Systems and photosystems: cellular limits of autotrophic productivity in cyanobacteria

Abstract

Recent advances in the modeling of microbial growth and metabolism have shown that growth rate critically depends upon the optimal allocation of finite proteomic resources among different cellular functions and that modeling growth rates becomes more realistic with the explicit accounting for the costs of macromolecular synthesis, most importantly, protein expression. The "proteomic constraint" is considered together with its application to understanding photosynthetic microbial growth. The central hypothesis is that physical limits of cellular space (and corresponding solvation capacity) in conjunction with cell surface-to-volume ratios represent the underlying constraints on the maximal rate of autotrophic microbial growth. The limitation of cellular space thus constrains the size the total complement of macromolecules, dissolved ions, and metabolites. To a first approximation, the upper limit in the cellular amount of the total proteome is bounded this space limit. This predicts that adaptation to osmotic stress will result in lower maximal growth rates due to decreased cellular concentrations of core metabolic proteins necessary for cell growth owing the accumulation of compatible osmolytes, as surmised previously. The finite capacity of membrane and cytoplasmic space also leads to the hypothesis that the species-specific differences in maximal growth rates likely reflect differences in the allocation of space to niche-specific proteins with the corresponding diminution of space devoted to other functions including proteins of core autotrophic metabolism, which drive cell reproduction. An optimization model for autotrophic microbial growth, the autotrophic replicator model, was developed based upon previous work investigating heterotrophic growth. The present model describes autotrophic growth in terms of the allocation protein resources among core functional groups including the photosynthetic electron transport chain, light-harvesting antennae, and the ribosome groups.

Keywords: cyanobacteria; growth rate; molecular crowding; optimization; photosynthesis; ribosomes.

Figure 1

Hypothetical cyanobacterial growth rate, μ, in response to substrate abundance falls into two regimes. Submaximal rates of growth occur when either the light intensity or nutrient availability is limited and growth rates increase in proportion to increases in the limiting commodity, as shown in the left portion of the hypothetical graph. When these are not limiting, the growth rate is the saturated, maximal rate, μ_max. This maximal rate is hypothetically limited by physical constraints such as packing all necessary molecular machinery, small molecules, and ions into the confined space (cytoplasmic and membrane) of the cell yet have small enough cell dimensions to allow sufficient nutrient exchange. Cells approach a maximal rate where internal factors, referred to as “intracellular crowding-limited” dominate. Figure adapted from O’Brien et al. (2013), but the “macromolecular expression (ME)-limited” or “proteome-limited” growth rate is here considered as limited intracellular crowding as discussed in the text.

Figure 2

Allocation of the proteome among different sectors as defined by the analysis of growth in the development of a phenomenological theory regarding its control (Scott et al., ; Scott and Hwa, 2011). Bacterial proteome consists of a fixed fraction, Q, whose proportion is constant and largely unaffected by the growth rate of the cells and may contain proteins for cell maintenance and ultrastructure. The remainder of the proteome minimally is partitioned into two additional fractions, R and P, which represent ribosome affiliated proteins and nutrient uptake and processing proteins, respectively. The R and the P fractions are observed to reciprocally change their proportions as a function of cell growth rate with the R fraction reaching its largest magnitude under fast growth conditions. This coincides with the observation that ribosomes are more abundant in faster growing cells compared to more slowly growing cells. This same theory was used to derive a Monod-like relationship of observed growth rate in relationship to nutrient availability as reflected by parameter κ_n, along with the translational capacity represented by the parameter κ_t.

Figure 3

A simplified autocatalytic replicator model of cyanobacterial growth. The model consists of a simple set of enzymes (blue outlined boxes), metabolites (yellow boxes), and membrane structural components (green objects) representing functional classes of molecules (e.g., enzyme “ribosome” represents are ribosomal proteins and those affiliated with protein synthesis). The proteins interrelated by a stoichiometric matrix and kinetic equations as described in the text. The model optimizes the allocation of finite proteomic resources among the different proteins (as protein synthesis, blue arrows) to achieve maximal growth rates. Consistent with the observation that microbial growth rates scale in direct proportion to the number of ribosomes, this “ribosome centric” model defines a set of “enzymes” (light blue boxes) that feed precursors to ribosomes and are, in turn, subject to synthesis by the ribosomes. Growth rates correspondingly correlate with flux rates for the generation of precursors for protein synthesis. The model was implemented in GAMS software environment (Andrei, 2013) using a previous model of heterotrophic growth (Molenaar et al., 2009).

Figure 4

Simulated effect of light intensity and inorganic substrate concentration on photoautotrophic growth rate and proteome allocation. Growth rates increase with light intensity, but rates saturate at different levels set by different levels of substrate concentration (Left). Allocation of the proteome to ribosomes (RIB) and photosynthetic electron transport (PSET) and light-harvesting complexes (LHC) as a function of growth rate (Right Panel) using data from the high light simulation shown in the left panel.

Figure 5

The effects of the expression of non-core, “niche-adaptive protein (NAP)” on growth and expression of core autotrophic functions. Upper graphs depict the simulated distribution of the proteome holding the NAPs at 5% (upper left) or 60% (upper right) of the total proteome and the corresponding growth rates (μ) at saturating levels of light (hν) and substrate (S). Lower graphs show that the relative proportions of the other sectors are similar despite the reduction of their net amount due to displacement by the NAPs. Sectors correspond to functional protein groups: inorganic substrate transport and assimilation proteins (STA), photosynthetic electron transport chain (PSET) that generates ATP and reductant, precursor biosynthesis enzymes (PRB). The main difference with the original models of Molenaar et al. (2009) is the energy source (light) and mechanism to generate the pool of precursors (prc) necessary for the synthesis of protein and lipid, which is now satisfied by the parallel action of the PSET and STA proteins. Collectively, these constitute the “core” proteins of the autotrophic replicator (see Figure 3).

Figure 6

Simulated diversion of energy precursors to excreted products alters the allocation of the proteome. Product diversion is defined as the excretion of 80% of the energy precursor for engineered product synthesis. Only ATP and reductant are considered in this highly simplified model, whereas a more realistic model will depend upon the chemical characteristics of the excreted product, most notably, the C/H ratio of its chemical formula. See Figure 5 and text for definitions of the functional protein groups of the model.