Pro_IBM

An individual-based model simulating the cell cycle of the marine cyanobacterium Prochlorococcus.

Introduction

Prochlorococcus is the smallest but mightiest of the phytoplankton, responsible for about 20% of global primary production. Their daily cycle of growth and division can be used to calculate division rates of field populations, and this individual-based model (IBM) simulates Prochlorococcus diel patterns and estimates cell cycle parameters including division rate (Hynes et al, 2015a; Hynes et al, 2015b).

Flowchart of model events. From Hynes et al (2015a), Fig. 1.

The IBM is fully described in Hynes et al (2015a). The flowchart shows the processes and decisions in the model. All cells grow and respire. Cells that are large anough and have been randomly selected can begin DNA replication, entering S phase. Cells that have completed DNA replication and have endured the duration of G2 can divide. All cells can be randomly selected to be grazed, and the grazing rate is chosen to balance population growth so the model does not become numerically overwhelmed.

The model is run for 30 days. During the last 3 days, grazing is turned off for analysis.

Functions

The model is written in MATLAB (devloped in R2012b, still runs in R2018b). Download the files in the m_files directory and either add them to your MATLAB search path OR put them in your working directory. Variables and usage for each function can be found by calling help function_name at the prompt.

• Pro_IBM runs the model with user-defined input parameters and calls the functions below.

• initialize_pro initializes the structure that stores cell data and the starting population.

• makepro_vectorized takes cells ready to divide and turns them into two daughter cells.

• killpro_vectorized randomly grazes cells at a fixed proportion.

• light_sine simulates light as a truncated sine wave given the time of day and the day length.

• exp_growth increases the size of cells according to current size, cellular growth rates, and light levels.

• calc_resp_bin calculates cellular respiration rate according to cellular growth rate and daylength under LD conditions with binary light.

• calc_resp_sine calculates cellular respiration rate according to cellular growth rate and daylength under LD conditions with sinusoidal light.

• calc_resp_cont calculates cellular respiration rate under continuous light conditions.

Variables

Cell cycle parameters and other variables are defined by the user:

[data_store, av_cell_size, av_cell_dna, tm, mu_pop, cells, S, G2, index] = Pro_IBM(mu_cell, T_S, T_G2, daylength, light_regime, Cg, Ps_width, Ps_zero)

Input/output variables and reasonable ranges for Prochlorococcus are summarized in the table below:

Input:

Name	Description	Values
mu_cell	Maximum cellular growth rate	1 - 3.5 d^(-1)
T_S	Duration of S phase	0.1 - 0.33 d
T_G2	Duration G2 phase	0.05 - 0.30 d
daylength	Length of daylight, sunrise to sunset	10 - 14 h
light_regime	String denoting whether light is binary, sinusoidal, or constant	'binary', 'sine', or 'constant'
Cg	Circadian gate	0.1 - 0.35 d
Ps_width	Parameter that controls the "width" of the probability function for cells entering S phase based on their size	85 fg C
Ps_zero	Parameter that states where the probability for cells entering S is zero	45

Output:

Name	Description	Values
data_store	Structure containing cellular information
av_cell_size	Average cell size	24 - 85 fg C per cell
av_cell_dna	Average DNA per cell	1 - 2 genome copies per cell
tm	Time vector	0 - 31 d
mu_pop	Population growth rate	0.35 - 0.85 d^(-1)
cells	Number of cells
S	Fraction of cells in S phase	0 - 1
G2	Fraction of cells in G2 phase	0 - 1
index	Indices for the last three days

References

• Hynes A. M., B. J. Blythe, and B. J. Binder (2015a). "An individual-based model for the analysis of Prochlorococcus diel cycle behavior," Ecol. Model. 301:1 - 15, doi: 10.1016/j.ecolmodel.2015.01.011.

• Hynes A. M., K. L. Rhodes, and B. J. Binder (2015b). "Assessing cell cycle-based methods of measuring Prochlorococcus division rates using an individual-based model," Limnol. Oceanogr. Methods 13:640 - 650, doi: 10.1002/lom3.10054.