Best practices and other tips

Where are we so far?

Introduction: vignette("gc01_gcplyr")
Importing and reshaping data: vignette("gc02_import_reshape")
Incorporating experimental designs: vignette("gc03_incorporate_designs")
Pre-processing and plotting your data: vignette("gc04_preprocess_plot")
Processing your data: vignette("gc05_process")
Analyzing your data: vignette("gc06_analyze")
Dealing with noise: vignette("gc07_noise")
Best practices and other tips: vignette("gc08_conclusion")
Working with multiple plates: vignette("gc09_multiple_plates")
Using make_design to generate experimental designs: vignette("gc10_using_make_design")

So far, we’ve imported and transformed our measures, combined them with our design information, pre-processed, processed, plotted, and analyzed our data. The only things left are a few notes on best practices for running statistics, merging growth curve analyses with other data, and additional resources for analyzing growth curves.

If you haven’t already, load the necessary packages.

library(gcplyr)
#> ## 
#> ## gcplyr (Version 1.9.0, Build Date: 2024-03-11)
#> ## See http://github.com/mikeblazanin/gcplyr for additional documentation
#> ## Please cite software as:
#> ##   Blazanin, Michael. 2023. gcplyr: an R package for microbial growth
#> ##   curve data analysis. bioRxiv doi: 10.1101/2023.04.30.538883
#> ##

library(dplyr)
#> 
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#> 
#>     filter, lag
#> The following objects are masked from 'package:base':
#> 
#>     intersect, setdiff, setequal, union
library(ggplot2)

Statistical analyses of growth curves data

At this point, we’ve now summarized our growth curves data into some metrics. How can we best go about drawing statistical conclusions from these data?

When should we average replicates?

I want to emphasize something we did not do in our workflow: averaging different wells together before summarization. In my opinion, averaging should only occur after summarization, not before. Why? Even wells that have the same contents (i.e. are technical replicates) can still differ in their growth due to biological variation (e.g. stochastic growth dynamics). If we average our density values at the beginning, we may introduce bias, and we will not have the ability to visualize or assess the biological variation present in our data.

Let’s look at a simple example to demonstrate this point. I’m going to simulate bacterial growth using logistic growth, which starts after a finite ‘lag period’ where the bacteria don’t grow at all.

\[\begin{equation} dN/dt = \begin{cases} 0 & t < lag \\ r N\left(1-\frac{N}{k}\right) & t \ge lag \end{cases} \end{equation}\]

Where \(N\) is the population size, \(r\) is the rate of growth, \(k\) is the carrying capacity of the population, and \(lag\) is the lag time.

In the code below, I’ve simulated the growth of 96 different wells of bacteria. All the bacteria grow at exactly the same rate, except they differ in their lag time (how long they wait before starting to grow).

sim_dat_tdy <- make_example(vignette = 8, example = 1)

Now, let’s calculate the growth rate of each well and plot the growth:

sim_dat_tdy <- mutate(group_by(sim_dat_tdy, Well),
                      percap_deriv = calc_deriv(y = Measurements, x = time,
                                                percapita = TRUE, blank = 0))

# Plot the growth in our wells
ggplot(data = filter(sim_dat_tdy, Well != "averaged"), 
       aes(x = time, y = Measurements, group = Well)) +
  geom_line(alpha = 0.1) +
  geom_line(data = filter(sim_dat_tdy, Well == "averaged"), color = "red") +
  scale_y_continuous(trans = "log10")

Here we’ve plotted each individual well in black, with the “average well” plotted in red. We can clearly see that our different wells are varying in how long their lag time is, but not their growth rate once they start. In contrast, our average well has a quite different shape. Does that affect its maximum growth rate?

# Summarize our data
sim_dat_sum <- summarize(group_by(sim_dat_tdy, Well),
                         max_growth_rate = max(percap_deriv, na.rm = TRUE))

# Plot the maximum per-capita growth rates of each well
#  as well as the 'average' well
ggplot(data = sim_dat_sum, 
       aes(x = Well == "averaged", y = max_growth_rate)) +
  geom_point(alpha = 0.5, position = position_jitter(width = 0.1)) +
  ylim(0.01, 0.03)

Here we can see that the maximum growth rate of the “average well” is far from the maximum growth rate of each well.

Moreover, this bias can show up in other summary metrics as well. An ‘average curve’ is rarely a good representative of the average of all curves, so I recommend against averaging wells together before summarizing.

Carrying out statistical testing

How do you go about running statistics on analyzed growth curve data? Typically, growth curves experiments will have a highly nested structure. You probably have multiple wells with the same contents (i.e. technical replicates) in each plate. You may also have multiple plates from different runs (creating the possibility of batch effects).

In order to pull apart these effects and test for differences between your treatments, you’ll likely need to do mixed-effects modeling. Unfortunately, it’s beyond the scope of this vignette to provide a sufficient explanation of how to do mixed-effects statistics. However, I can provide some guidance:

For frequentist statistics, the R package lme4 is one of the most-popular implementations of mixed-effects modeling.

For Bayesian statistics, the R packages brms or rstanarm are popular implementations that can incorporate mixed-effects modeling.

Regardless of your approach, you should:

use your your summarized statistics (e.g. auc, max_growth_rate, lag_time, etc.) as your response variable
use your design elements (e.g. Bacteria_strain, Phage) as your explanatory variables (i.e. fixed effects)
incorporate random effects for any technical replicates you have
incorporate random effects for any potential batch effects in-play

There are a number of excellent resources out there to learn how to do this sort of mixed-effects modeling, including what I think is a good introductory guide to the process by Michael Clark.

Combining growth curves data with other data

As you approach the end of your growth curves analyses, you have summarized the dynamics of your growth curves into one or a few metrics. At this point, you may wish to pull in other sources of data to compare to your growth curves metrics. Just like merging multiple growth curves data frames together, this can be achieved with merge_dfs.

We’ll focus on the area-under-the-curve metric, and on just the bacteria grown in the absence of phages.

# This code was previously explained
# Here we're re-running it so it's available for us to work with
example_tidydata <- trans_wide_to_tidy(example_widedata_noiseless,
                                       id_cols = "Time")
ex_dat_mrg <- merge_dfs(example_tidydata, example_design_tidy)
#> Joining with `by = join_by(Well)`
ex_dat_mrg_sum <-
  summarize(group_by(dplyr::filter(ex_dat_mrg, Phage == "No Phage"),
                     Well, Bacteria_strain, Phage),
            auc = auc(x = Time, y = Measurements))
#> `summarise()` has grouped output by 'Well', 'Bacteria_strain'. You can override
#> using the `.groups` argument.

Imagine that, separately, we’ve measured the resistance of each of our example bacteria to antibiotics, and we want to know if there’s any relationship between the antibiotic resistance of the bacteria and their growth. make_example has some mock antibiotic resistance data we can use. Importantly, the antibiotic data must have matching headers to our growth curve data so that merge_dfs knows how to merge them.

Here we’ll generate some mock antibiotic resistance data. Importantly, our data must have matching headers as our growth curve data so that merge_dfs knows how to merge the data.frame’s. We’ll put whether or not the strain is resistant to the antibiotic under the Antibiotic_resis column, with a TRUE for resistance, and FALSE for sensitivity. Don’t worry exactly how this code works, since it’s just simulating data that you would have collected in the lab.

antibiotic_dat <- make_example(vignette = 8, example = 2)
#> Joining with `by = join_by(Well)`

head(antibiotic_dat)
#>   Bacteria_strain Antibiotic_resis
#> 1        Strain 1             TRUE
#> 2        Strain 2            FALSE
#> 3        Strain 3             TRUE
#> 4        Strain 4            FALSE
#> 5        Strain 5            FALSE
#> 6        Strain 6             TRUE

Great, now we merge our two data frames and see if there’s a relationship.

growth_and_antibiotics <- 
  merge_dfs(ex_dat_mrg_sum, antibiotic_dat)
#> Joining with `by = join_by(Bacteria_strain)`
head(growth_and_antibiotics)
#> # A tibble: 6 × 5
#> # Groups:   Well, Bacteria_strain [6]
#>   Well  Bacteria_strain Phage       auc Antibiotic_resis
#>   <chr> <chr>           <chr>     <dbl> <lgl>           
#> 1 A1    Strain 1        No Phage 57291. TRUE            
#> 2 A2    Strain 2        No Phage 69361. FALSE           
#> 3 A3    Strain 3        No Phage 54460. TRUE            
#> 4 A4    Strain 4        No Phage 72280. FALSE           
#> 5 A5    Strain 5        No Phage 73112. FALSE           
#> 6 A6    Strain 6        No Phage 45970. TRUE

ggplot(data = growth_and_antibiotics, 
       aes(x = Antibiotic_resis, y = auc)) +
  geom_point()

There is! We can see that the antibiotic resistant strains (TRUE) have a smaller area-under-the-curve than the antibiotic sensitive strains (FALSE) (although, to be fair, I did simulate the data so we’d get that result).

Other growth curve analysis packages

A number of other software tools besides gcplyr facilitate analysis of growth curves data or data wrangling of plate reader data. Here I’ll provide some brief notes on how gcplyr compares to these other tools, for a more detailed comparison please see: Blazanin, M. “gcplyr: an R package for microbial growth curve data analysis.” bioRxiv (2023)

There are, broadly speaking, two ways to analyze growth curves data:

directly quantify attributes of the growth dynamics
fit the growth dynamics with a mathematical model, then extract parameters from the fitted model

While gcplyr and some other R packages focus on the first analysis approach (direct quantification of growth curves dynamics), many other R packages focus on fitting growth dynamics with a mathematical model.

Generally, fitting growth dynamics with a model has greater power to accurately quantify the underlying traits. However, it also takes much more effort to be rigorous when fitting data with a model. You have to carefully choose a model whose assumptions your data meet. You also have to evaluate the fits to ensure that the optimization algorithms arrived on reasonable solutions.

Here are some other software tools for growth curve data analysis, for you to explore. I’ve italicized several tools which might be particularly compatible with gcplyr because they can import the tidy-shaped data that gcplyr generates.

growthcurver
growthrates
biogrowth
opm
QurvE
AUDIT
bletl
AMiGA
fitderiv
phenom
B-GREAT
PMAnalyzer
GrowthRates
GCAT
PRECOG
IPMP 2013
GATHODE
Microrisk Lab
CarboLogR
YODA
BGFit

Additionally, some software doesn’t analyze growth curve data, but does contain useful functionality for plate-reader data wrangling:

plater
Parsley

What’s next?

You’ve finished all of the core documentation. Congratulations! gcplyr is a powerful framework to build additional analyses on, since the data is nicely organized. Feel free to reach out to me with any questions, comments, or concerns you might have. I’d love to continue making gcplyr as useful for others in the scientific community as it has been for me. You can reach me at mikeblazanin [at] gmail [dot] com.

If you’d like to read about how to work with multiple plates of data at once, check out our final vignette: vignette("gc09_multiple_plates")

Introduction: vignette("gc01_gcplyr")
Importing and reshaping data: vignette("gc02_import_reshape")
Incorporating experimental designs: vignette("gc03_incorporate_designs")
Pre-processing and plotting your data: vignette("gc04_preprocess_plot")
Processing your data: vignette("gc05_process")
Analyzing your data: vignette("gc06_analyze")
Dealing with noise: vignette("gc07_noise")
Best practices and other tips: vignette("gc08_conclusion")
Working with multiple plates: vignette("gc09_multiple_plates")
Using make_design to generate experimental designs: vignette("gc10_using_make_design")