# Finding the not-light-limited state in Synechocystis PCC 6803

### Overview

- Settings of each experiment
- Data Overview
- Growth rate calculation
- Growth rate and light: model fitting

In this report I combine and analyse the data from the turbidostat experiments of 28-02-2015 and 09-09-2015. In these experiments I tried to determine at what light intensities *Synechocystis* PCC 6803's growth is light limited.

To determine this the light was increased from 20 *micro Einstein per square metre per second* to 50-60 *micro Einstein per square metre per second* in increments of 5 *micro Einstein per square metre per second*. Using the turbidostat the growth rate was monitored at each light intensity.

In this report the Optical Density measurements along with data on pump activity is used to determine the growth rate during the experiment and to correlate this to the applied light intensity.

### Settings of each experiment

#### Experiment 28-02-2015

`breach size`

= 1 (number of measurements above threshold before activating pump)`threshold`

=*0.408 (OD 720)*`dispense volume`

= 4.8 mL`pump flow rate`

= X.X mL/min`pump pause`

= 170 seconds (length of time waiting before removing excess liquid)`od repeats`

= 3 (number of readings averaged by MC)`od samples`

= 1 (number of OD samples collected by software)`od aggregate`

= None (how samples are aggregated into single values)`gas pause`

= 6 seconds`intensity solver`

= Simple (how to correct for light contamination)

#### Experiment 09-09-2015

`breach size`

= 2 (number of measurements above threshold before activating pump)`threshold`

=*0.35 (OD 720)*`dispense volume`

= 4.8 mL`pump flow rate`

= 7.7 mL/min`pump pause`

= 180 seconds (length of time waiting before removing excess liquid)`od repeats`

= 3 (number of readings averaged by MC)`od samples`

= 5 (number of OD samples collected by software)`od aggregate`

= minimum (how samples are aggregated into single values)`gas pause`

= 6 seconds`intensity solver`

= None (how to correct for light contamination)

# Data Overview

Optical Densities during both experiments (5 hour averages, area of 1 standard deviation from mean is colored red ).

Time plot of the light intensity during the experiment

## Cleaning the data

To improve the results I remove some data: channel 1 of 2015-02-28 is removed since I cannot explain why that channel ran at OD 0.6 instead of 0.408, so I decided this result is not thrustworthy.

From all experiments the inoculation period is removed by removing measurements from the first decision period. A decision is the activation of the media pump by the software and a decision cycle includes all measurements after that decision until the next decision. In mathematical terms, the timepoints of measurements `t(m)`

that correspond to decision `D`

are collected after the timepoint that previous decision `t(D-1)`

was made and include the moment that decision `t(D)`

was made:

`t(D-1) < t(m) <= t(D)`

To improve growth estimation outlying Optical Densities measurements are removed per following rules:

- For
`2015-02-28`

: 0.37 < OD < 0.42 - For
`2015-09-09`

: 0.33 < OD < 0.36

For the `2015-02-28`

all measurements after 295 hours are removed.

Optical Densities during both experiments (5 hour averages, area of 1 standard deviation from mean is colored red ).

# Growth rate calculation

To calculate growth rates, different methods are available. I will use some of the available methods as I trust these the most (and I have a reliable pipeline for them).

Reliable methods (used in this document):

`slopes`

: fits linear models to each decision cycle.`dxdt`

: calculates change in OD over time

Unreliable methods (not used in this document):

`dilution`

: calculates dilution rate from dispense volume and estimated vessel volume.

This method was considered unreliable because of the huge variation in estimating the volume vessel which caused the dilution rate to vary a lot. It could be improved by using a constant for the vessel volume, but this value was not available (for the measurements from `28-02-2015`

).

## Calculting growth rate with *slopes* method

Method works by fitting one linear model each dilution cycle describing the following equation. The estimated coefficient (`a`

), standard error of the estimation, the p-value of the estimate (`a != 0`

) and the R squared of the fit, the number of points included in the decision cycle and the number of points used to fit the model are recorded. Each fit is attributed to the time point of the decision (`t(D)`

) that ends to cycle.

`log(OD) = a * t + c`

### Filter statistics

Plots below show the data and colour based on a selection metric. Goal is to determine selection criteria that reduce the spread of growth rates at each light regime. The median is indicated as the *true value*. Data is shown per experiment (columns) and channel (rows). Points with r squared below 0.5 are already removed.

Colour by **r squared**

Coloured by fit_size

Coloured by Slope Std. Error.

Coloured by standard deviation in OD values used to fit the data.

### Cleaned data with filters

Remove points with R squared < 0.85 and fit size < 6.

Coloured by r squared (**Scale changed!**)

## Calculting growth rate with *dxdt* method

The *dxdt* method calculates the growth rate using the formula given below.

`mu = (dx) / (dt) = (log(ODmax) - log(ODmin)) / (tmax - tmin)`

At least three growth rates are calculated from the data using combinations of points. The median and standard deviation of the collected slopes is returned. The following combinations are calculated (if enough data is available).

- t(min) vs t(max) (
`fit_size > 3`

) - t(min+1) vs t(max) (
`fit_size > 4`

) - t(min) vs t(max-1) (
`fit_size > 4`

) - t(min+1) vs t(max-1) (
`fit_size > 5`

) - t(min+2) vs t(max) (
`fit_size > 5`

) - t(min) vs t(max-2) (
`fit_size > 5`

) - t(min+2) vs t(max-1) (
`fit_size > 6`

) - t(min+1) vs t(max-2) (
`fit_size > 6`

) - t(min+2) vs t(max-2) (
`fit_size > 7`

)

### Filter statistics

Plots below show the data and colour based on a selection metric. Goal is to determine selection criteria that reduce the spread of growth rates at each light regime. The median is indicated as the *true value*. Data is shown per experiment (columns) and channel (rows). Points with standard deviation above 0.75 are already removed.

Colour by **std. dev of slopes**

Coloured by **fit size**.

Colour by **std. dev of OD**

### Cleaned data with filters

Remove points with Std. dev. of obtained sloped > 0.08 and a fit size < 8.

# Growth rate and light: model fitting

In this part I use the obtained growth rates to create models that relate growth rate to light intensity.

## Data overview

To see how all the data fits together and what fitted models would look like.

**Without** data aggregation

2nd degree polynomial fitted to each channel/experiment combination.

### Data aggregated per **method, dataset, channel**

2nd degree polynomial fitted to each combination of method, experiment and channel

### Data aggregated per **method, experiment**

2nd degree polynomial fitted to each combination of method and experiment

### Data aggregated per **method**

2nd degree polynomial fitted to each method

## Fitting models to subsets of the data (Partial models)

Here I fit 1st degree linear models to subsets of the data. I create subsets that span different amounts of light regimes, by extending the span from the lowest 4 light regimes to all light regimes.

### Fitting to **unaggregated** data

The best partial models (highest **r squared**) of each combination of experiment and method

### Fitting to data aggregated **per method, experiment, channel**

**NOTE:** I create partial models per combination of method and experiment (and NOT per channel) and I show data points aggregated per method, experiment and channel

The best partial models (highest **r squared**) of each combination of method and experiment.

### Fitting to data aggregated **per method, experiment**

The best partial models (highest **r squared**) of each combination of method and experiment

### Fitting to data aggregated **per method**

The best partial models (highest **r squared**) of each method

## Determine non-light-limited state

### Using max growth rate

### Using deviation from best fit

## Compare results with photonfluxostat data

## Converting to mol photons per gDW per hour

Using the conversion values obtained from the photonfluxostat paper, to convert to *mol photons per gDW per hour*.

## Coefficient analysis

The following significance labels are used:

`ns`

: P > 0.05`*`

: P <= 0.05`**`

: P <= 0.01`***`

: P <= 0.001`****`

: P <= 0.0001