Use of Agent-Based Modeling To Explore the Mechanisms of Intracellular Phosphorus Heterogeneity in Cultured Phytoplankton

Abstract

There can be significant intraspecific individual-level heterogeneity in the intracellular P of phytoplankton, which can affect the population-level growth rate. Several mechanisms can create this heterogeneity, including phenotypic variability in various physiological functions (e.g., nutrient uptake rate). Here, we use modeling to explore the contribution of various mechanisms to the heterogeneity in phytoplankton grown in a laboratory culture. An agent-based model simulates individual cells and their intracellular P. Heterogeneity is introduced by randomizing parameters (e.g., maximum uptake rate) of daughter cells at division. The model was calibrated to observations of the P quota of individual cells of the centric diatom Thalassiosira pseudonana, which were obtained using synchrotron X-ray fluorescence (SXRF). A number of simulations, with individual mechanisms of heterogeneity turned off, then were performed. Comparison of the coefficient of variation (CV) of these and the baseline simulation (i.e., all mechanisms turned on) provides an estimate of the relative contribution of these mechanisms. The results show that the mechanism with the largest contribution to variability is the parameter characterizing the maximum intracellular P, which, when removed, results in a CV of 0.21 compared to a CV of 0.37 with all mechanisms turned on. This suggests that nutrient/element storage capabilities/mechanisms are important determinants of intrapopulation heterogeneity. Phytoplankton play an important role in the ecology and biogeochemistry of freshwater and marine systems. Thus, understanding their composition and physiology (e.g., carbon fixation rate) is important. The elemental composition of phytoplankton was originally considered to be relatively uniform (1). However, subsequent research has shown that it can vary between species (2) or clones (3) and within a species under different conditions (4, 5). The composition can also vary within a species under the same conditions. Two measurements of intracellular P are commonly made: cell-based P (mol P/cell), which we refer to as P quota, and biomass-normalized P (mol P/mol C), which we call internal P content. While P quota is generally easier to measure on a cellspecific basis, it is the internal P content that is important for many physiological processes. Recent observations of intracellular P in individual cells have shown significant intraspecific heterogeneity in laboratory and field populations, with coefficients of variations (CV) ranging from 0.08 to 2.11 for P quota and 0.10 to 2.10 for internal P content (Table 1).Heterogeneity in intracellular P may have important consequences because it can result in heterogeneity in physiology (e.g., photosynthesis rate), which can have significant effects on community ecology (6). Specifically, for phytoplankton the specific growth rate (biomass accumulation) is generally considered to depend on the cell quota of the limiting nutrient according to Droop's function (4). Because the function is nonlinear, heterogenei...

Turbulent mixing and phytoplankton life history: a Lagrangian versus Eulerian model comparison

“…The sensitivity analysis revealed that the magnitude of the error is very sensitive to the maximum nitrate storage quota Q max , which plays a key role in controlling the range of internal nitrate that an individual cell can carry and therefore modulates the variability between individuals. This result is consistent with Fredrick et al (2013), who explored the relative contribution of several biological parameters to intra-population variability in terms of the internal phosphorus content of the planktonic diatom Thalassiosira pseudonana. They found that the variability of Q max was the main factor influencing intra-population heterogeneity, in agreement with our results.…”

“…For instance, Bucci et al (2012) studied variability in terms of phosphate cell quota in enhanced biological phosphorus removal and showed that the Eulerian model can produce approximately the same results as the Lagrangian version only if the value of the growth rate is reduced by 55%. In a similar experiment, Fredrick et al (2013) showed that the Eulerian formulation overestimates biomass by > 40%. It is noticeable that in these studies, differences among individuals emerged from phenotypical variability introduced explicitly in the Lagrangian model by randomizing cell parameters during cell division.…”

“…For example, classical Michaelis-Menten kinetics was gradually being superceded by Droop kinetics (Droop 1974), in which growth is decoupled from nutrient uptake, meaning that growth depends on an internal nutrient cell quota rather than on external nutrient concentrations. Nevertheless, ad ding these types of equations in the classical Eulerian paradigm remains fundamentally inaccurate (Woods & Onken 1982, Schuler 2005, Fredrick et al 2013. As Bolnick et al (2011) illustrated, the reason behind this inaccuracy is rooted in the so-called Jensen inequality (Jensen 1906), which states that 'averaging non-linear functions before integrating them is mathematically different than averaging the results of a non-linear integration'.…”

Silicon content of individual cells of Synechococcus from the North Atlantic Ocean

“…In other words, most quota distributions have a notable positive skew even after logarithmic transformation. The phenomenon of high-quota cells driving population heterogeneity has been shown previously in a diatom growth model for P utilization when modeled under conditions of non-limiting nutrient availability (Fredrick et al, 2013). Such results are consistent with Si's putatively non-essential nature in Synechococcus and also the general availability (non-limiting nature) of S in the marine environment.…”

High performance computing for three-dimensional agent-based molecular models

“…Today, the range of agent-based model applications is quite broad. For example, these models have been used to represent the Ras-MAPK [17] and NF-kB [38] intracellular signalling pathways, Escherichia coli cytoplasm dynamics [30], bacterial phenotypic switching [46], epithelial host-pathogen interactions [45], cancer systems biology [29], development of restenosis in blood vessels [12], autophagy dynamics and sub-mitochondrial heterogeneity [8], intracellular phosphorus heterogeneity in cultured phytoplankton [16], oxygen metabolism in aerobic-anaerobic respiration [5], and the design of cellulase systems [3].…”