Regulation of chain length in two diatoms as a growth-fragmentation process

Chain formation in diatoms is relevant because of several aspects of their adaptation to the ecosystem. However, the tools to quantify the regulation of their assemblage and infer specific mechanisms in a laboratory setting are scarce. To address this problem, we define an approach based on a statistical physics model of chain growth and separation in combination with experimental evaluation of chain-length distributions. Applying this combined analysis to data from Chaetoceros decipiens and Phaeodactylum tricornutum, we find that cells of the first species control chain separation, likely through a cell-to-cell communication process, while the second species only modulates the separation rate. These results promote quantitative methods for characterizing chain formation in several chain-forming species and in diatoms in particular.

Figure 1

Workflow of the experiments. (a) Cells were cultivated and kept in exponential growth phase until inoculum. After inoculum into fresh culture medium, cultures were poured into flasks. In the time bar, white boxes identify illuminated periods (12 h), and black boxes identify dark periods (12 h) for experiments with C. decipiens; P. tricornutum was kept in a 24-h light photoperiod. (b) Daily microscopic inspection led to the growth curves and the chain-length histograms for each replicate for each time point, which were analyzed with the model.

Figure 2

Biased chain separation in C. decipiens. (a) Typical chain-length distributions show that the most common chain is a few cells long, compatible with the presence of a bias suppressing the separation of shorter chains. The three plots correspond to times 1 d apart from each other. Blue dots are experimental data (error bars estimated as Poissonian counting errors are smaller than the points), dashed lines are the initial condition at $t=0$, and red solid lines are the predictions of the model with bias. (b) Suppression of short-chain formation is manifested by the preference for a cutoff length $k_0=2$ in the biased model. Data and simulations are compared through the Kolmogorov-Smirnov distances (vertical axis) between the chain-length distributions at $t=2$ d. Curves corresponding to different cutoffs $k_0=0,1,2,3$ (numbers near the lines) realize the optimum overlap with the data at different values of the separation rate per junction $\beta$ (horizontal axis, in separations per day).

Figure 3

Formation of setae in C. decipiens shows suppression of single-cell subchains and enrichment of odd lengths greater than 1. Subchains are defined as the consecutive cells lying between two terminal setae (or chain boundaries). The proportion of subchains ($y$ axis) with a given number of cells ($x$ axis) is shown both for empirical data (blue circles; the dashed line is a guide to the eye) and for a simulated null model (red) where terminal setae are uncorrelated and randomly distributed along the empirical chains. For empirical data (1113 subchains in total), error bars estimated as Poissonian counting errors are approximately the size of the data points (slightly larger for the data at subchain length 3). For simulations, symbols and boxes denote mean values and standard deviations, respectively, while whiskers are 1st and 99th percentiles. Inset: a C. decipiens cell chain showing one separation point. Arrows indicate terminal setae on two adjacent intercalary separating cells, i.e., the junctions where the chain will separate into two subchains.

Figure 4

Null growth-fragmentation behavior in P. tricornutum mutants. (a) The mean chain length ($y$ axis) grows linearly with the growth rate ($x$ axis), as predicted by the model, Eq. (2). Circles are colored according to their mean chain length. Small circles are those lying below the threshold $〈k〉=2$, which are discarded from the analysis in (b). The dashed line is the model prediction, Eq. (2), with $\beta =0.27$ fitted from the data. (b) Cumulative distributions of chain lengths for P. tricornutum mutants (data at $t=2$ d for the 11 experiments with $〈k〉\le 2$) and for C. decipiens (data at $t=1,2,3$ d), rescaled by mean length (separately for each condition), show remarkable collapse for the two different species on two distinct behaviors. (c) The rescaled chain-length histograms (bin width of 0.4) of P. tricornutum computed with data pooled from all available conditions [this combination is possible thanks to the agreement shown in panel (a)] follow the exponential form predicted by the model (dashed line).

Figure 5

(a) Wild-type P. tricornutum forms short chains, whose lengths are compatible with the null growth-fragmentation model (dashed line); (b) however, the growth rate has undetectable influence on the average length. Data in (a) are rescaled and binned as in Fig. 4. Small gray points in (b) are the same data as in Fig. 4; the larger points are the WT data, shaded according to their mean chain length (on the $y$ axis), as in Fig. 4.