This experiment compares Amicon filters (30 kDa and 100 kDa) vs the InnovaPrep Concentrating Pipette (two tip types).

library(tidyverse)
library(googlesheets4)
library(fs)
library(here)

library(knitr)

library(broom)

# plotting helpers
library(cowplot)
library(patchwork)
library(ggbeeswarm)

theme_set(theme_cowplot())

# Okabe Ito color scheme with amber for yellow; see https://easystats.github.io/see/reference/scale_color_okabeito.html
colors_oi <- grDevices::palette.colors()  
colors_oi['yellow'] <- "#F5C710"

# Custon qPCR helpers
source('_functions.R')

Data import

Metadata is stored in a Google Sheet,

url <- 'https://docs.google.com/spreadsheets/d/1qBD6ZhDDtGBx1iYgcIJf6GZJhOZoS6B15vtvhJYdkoo'
meta_samples <- read_sheet(url, sheet = 'Samples', na = c("", "NA")) %>%
  glimpse

Rows: 12
Columns: 9
$ sample_qpcr     <chr> "N_30", "N_100", "N_0.05", "N_Ultra", "S_30"…
$ treatment_group <dbl> 1, 2, 3, 4, 1, 2, 3, 4, 5, 6, 5, 6
$ sample_number   <dbl> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
$ filter          <chr> "30 kDa", "100 kDa", "0.05 CPT", "Ultra CPT"…
$ sewer_system    <chr> "N", "N", "N", "N", "S", "S", "S", "S", "N",…
$ volume          <dbl> 40, 40, 40, 40, 40, 40, 40, 40, 80, 80, 80, …
$ amicon_mwco     <dbl> 30, 100, NA, NA, 30, 100, NA, NA, NA, NA, NA…
$ method          <chr> "Amicon Ultra centrifugal filter", "Amicon U…
$ method_short    <chr> "Amicon", "Amicon", "CP", "CP", "Amicon", "A…

meta_targets <- read_sheet(url, sheet = 'Targets', na = c("", "NA")) %>%
  glimpse

Rows: 5
Columns: 2
$ target_qpcr <chr> "CrA", "phg", "Cov2", "Noro", "16S"
$ target      <chr> "CrAssphage", "Phagemid tracers", "SARS-CoV-2", …

Results are in CSV files.

'_data' %>% dir_ls(recurse = TRUE, glob = '*Result*')

_data/16S data files/2023-06-23_CPAmicon_16S_Replicate Group Result_20230625 111656.csv
_data/16S data files/2023-06-23_CPAmicon_16S_Results_20230625 111656.csv
_data/16S data files/2023-06-23_CPAmicon_16S_Standard Curve Result_20230625 111656.csv
_data/CoV2 and Noro data files/2023-06-23_AmiconCP-COVNORO_Replicate Group Result_20230623 171728.csv
_data/CoV2 and Noro data files/2023-06-23_AmiconCP-COVNORO_Results_20230623 171728.csv
_data/CoV2 and Noro data files/2023-06-23_AmiconCP-COVNORO_Standard Curve Result_20230623 171728.csv
_data/CrA and phagemid data files/2023-06-23_CrAPhg_Replicate Group Result_20230623 171458.csv
_data/CrA and phagemid data files/2023-06-23_CrAPhg_Results_20230623 171458.csv
_data/CrA and phagemid data files/2023-06-23_CrAPhg_Standard Curve Result_20230623 171458.csv

There are three different types. Here I’ll use the ‘Standard Curve Result’ files, which include what is in the ‘Results’ files but also have standard curve (SC) calibrations,

fns <- '_data' %>%
  dir_ls(recurse = TRUE, glob = '*_Standard Curve Result_*.csv')
fns %>% path_file

[1] "2023-06-23_CPAmicon_16S_Standard Curve Result_20230625 111656.csv"    
[2] "2023-06-23_AmiconCP-COVNORO_Standard Curve Result_20230623 171728.csv"
[3] "2023-06-23_CrAPhg_Standard Curve Result_20230623 171458.csv"

results_raw <- tibble(file = fns) %>%
  mutate(.keep = 'unused',
    data = map(file, read_qpcr_results_csv)
  ) %>%
  unnest(data)

results <- results_raw %>%
  rename(target_qpcr = target) %>%
  left_join(meta_samples, by = c('sample' = 'sample_qpcr')) %>%
  left_join(meta_targets, by = 'target_qpcr') %>%
  mutate(
    across(c(treatment_group, amicon_mwco, volume, method_short, filter), as.factor),
    across(method_short, ~fct_relevel(.x, 'Amicon')),
    across(filter, ~fct_relevel(.x, '30 kDa')),
    method_filter = interaction(method_short, filter, drop = TRUE, sep = ': ', lex.order = TRUE)
  )

results %>% count(task, cq_status)

# A tibble: 5 × 3
  task     cq_status        n
  <chr>    <chr>        <int>
1 NTC      Determined       3
2 NTC      Undetermined     5
3 STANDARD Determined      29
4 STANDARD Undetermined     1
5 UNKNOWN  Determined     180

In this experiment, the Cq value was determined for all the non-control samples.

results %>%
  count(target_qpcr, target)

# A tibble: 5 × 3
  target_qpcr target               n
  <chr>       <chr>            <int>
1 16S         Bacterial 16S       54
2 Cov2        SARS-CoV-2          54
3 CrA         CrAssphage          36
4 Noro        Norovirus           38
5 phg         Phagemid tracers    36

Load amplification data,

fns_amp <- '_data' %>%
  dir_ls(recurse = TRUE, glob = '*_Amplification Data_*.csv') %>%
  str_subset(negate = TRUE, 'Raw')

amp <- tibble(file = fns_amp) %>%
  mutate(.keep = 'unused',
    data = map(file, read_qpcr_amplification_csv)
  ) %>%
  unnest(data) %>%
  rename(target_qpcr = target) %>%
  left_join(results)

TODO: find a better way to import the amplification data and results at the same time

Get the baseline coordinates for plotting,

baselines <- results %>%
  pivot_longer(
    cols = c(baseline_start, baseline_end),
    names_to = 'baseline_boundary',
    values_to = 'cycle_number',
    names_prefix = 'baseline_',
  ) %>%
  left_join(
    amp %>% select(well_position, cycle_number, rn, d_rn), 
    by = c('well_position', 'cycle_number')
  )

Analysis

The source samples are either from the N or S sewer system.

The treatment group is determined by

Amicon vs InnovaPrep Concentrating Pipette (CP)
Filter pore size: Amicon MWCO (30 kDa or 100 kDa) or CP tip type (0.05um or ‘Ultra’)
Volume used (40 mL or 80 mL); only applies to CP

results %>%
  count(treatment_group, method_short, filter, volume)

# A tibble: 7 × 5
  treatment_group method_short filter    volume     n
  <fct>           <fct>        <fct>     <fct>  <int>
1 1               Amicon       30 kDa    40        30
2 2               Amicon       100 kDa   40        30
3 3               CP           0.05 CPT  40        30
4 4               CP           Ultra CPT 40        30
5 5               CP           0.05 CPT  80        30
6 6               CP           Ultra CPT 80        30
7 <NA>            <NA>         <NA>      <NA>      38

Plot Cq estimates

For these plots, in cases where the Cq value could not be determined, I set the value to 40.

results %>%
  filter(!is.na(treatment_group)) %>%
  mutate(cq = ifelse(is.na(cq), 40, cq)) %>%
  ggplot(aes(x = cq, y = method_filter, color = volume)) +
  theme(
    legend.position = 'bottom',
    panel.spacing = unit(2, 'char'),
    # panel.spacing.x = unit(4, 'char'),
  ) +
  scale_x_continuous(n.breaks = 4) +
  labs(
    y = 'Method : Filter',
    x = 'Cq',
    color = 'Volume (mL)',
  ) +
  facet_grid(sewer_system ~ target, scales = 'free') +
  scale_color_manual(values = colors_oi %>% unname) +
  geom_quasirandom()

results %>%
  filter(!is.na(treatment_group)) %>%
  mutate(cq = ifelse(is.na(cq), 40, cq)) %>%
  ggplot(aes(x = cq, y = method_filter, color = volume)) +
  # theme_minimal_vgrid() +
  theme(
    legend.position = 'bottom',
    panel.spacing = unit(2, 'char'),
    # panel.spacing.x = unit(4, 'char'),
  ) +
  labs(
    y = 'Method : Filter',
    x = 'Cq',
    color = 'Volume (mL)',
  ) +
  # facet_grid(sewer_system ~ target, scales = 'free') +
  facet_wrap(
    target ~ sewer_system , scales = 'free_x', ncol = 2, 
    labeller = function(x) label_value(x, multi_line = FALSE)
  ) +
  scale_color_manual(values = colors_oi %>% unname) +
  geom_quasirandom()

Note that for the CP 0.05 um filter, it appears that the 80mL sample led to a lower concentration for the four naturally-occurring targets (Bacterial 16S, CrAssphage, Norovirus, and SARS2). This is surprising and the only one of four 80mL samples where the measured concentrations were lower. Might this indicate a mistake in the sample preparation?

The N Amicon 100 sample led to much lower measured concentrations than the N Amicon 30 sample for everything except SARS2. Possibly there was a handling error or the Amicon filter was defective.

Analysis for illustration purposes

Inspect SARS2 amplification curves

delta_rn_min <- 1e-3
ct_threshold <- results %>% filter(target == 'SARS-CoV-2') %>% pull(threshold) %>% unique
stopifnot(length(ct_threshold) == 1)

amp %>%
  filter(
    target == 'SARS-CoV-2',
    !is.na(treatment_group)
  ) %>%
  ggplot(aes(cycle_number, pmax(d_rn, delta_rn_min), color = method_filter)) +
  facet_grid(sewer_system ~ volume, scales = 'free') +
  scale_color_manual(values = colors_oi %>% unname) +
  scale_y_log10() +
  geom_line(aes(group = well)) +
  geom_hline(yintercept = ct_threshold, alpha = 0.3) +
  # scale_color_brewer(type = 'qual') +
  # geom_point(data = baselines, aes(shape = baseline_boundary), size = 3) +
  # scale_shape_manual(values = c(1, 4)) +
  labs(y = 'Delta Rn', x = 'Cycle', color = 'Target')

Plot concentration estimates

In this results output, only the 16S and SARS2 results have standard curves loaded and calibrated concentrations estimated,

results %>%
  count(target, is.na(slope), is.na(quantity))

# A tibble: 7 × 4
  target           `is.na(slope)` `is.na(quantity)`     n
  <chr>            <lgl>          <lgl>             <int>
1 Bacterial 16S    FALSE          FALSE                51
2 Bacterial 16S    FALSE          TRUE                  3
3 CrAssphage       TRUE           TRUE                 36
4 Norovirus        TRUE           TRUE                 38
5 Phagemid tracers TRUE           TRUE                 36
6 SARS-CoV-2       FALSE          FALSE                51
7 SARS-CoV-2       FALSE          TRUE                  3

I believe that is because only these two targets had SC controls run in this experiment, and old SCs were not loaded into the software. I’ll make the plot as if all targets had SCs and calibrated concentration estimates, for illustration purposes.

results %>%
  filter(!is.na(treatment_group)) %>%
  ggplot(aes(x = quantity, y = method_filter, color = volume)) +
  theme(
    legend.position = 'bottom',
    panel.spacing = unit(2, 'char'),
    # panel.spacing.x = unit(4, 'char'),
  ) +
  scale_x_log10() +
  labs(
    y = 'Method : Filter',
    x = 'Concentration',
    color = 'Volume (mL)',
  ) +
  facet_grid(sewer_system ~ target, scales = 'free') +
  scale_color_manual(values = colors_oi %>% unname) +
  geom_quasirandom()

Note that concentration varies in opposition to exp(Cq); it is higher when Cq is lower.

Fitting and using standard curves

sars2 <- results %>% filter(target == 'SARS-CoV-2')

sc_params <- sars2 %>% select(y_intercept, slope) %>% distinct %>% unlist %>% print

y_intercept       slope 
    39.1983     -3.0463

For the SC controls, the sample name records the concentration (I’m unsure on the units).

sars2_sc <- sars2 %>% 
  filter(task == 'STANDARD') %>%
  mutate(conc = as.numeric(sample), conc_log10 = log10(conc))

Note that the Cq wasn’t determined for one of the SC controls, so we’ll need to decide how to treat that.

sars2 %>% count(task, cq_status)

# A tibble: 4 × 3
  task     cq_status        n
  <chr>    <chr>        <int>
1 NTC      Undetermined     3
2 STANDARD Determined      14
3 STANDARD Undetermined     1
4 UNKNOWN  Determined      36

A simple but potentially misleading thing to do is drop that data point (also what R’s lm() function does by default).

To fit the standard curve with standard linear regression in R, we can use the lm() function.

fit <- lm(data = sars2_sc, cq ~ conc_log10, na.action = na.omit)

coef(fit)

(Intercept)  conc_log10 
  39.198343   -3.046335

sc_params

y_intercept       slope 
    39.1983     -3.0463

This approach mathces the SC from QuantStudio’s output, suggesting that simple linear regression, omitting the missing data point, was also used by OH in QuantStudio.

Let’s plot the fitted line with the data.

sars2_sc %>%
  ggplot(aes(log10(conc), cq)) +
  # geom_abline(
  #   intercept = sc_params['y_intercept'], 
  #   slope = sc_params['slope'],
  # ) +
  geom_abline(
    intercept = coef(fit)[1],
    slope = coef(fit)[2],
    linetype = 2
  ) +
  geom_point(alpha = 0.5)

The outlier point at the second-lowest concentration still seems to be having a big impact on the fit. In future, we can consider using more robust regression methods to handle this situation as well as the drop-out/undetermined Cq.

To perform a SC calibration on the samples with unknown concentrations, we can apply the inverse function of the fitted line to get log10(conc), and then take 10 raised to this number.

intercept = coef(fit)[1]
slope = coef(fit)[2]

sars2_cal <- sars2 %>%
  mutate(
    log_conc_hat = (cq - intercept) / slope,
    conc_hat = 10^log_conc_hat
  )

Let’s compare to the quantity column to confirm that we’re getting the same result as the software for the ‘unknown’ samples,

sars2_cal %>%
  filter(task != 'NTC') %>%
  ggplot(aes(conc_hat, quantity, color = task))  +
  scale_color_manual(values = colors_oi[2:3] %>% unname) +
  scale_y_log10() +
  scale_x_log10() +
  geom_point()

What about estimating the efficiency from the SC? The estimate from the QuantStudio software is

sars2 %>% pull(efficiency) %>% unique

[1] 112.943

Note that the software resports the efficiency as a percentage (here, about 113%).

We can also estimate the efficiency from the slope of the standard curve using the standard formula,

efficiency_hat <- (10^(-1/slope) - 1) * 100
efficiency_hat

conc_log10 
   112.943

We can form interval estimates from a confidence interval on the slope estiamte. For example, a 90% confidence interval,

slope_ci <- confint(fit, parm = 'conc_log10', level = 0.9)
efficiency_ci <- (10^(-1/slope_ci) - 1) * 100
efficiency_ci

               5 %     95 %
conc_log10 102.943 125.0085

Linear modeling

Fit linear model to assess the effect of conditions on the Cq value on each target. Quick but perhaps unreliable analysis.

Measure effect on average Cq value of the concentration treatment relative to the Amicon 30 kDa treatment. A positive effect corresponds to a decrease in concentration.

fits <- results %>%
  filter(!is.na(treatment_group), volume == 40) %>%
  summarize(
    .by = c(target, method_short, method_filter, sewer_system),
    across(cq, mean)
  ) %>%
  nest(.by = target) %>%
  mutate(.keep = 'unused',
    fit = map(data, ~lm(data = .x, cq ~ sewer_system + method_filter)),
    # fit_tidy = map(fit, broom::tidy)
  )
fits_summary <- fits %>%
  mutate(.keep = 'unused',
    tidy = map(fit, broom::tidy)
  ) %>%
  unnest(tidy)

fits_summary %>%
  filter(str_detect(term, 'method_filter')) %>%
  mutate(
    method_filter = str_replace(term, 'method_filter', '')
  ) %>%
  select(target, method_filter, estimate, std.error, p.value)

# A tibble: 15 × 5
   target           method_filter   estimate std.error p.value
   <chr>            <chr>              <dbl>     <dbl>   <dbl>
 1 Bacterial 16S    Amicon: 100 kDa   0.576      0.246 0.101  
 2 Bacterial 16S    CP: 0.05 CPT      0.390      0.246 0.211  
 3 Bacterial 16S    CP: Ultra CPT    -0.222      0.246 0.433  
 4 SARS-CoV-2       Amicon: 100 kDa  -0.0981     0.249 0.720  
 5 SARS-CoV-2       CP: 0.05 CPT     -0.954      0.249 0.0313 
 6 SARS-CoV-2       CP: Ultra CPT    -0.937      0.249 0.0328 
 7 Norovirus        Amicon: 100 kDa   0.446      0.306 0.241  
 8 Norovirus        CP: 0.05 CPT     -0.385      0.306 0.298  
 9 Norovirus        CP: Ultra CPT    -0.507      0.306 0.196  
10 CrAssphage       Amicon: 100 kDa   1.54       1.25  0.307  
11 CrAssphage       CP: 0.05 CPT     -0.276      1.25  0.840  
12 CrAssphage       CP: Ultra CPT    -0.796      1.25  0.569  
13 Phagemid tracers Amicon: 100 kDa   0.395      0.194 0.134  
14 Phagemid tracers CP: 0.05 CPT      1.38       0.194 0.00572
15 Phagemid tracers CP: Ultra CPT     0.502      0.194 0.0807

fits_summary %>%
  filter(
         str_detect(term, 'method_filter'),
         # str_detect(term, 'CP:'),
  ) %>%
  mutate(
    method_filter = str_replace(term, 'method_filter', '')
  ) %>%
  ggplot(aes(y = target, x = estimate, 
             xmin = estimate - 2 * std.error, 
             xmax = estimate + 2 * std.error, 
             color = method_filter
             )) +
  scale_color_manual(values = colors_oi %>% unname) +
  geom_vline(xintercept = 0, color = 'grey') +
  geom_pointrange(position = ggstance::position_dodgev(height = 0.3))

Session info

Click for session info

sessioninfo::session_info()

─ Session info ─────────────────────────────────────────────────────────
 setting  value
 version  R version 4.3.1 (2023-06-16)
 os       Arch Linux
 system   x86_64, linux-gnu
 ui       X11
 language (EN)
 collate  en_US.UTF-8
 ctype    en_US.UTF-8
 tz       America/New_York
 date     2023-07-03
 pandoc   3.1.2 @ /usr/bin/ (via rmarkdown)

─ Packages ─────────────────────────────────────────────────────────────
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 tidyverse     * 2.0.0   2023-02-22 [1] CRAN (R 4.3.0)
 timechange      0.2.0   2023-01-11 [1] CRAN (R 4.3.0)
 tzdb            0.4.0   2023-05-12 [1] CRAN (R 4.3.0)
 utf8            1.2.3   2023-01-31 [1] CRAN (R 4.3.0)
 vctrs           0.6.2   2023-04-19 [1] CRAN (R 4.3.0)
 vipor           0.4.5   2017-03-22 [1] CRAN (R 4.0.0)
 vroom           1.6.3   2023-04-28 [1] CRAN (R 4.3.0)
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 xfun            0.39    2023-04-20 [1] CRAN (R 4.3.0)
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 [1] /home/michael/.local/lib/R/library
 [2] /usr/lib/R/library

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Evaluate viral MGS protocols: Amicon centrifugal filters vs InnovaPrep Concentrating Pipette