Using fluorescence lifetime to measure pre-existing lac expression

Decay curves

Import from Ludovit’s analysis (offset adjusted manually so that the exponential fit looks straight in semi-log scale):

(myplots[['FLIM_decay']] <- bind_rows(
  read_delim(here('./data_FLIM/decay_curves/decay_GFP.dat'), delim='\t', skip=2, na = "---",
             col_names=c("time_IRF", "IRF", "time_decay", "decay", "time_fit", "fit", "time_resid", "resid")) %>%
    mutate(sample='LacZ-GFPmut2',
           time_decay=time_decay - .3, time_fit=time_fit - .3,
           decay=decay/max(decay) - .0011, fit=fit/max(fit, na.rm=T) - .0011) ,
  read_delim(here('./data_FLIM/decay_curves/decay_noGFP.dat'), delim='\t', skip=2, na = "---", 
             col_names=c("time_decay", "decay", "time_fit", "fit", "time_resid", "resid")) %>% 
    mutate(sample='Autofluorescence',
           decay=decay-.0131, fit=fit-.0131) , 
) %>% 
  ggplot(aes(group=sample)) +
  geom_point(aes(time_decay, decay, col=sample), size=1, stroke=0, alpha=.5) +
  geom_line(aes(time_fit, fit)) +
  scale_y_log10() +
  coord_cartesian(xlim=c(0, 17), ylim=c(1e-2, 1)) +
  labs(x= 'decay time (ns)', y='normalised count') +
  guides(col=guide_legend(override.aes = list(size=3, alpha=1))) +
  theme(legend.position = c(.99, .99), legend.justification = c(1, 1)) +
  NULL)

# ggsave('GFPmut2_decay.pdf', width=5, height=4)

FLCS snapshot

First, we compare the proportions of cells with detectable LacZ-GFP in FLCS snapshots and the fraction of cells with short lags

(myplots[['FLIM_snapshot_hist']] <- bind_rows(
  readxl::read_xlsx(here("./data_FLIM/FLCS_lacInduction.xlsx"), sheet='Snapshot', range = "A1:C228") %>% 
    filter(is.na(date), gfp!='-1') %>% 
    mutate(gfp=as.numeric(gfp)) %>% 
    summarise(n=sum(!is.na(gfp)), p=sum(gfp==1)/n, p_se=sqrt(p*(1-p)/n)) %>% 
    mutate(method='LacZ-GFP\n(FLCS)'),
  tibble(n=1633, p=0.3, p_se=sqrt(p*(1-p)/n), method='short lag\n(microfluidics)'),
) %>% 
  ggplot(aes(method, p)) +
  geom_bar(stat='identity', width=0.7) +
  geom_errorbar(aes(ymin=p-p_se, ymax=p+p_se), width=.2) +
  geom_text(aes(method, y=0.5, label=paste0('(n = ', n, ')'))) +
  expand_limits(y=0.5) +
  labs(y='proportion of cells') +
  theme(axis.title.x = element_blank()) +
  NULL)

bind_cols(
  readxl::read_xlsx(here("./data_FLIM/FLCS_lacInduction.xlsx"), sheet='Snapshot', range = "A1:C228") %>% 
    filter(is.na(date), gfp!='-1') %>% 
    mutate(gfp=as.numeric(gfp)) %>% 
    summarise(n=sum(!is.na(gfp)), p=sum(gfp==1)/n, p_se=sqrt(p*(1-p)/n)) %>% 
    rename_all(~paste0(., '_FLCS')),
  tibble(n=1633, p=0.3, p_se=sqrt(p*(1-p)/n)) %>% 
    rename_all(~paste0(., '_lags')),
) %>% 
  ggplot(aes(p_FLCS, p_lags)) +
  geom_abline(lty='dashed', size=.2) +
  ggforce::geom_ellipse(aes(x0=p_FLCS, y0=p_lags, a=p_se_FLCS, b=p_se_lags, angle=0), fill='gray20', size=.2, alpha=.2) +
  geom_point(col=ggCustomTJ::brewer_cols[1]) +
  # geom_errorbar(aes(ymin=p-p_se, ymax=p+p_se), width=.5) +
  expand_limits(x=c(0, 0.5), y=c(0, 0.5)) +
  coord_fixed() +
  labs(x='proportion of cells\nwith LacZ-GFP (FLCS)', y='proportion of cells with\nshort lags (microfluidics)')+
  NULL

FLCS with timelapse

We do mother machine experiments where growth and LacZ-GFP expression are measured using FLIM. Before the switch, one to 2 cells per growth channel is measured with FLCS (and analysed using filters pattern-matched to LAcZ-GFP decay curves).

Cells must match 3 criteria in order to be called GFP positive:

• the distribution of count per molecule looks like a mixture of normal + uniform, where the normal distibution correspond to cells with very low CPM and hence no GFP. Criteria 1 is that CPM must be higher than mean + 5 standard deviations of the background.
• the fitted number of molecules must be low enough that it is not detected in the difference of signal intensity (we set the threshold at 20 molecules which discards 3 cells (note that cells called GFP positive all have fitted numbers flower than 12 molecules).
• the diffusion time should be compatible with what is know for LacZ-GFP, between 3 and 30ms on our setup (which corresponds to diffusion coefficients between 1 and 10 µm2/sec).

(myplots[['flim_gfp_criteria_cpm']] <- 
   bind_cols(
     readxl::read_xlsx(here("./data_FLIM/FLCS_lacInduction.xlsx"), sheet="MotherMachine", range = "A1:C75"),
     readxl::read_xlsx(here("./data_FLIM/FLCS_lacInduction.xlsx"), sheet='MotherMachine', range = "K2:P75", col_types="numeric",
                       col_names = c('n', 'n_se', 'D', 'D_se', 'cpm', 'cpm_se')),
   ) %>%
   mutate(gfp=as.numeric(gfp),
          ncpm = cpm / median(cpm, na.rm=T),
          d_time = .33^2/(4*D) * 1000,
   ) %>% 
   # filter(!is.na(ncpm))
   ggplot(aes(ncpm, fill=factor(gfp))) +
   geom_histogram(binwidth = .4) +
   geom_vline(xintercept = 2.55, lty='dashed') +
   scale_fill_discrete(limits=c(0, 1, -1), labels=c('undetected', 'detected', 'dubious')) +
   coord_cartesian(xlim=c(0, 28)) +
   labs(x='normalized CPM (AU)')+
   theme(legend.position = 'none') +
   NULL)

(myplots[['flim_gfp_criteria_nb']] <- 
    bind_cols(
      readxl::read_xlsx(here("./data_FLIM/FLCS_lacInduction.xlsx"), sheet="MotherMachine", range = "A1:C75"),
      readxl::read_xlsx(here("./data_FLIM/FLCS_lacInduction.xlsx"), sheet='MotherMachine', range = "K2:P75", col_types="numeric",
                        col_names = c('n', 'n_se', 'D', 'D_se', 'cpm', 'cpm_se')),
    ) %>%
    mutate(gfp=as.numeric(gfp),
           ncpm = cpm / median(cpm, na.rm=T),
           d_time = .33^2/(4*D) * 1000,
    ) %>% 
    ggplot(aes(ncpm, n, col=factor(gfp))) +
    geom_point() +
    geom_vline(xintercept = 2.55, lty='dashed') +
    geom_hline(yintercept = 20, lty='dashed') +
    scale_y_log10() +
    scale_colour_discrete(limits=c(0, 1, -1), labels=c('undetected', 'detected', 'dubious')) +
    coord_cartesian(xlim=c(0, 28)) +
    labs(y='fitted number of\nGFP molecules')+
    theme(legend.position = 'none') +
    NULL)

(myplots[['flim_gfp_criteria_diff']] <- 
    bind_cols(
      readxl::read_xlsx(here("./data_FLIM/FLCS_lacInduction.xlsx"), sheet="MotherMachine", range = "A1:C75"),
      readxl::read_xlsx(here("./data_FLIM/FLCS_lacInduction.xlsx"), sheet='MotherMachine', range = "K2:P75", col_types="numeric",
                        col_names = c('n', 'n_se', 'D', 'D_se', 'cpm', 'cpm_se')),
    ) %>%
    mutate(gfp=as.numeric(gfp),
           ncpm = cpm / median(cpm, na.rm=T),
           d_time = .33^2/(4*D) * 1000,
    ) %>% 
    ggplot(aes(ncpm, d_time, col=factor(gfp))) +
    geom_point() +
    geom_vline(xintercept = 2.55, lty='dashed') +
    geom_hline(yintercept = 3, lty='dashed') +
    geom_hline(yintercept = 30, lty='dashed') +
    scale_y_log10() +
    scale_colour_discrete(limits=c(0, 1, -1), labels=c('undetected', 'detected', 'dubious')) +
    coord_cartesian(xlim=c(0, 28)) +
    labs(y='fitted diffusion\ntime (ms)')+
    theme(legend.position = 'none') +
    NULL)

For all cells measured by FLCS (sample biased for cells with short lags), I estimated the lag visually (as the first frame where the GFP fluorescence become higher than the noise in uninduced neighbouring cells).

This reveals that:

1. the short lags estimated this way are between 20 and 35 minutes,
2. that virtually no cell with long lag had GFP before the switch (which would be explained e.g. due to presence of LacZ but no LacY, or LacZ but not as functionnal tetramers).

It is remarkable that 8 out of 22 cells featuring short lags have no GFP detected. This can be due to

• LacZ-GFP not diffusing freely (hence not detected in the focal volume)
• unsufficient sensitivity
• bleaching of the existing GFP tetramer(s)

(myplots[['FLIM_lag_hist']] <- left_join(
  readxl::read_xlsx(here("./data_FLIM/FLCS_lags.xlsx"), range = "A1:E75"),
  readxl::read_xlsx(here("./data_FLIM/FLCS_lacInduction.xlsx"), sheet="MotherMachine", range = "A1:C75"),
) %>% 
  mutate(frame=as.numeric(frame), lag=as.numeric(lag), gfp=as.numeric(gfp)) %>% 
  filter(!is.na(gfp)) %>%
  mutate(lag=ifelse(is.infinite(lag) & date==20200122, 252, lag)) %>% 
  mutate(lag=ifelse(is.infinite(lag) & date==20200123, 261, lag)) %>% 
  mutate(lag=ifelse(is.infinite(lag) & date==20200128, 180, lag)) %>% 
  # filter(!is.na(lag), !is.na(gfp))
  # summarise(n_s=sum(lag<35, na.rm=T)/sum(!is.na(lag)))
  # filter(lag<30, gfp==0)
  ggplot(aes(lag, fill=factor(gfp))) +
  geom_histogram(position='stack', binwidth=6) +
  geom_vline(xintercept=35, lty='dotted') +
  expand_limits(x=0) +
  scale_fill_discrete(limits=c(0, 1, -1), labels=c('undetected', 'detected', 'dubious')) +
  labs(x=lac_lags_label, fill='LacZ-GFP status\nbefore the switch') +
  # labs(x=lac_lags_label, fill='GFP status\n(FLCS)') +
  NULL)

Noticeably, the distribution of fitted number of GFP is discontinuous in mother machine experiments. We believe that this is a side effect of the complicated optical environemnt created by PDMS channel which resulted in poor signal-to-noise ratio.

bind_rows(
  bind_cols(
  readxl::read_xlsx(here("./data_FLIM/FLCS_lacInduction.xlsx"), sheet='Snapshot', range = "A1:C228"),
  readxl::read_xlsx(here("./data_FLIM/FLCS_lacInduction.xlsx"), sheet='Snapshot', range = "K2:L228", col_names = c('n', 'se')),
) %>% 
  select(gfp, n) %>% mutate(dataset='snapshot'), 

  bind_cols(
    readxl::read_xlsx(here("./data_FLIM/FLCS_lacInduction.xlsx"), sheet="MotherMachine", range = "A1:C75"),
    readxl::read_xlsx(here("./data_FLIM/FLCS_lacInduction.xlsx"), sheet="MotherMachine", range = "K2:L75",
                      col_names = c('n', 'se')),
  ) %>% 
  mutate(gfp=as.numeric(gfp), n=as.numeric(n), se=as.numeric(se), dataset='mother machine') %>% 
  select(dataset, gfp, n), 
) %>%
  # filter(gfp==1) %>% 
  mutate(n = ifelse(gfp==0, 0, n), n = ifelse(gfp==-1, NA, n)) %>%
  mutate(dataset = relevel(factor(dataset), 'snapshot')) %>% 
  ggplot(aes(n)) +
  facet_wrap(~dataset, ncol=1, scales = 'free_y') +
  geom_histogram(binwidth = 1) +
  expand_limits(x=0) +
  # scale_y_log10() +
  # xlim(0, 20) +
  labs(x='number of GFP') +
  NULL

# ggsave('gfp_histo_FLCS_MoM.pdf', width=5, height=3)


  bind_cols(
  readxl::read_xlsx(here("./data_FLIM/FLCS_lacInduction.xlsx"), sheet='Snapshot', range = "A1:C228"),
  readxl::read_xlsx(here("./data_FLIM/FLCS_lacInduction.xlsx"), sheet='Snapshot', range = "K2:L228", col_names = c('n', 'se')),
  ) %>% 
    filter(gfp==1) %>% 
    pull(n) %>% sd()

## [1] 3.475612

Let’s look at the CPM critera for each class:

left_join(
  readxl::read_xlsx(here("./data_FLIM/FLCS_lags.xlsx"), range = "A1:E75"),
  bind_cols(
    readxl::read_xlsx(here("./data_FLIM/FLCS_lacInduction.xlsx"), sheet="MotherMachine", range = "A1:C75"),
    readxl::read_xlsx(here("./data_FLIM/FLCS_lacInduction.xlsx"), sheet="MotherMachine", range = "H2:H75", col_names ='ncpm'),
    readxl::read_xlsx(here("./data_FLIM/FLCS_lacInduction.xlsx"), sheet="MotherMachine", range = "O2:O75", col_names ='cpm_flcs'),
  )
) %>%
  mutate(frame=as.numeric(frame), lag=as.numeric(lag), gfp=as.numeric(gfp), 
         ncpm=as.numeric(ncpm), cpm_flcs=as.numeric(cpm_flcs),
         ncpm_flcs = cpm_flcs / median(cpm_flcs, na.rm=T),
         ) %>% 
  # filter(!is.na(gfp)) %>%
  # mutate(lag=ifelse(is.infinite(lag) & date==20200122, 252, lag)) %>% 
  # mutate(lag=ifelse(is.infinite(lag) & date==20200123, 261, lag)) %>% 
  # mutate(lag=ifelse(is.infinite(lag) & date==20200128, 180, lag)) %>% 
  mutate(lag_type=lag, lag_type=ifelse(lag<35, 'short', lag_type), lag_type=ifelse(lag>=35, 'long', lag_type)) %>% 
  ggplot(aes(ncpm_flcs)) +
  facet_grid(lag_type~.) +
  geom_histogram(binwidth = .5) +
  expand_limits(x=0) +
  # xlim(NA, 20) +
  # labs(title='mother machine') +
  NULL

FLIM sensitivity

In order to estimate whether FLIM intensity (without FLCS) can be used to measure difference in GFP before the switch, we proceed as follow:

• for one experiment, FLIM data are analysed using pattern matching (for GFP decay),
• based on GFP intensity at frame 12 in lactose (after 36 min, as identified in the FLCS analysis), cells are classified as short or long lags
• a ROI is drawn manually for each parent cell on frame 1, the intensity is exported for both channels (GFP / noGFP decay)
• we compare the distribution for cells with short and long lags of several staticstics of fuorescence (intden is the total fluorescence in the ROI)

bind_rows(
  read_csv(here('./data_FLIM/20200128_lac1_shortLags.csv')) %>% 
    mutate(lag='short'),
  read_csv(here('./data_FLIM/20200128_lac1_longLags.csv')) %>% 
    mutate(lag='long'),
) %>% 
  rename_all(tolower) %>% 
  separate(label, c('img', 'roi', 'frame'), sep=":") %>% 
  select(-x1, -img) %>% 
  mutate(ch_type=c('GFP', 'noGFP')[ch]) %>% 
  filter(ch_type=='GFP') %>% 
  gather(var, value, intden, mean, mode, max) %>% 
  ggplot(aes(value, col=lag)) +
  facet_wrap(~var, scales = 'free') +
  geom_freqpoly() +
  labs(col='type of lag') +
  # theme(legend.position='top') +
  NULL

# ggsave('FLIM_sensitivity.pdf', width=8, height=3.5)

Unfortunately, we cannot find any statistics capable of separating the 2 types of cells…

Sanity check

Let’s look at the total intensity of GFP channel vs total intensity of noGFP channel. From the epifluorescence measurement on cells with no GFP sequence, we know that autofluo fluctuates by ± 20 equivalent GFP molecules; here there is a 3-fold change (would correspond to e.g. 40 ± 20 for epifluo measurements).

bind_rows(
  read_csv(here('./data_FLIM/20200128_lac1_shortLags.csv')) %>% 
    mutate(lag='short'),
  read_csv(here('./data_FLIM/20200128_lac1_longLags.csv')) %>% 
    mutate(lag='long'),
) %>% 
  rename_all(tolower) %>% 
  separate(label, c('img', 'roi', 'frame'), sep=":") %>% 
  select(-x1, -img) %>% 
  mutate(ch_type=c('GFP', 'noGFP')[ch]) %>% 
  select(roi, ch_type, lag, intden) %>% 
  pivot_wider(names_from=ch_type, values_from=intden) %>% 
  ggplot(aes(GFP, noGFP)) +
  geom_abline() +
  stat_density_2d(fill=rgb(0,0,0,.1), geom = "polygon", show.legend=FALSE) +
  geom_point(aes(col=lag)) +
  expand_limits(x=0, y=0) +
  labs(title='total intensity', col='lag') +
  NULL

# bind_rows(
#   read_csv(here('./data_FLIM/20200128_lac1_shortLags.csv')) %>% 
#     mutate(lag='short'),
#   read_csv(here('./data_FLIM/20200128_lac1_longLags.csv')) %>% 
#     mutate(lag='long'),
# ) %>% 
#   rename_all(tolower) %>% 
#   separate(label, c('img', 'roi', 'frame'), sep=":") %>% 
#   select(-x1, -img) %>% 
#   mutate(ch_type=c('GFP', 'noGFP')[ch]) %>% 
#   select(roi, ch_type, lag, intden) %>% 
#   pivot_wider(names_from=ch_type, values_from=intden) %>% 
#   filter(GFP  < 26) %>%
#   with(cor(noGFP, GFP)^2)