether the coordination of C4 101 machineries are on a walk toward or have already reached the optimal state. Vpmax/Vcmax might also vary in C4. Sage and McKown (2006) proposed that C4 may show less 119 plasticity and acclimation in phenotypical traits in response to global climate change, due to 120 their complex anatomical and biochemical features, e.g., the structural and physiological 121 integration of the mesophyll-bundle sheath complex. Combining theoretical predictions and 122 empirical examination of how Jmax/Vcmax and Vpmax/Vcmax vary with environment could 123 elucidate the acclimation capability C4 and further show if acclimation occurs in an optimal 124 manner. Such an understanding of C4 responses to changing climate would reduce the 125 8 in which NP represents the nitrogen in pigment proteins, NE represents the nitrogen for the 183 is the concentration of chlorophyll per unit area (μmol Chl m -2 ), 0.079 is in mmol N s 195 (μmol) -1 , and 0.0331 is in mmol N (μmol Chl) -1 , ≈ 0.3 (mmol N s (μ mol) -1 . Vcr is the 196 specific activity of Rubisco (the maximum rate of RuBP carboxylation per unit Rubisco; ≈ 197 20.5 μmol CO2 (g Rubisco) -1 s -1 ) and 6.25 is grams RuBisCO per gram nitrogen in RuBisCO. 198 Vpr is the specific activity of PEPc, that is, the maximum rate of RuBP carboxylation per unit 199 When the light intensity varies, the following function is used to adjust the electron transport 210 rate (Ögren & Evans, 1993): 211 (8) 212 Also, all the photosynthetic parameters are temperature-sensitive (Zhou et al., 2018). 213 In the optimal modeling processes, we set Norg-NO as constant of 129 mmol N m -2 (which 214 yield a Vcmax= 39 μmol m -2 s -1 , Jmax= 195 μmol m -2 s -1 and Vpmax= 78 μmol m -2 s -1 , if assuming 215 Jmax/Vcmax=5 and Vpmax/Vcmax=2). Using these models, we modeled the assimilation rates with 216 different Jmax/Vcmax from 1 to 8 of 0.01 interval and different Vpmax/Vcmax from 0.5 to 5 of 0.01 217 to find the globally optimal assimilation rate with respect to both Jmax/Vcmax and Vpmax/Vcmax. 218 The corresponding Jmax/Vcmax or Jmax/Vcmax under the highest assimilation rates represent the 219 optimal ratios. Then, we also model the locally optimal Jmax/Vcmax and Vpmax/Vcmax when 220 constraining the corresponding Vpmax/Vcmax and Jmax/Vcmax with the average measured values 221 respectively. 222 Using the model described above, we were able to model the optimal Jmax/Vcmax and 223 Vpmax/Vcmax under different environmental gradients: CO2 of 200, 300, 400, 500 and 600 ppm; 224 VPD and yS of (0 MPa, 0.15) (0.625, -0.5), (1.25, -1), (1.875, -1.5), and (2.5, -2); light 225 intensity of 2000, 1600, 1200, 800 and 400 μmolm -2 s -1 ; temperature of 15, 20, 25, 30 and 35 226 analysis for stoichiometry of PEPC by varying the 1/(6.72´Vpr ´ ) term in Eq. 5 from 50% 230 to 800%. For the C3 pathway, all the modeling process are similar with the C4 and a same 231 value of Norg-NO is used, except that a simplified version of equation (7)   anhydrase and Vcmax with a very low criteria of 5 Pa or below. We let the data points with Ci 254 ranging from 5 to 60 Pa CO2 to be freely determined by which of the four potential 255 limitation states to minimize the estimation error. Using this method, we avoided the 256 potential bias of including optimal perspectives to the estimation method which could occur 257 when directly assigning the cross points co-limited by Vcmax, Vpmax and Jmax.

Chlorophyll measurements and leaf nitrogen 271
Chlorophyll were measured using the spectrophotometer method (Porra et al., 1989). We cut 272 the fresh leaves of species into pieces of 0.5 mm long (total leaf area was measured) and 273 submerged the fragments into DMF. After all the Chlorophyll was extracted and the leave 274 turned white, the supernatant was used to measure the absorption under 663.8 nm and 646 275 nm. Total Chlorophyll concentrations were calculated using the equation of Porra et al. 276 (1989). We measure leaf nitrogen contents for each sample using the CHNOS analyzer

Phylogenetic analysis 280
We fitted each of the photosynthetic parameters (Vcmax, Jmax, Jmax/Vcmax, Total Chl, flr-281 ETR/Jmax, flr-ETR, Vpmax and Vpmax/Vcmax) to six different evolutionary models falling into 282 Brownian Motion model and Ornstein-Uhlenbeck Model using the R package of 283 "mvMORPH" (Table S1). The small-sample-size corrected version of Akaike information 284 criterion (AICc, the lower AICc, the better fit) and Akaike weights (AICw, the higher AICw, 285 the better fit) were used as criteria to figure out the best-fitted model. We used likelihood-286 ratio test (LRT) method to test whether one model variant performs significantly better than 287 others and to determine whether there are significant differences between C3 and C4 species. 288 We also extract the evolutionary ages for each C4 species from the dated phylogeny (Spriggs 289 et al., 2014). We regressed the above photosynthetic traits with evolutionary ages to detect 290 potential evolutionary trends. 291 292

In vivo and in vitro Jmax/Vcmax follow the global optima in C4, but Vpmax/Vcmax does not. 294
In vivo and in vitro Jmax/Vcmax are consistent with the optimal predictions under current CO2 295 conditions, but Vpmax/Vcmax fell in to the optimal range under CO2 of 200 ppm. The global 296 optima modelling results indicated maximal photosynthesis at the Jmax/Vcmax of 5-6.2, which 297 is relatively constant across different CO2 concentrations, while the optimal range for 298 Vpmax/Vcmax for C4 species is 1.4-2.2 at CO2 of 200 ppm, but decreases to 1-1.6 when CO2 299 reaches 400 and 600 ppm (Fig. 1b, d, f). The averaged in vitro and in vivo Jmax/Vcmax are 300 consistent with the global optimal predictions under CO2 of 400 ppm (Fig. 1, Fig. 2a, 301 Supplementary Material I), as well as the locally optimal predictions controlling Vpmax/Vcmax 302 at the in vivo and in vitro level (Fig. 2). However, the averages of in vitro and in vivo measurement results are consistent with the optimal condition at CO2 of 200 ppm ( Fig. 1, 3, 305 4, S2, Supplementary Material I). The 3D images and the contour plots also illustrate that 306 when Jmax/Vcmax is at the optimal range, beyond the optimal range of Vpmax/Vcmax, the 307 assimilation surface is quite flat: photosynthesis declines, but quite slowly; however, when 308 Vpmax/Vcmax drops outside of the optimal ranges, there are sharp decreases of photosynthesis 309

C4 species have higher Jmax/Vcmax and lower flr-ETR/Jmax than C3 species. 314
Phylogenetic analysis shows the Jmax/Vcmax follows the Ornstein-Uhlenbeck model with a 315 higher stable state for C4 species and a lower stable state for C3 (Table 1; Fig. 1a). Such an 316 empirical relationship is consistent with the optimal modeling predictions for C3 and C4. We 317 looked further into how such a higher Jmax/Vcmax in C4 species is reached by comparing 318 individual empirical parameters. C4 species has significantly higher stable states of Jmax, but 319 significantly lower stable states of Vcmax and nitrogen content than their closely-related C3 320 (Table 1). In order to examine the potential effects of decreasing Vcmax on assimilation rate, 321 we held the Jmax as constant and changed the Vcmax from 100% to 50% of the original C3 322 parameter values in the C3 and C4 models. A decrease in Vcmax will significantly decrease the 323 assimilation rates of C3 species from 10 o C to 35 o C under different CO2 concentrations, while 324 decreasing Vcmax has little effects on the assimilation rates of C4 species (Fig. 5). 325

326
The flr-ETR/ Jmax was significantly higher in C3 species than that in their closely related C4 327 species, with the stable states of 1.08 and 0.64 for C3 and C4 respectively (Table 1). has a higher total electron transport rate, Jmax (Table 1). 330

331
The positive evolutionary trends of photosynthetic parameters 332 Plotting the photosynthetic parameters with evolutionary ages, extracted from a dated 333 phylogeny for the multiple lineages, allows us to look for further evolutionary trends in C4 334 and their closely related C3 species. Regressions of evolutionary age versus photosynthetic 335 traits provide signals for long-term directional trends in photosynthetic machinery following 336 the establishment of C4 photosynthesis (Fig. 6). Amax, Jmax, total chlorophyll, Vcmax and Vpmax 337 showed significant positive correlations with evolutionary age in C4 species, but not C3 338 species, while nitrogen, Jmax/Vcmax, Vpmax/Vcmax and flr-ETR/Jmax did not show significant 339 correlation with the evolutionary age. 340 341

Optimal variation of Jmax/Vcmax and Vpmax/Vcmax with environmental conditions. 342
To understand how the Jmax/Vcmax and Vpmax/Vcmax varied theoretically in response to 343 environmental changes (Fig. 7a, b, Fig. S3a, b), we calculated their optimal value for varying 344 CO2 concentrations, water limitations, temperatures, and light intensities. The optimal 345 Jmax/Vcmax is predicted to increase linearly in C3 and, but increase a little bit and maintain 346 relatively constant in C4 species with increasing CO2 concentration (Fig. 7a). The optimal 347 and increases similarly with decreasing light intensity and increasing temperatures (Fig. 7). 349 The changes of Jmax/Vcmax with water limitation, light intensity, and temperature are non-350 linear, with the rate-of-change increasing greatly after a threshold (water limitation of yS=-1, 351 VPD=1.25, the light intensity of 800 µmol m -2 s -1 and temperature of 30 o C). The optimal 352 Vpmax/Vcmax decreases along with the increase of the CO2 concentration, especially when CO2 increases from 200 ppm to 300 ppm, but the change is little when CO2 is above 400 ppm 354 ( Fig. 7c, S3c). However, Vpmax/Vcmax is relatively constant with the varying of water limitation 355 conditions and light intensity (Fig. 7c,d, S3c,d). Vpmax/Vcmax decreases with the rise in 356 temperature from 15 to 35 o C (Fig. 7d, S3d). 357 358

Sensitivity analysis for optimal Jmax/Vcmax and Vpmax/Vcmax 359
Since there is a great variation of total nitrogen content in plants and there is uncertainty in 360 the stoichiometry of PEPC, we performed sensitivity analysis and found the optimal 361 modeling of Jmax/Vcmax and Vpmax/Vcmax are robust. For C3 photosynthesis, optimal Jmax/Vcmax 362 increases slightly with decreasing total nitrogen (7.7% increase of Jmax/Vcmax with 50% 363 reduction in total nitrogen), while for C4, optimal Jmax/Vcmax decreases with total nitrogen 364 (16.2% increase of Jmax/Vcmax with 50% reduction in total nitrogen) (Fig. S4a). The optimal 365 Vpmax/Vcmax increases somewhat with decreasing total nitrogen (8.7% increase of Vpmax/Vcmax 366 with 50% reduction in total nitrogen) (Fig. S4a). The optimal Jmax/Vcmax is relatively constant 367 with the change of stoichiometry of PEPC from 50% to 200%, but increases as the 368 stoichiometry increases from 200% to 800% (Fig. S3b). The optimal Vpmax/Vcmax is relatively 369 robust with the change of stoichiometry of PEPC.     Light intensity Μmol m 2 s 1