Division rates of a marine cyanobacterium from cell size distributions and a matrix population model
The marine cyanobacterium Synechococcus is an important primary producer, fixing up to 20% of the carbon in coastal systems. We need to understand the factors that determine its abundance over time. Key to this are estimates of cell division rate. This metric allows separation of the affect of cell division on changes in abundance and also provides information about the physiological state of the population. The challenge is to obtain rate estimates at the appropriate temporal scale (daily for Synechococcus) for extended periods of time.
We use a matrix population model that represents changes in cell volume to estimate a daily population division rate. Cell size (volume) distributions of Synechococcus exhibit distinct diel patterns; distributions shift towards larger cell sizes during photosynthesis and to smaller sizes during cell division. Our model attempts to reproduce daily volume dynamics with construction of 24 hourly transition matrices. Cells are grouped into distinct size classes and possible transitions include growth into the next size class, division into a smaller size class, or stasis. Cell growth depends on incident radiation and cell division on size class. As such, the model is time-variant. Parameters for these growth and division functions, as well as a starting hour cell size distribution, are estimated from observed cell size distributions with a maximum likelihood approach. From the fitted model, we estimate a population division rate by keeping track of all model-produced cells specified from the division function. The model does not include cell loss. Instead, we calculate a loss rate from the change in cell abundance and our estimated division rate.
We apply this model to a time series of cell size distributions measured with a custom, automated, flow cytometer (‘FlowCytobot’, FCB, Olson et al. 2003). This instrument has enabled hourly observations of the Synechococcus population at the Martha’s Vineyard Coastal Observatory since 2003.
The model allows us to estimate a daily population division rate from in situ observations of cell size distributions. Application of this model to observations from FCB yields an 11-year time series of daily division rates. We use this time series to investigate seasonal environmental controls (e.g., light, temperature) on cell division. We further investigate how the balance between cell division and loss produce the annual pattern of Synechococcus cell abundance. The model structure presented here is applicable to other phytoplankton species, provided that appropriate temporal observations of taxon-specific cell volume are available.