Lifetime Distributions from Tracking Individual BC3H1 Cells Subjected to Yessotoxin

Abstract

This work shows examples of lifetime distributions for individual BC3H1 cells after start of exposure to the marine toxin yessotoxin (YTX) in an experimental dish. The present tracking of many single cells from time-lapse microscopy data demonstrates the complexity in individual cell fate and which can be masked in aggregate properties. This contribution also demonstrates the general practicality of cell tracking. It can serve as a conceptually simple and non-intrusive method for high throughput early analysis of cytotoxic effects to assess early and late time points relevant for further analyzes or to assess for variability and sub-populations of interest. The present examples of lifetime distributions seem partly to reflect different cell death modalities. Differences between cell lifetime distributions derived from populations in different experimental dishes can potentially provide measures of inter-cellular influence. Such outcomes may help to understand tumor-cell resistance to drug therapy and to predict the probability of metastasis.

Full text

METHODS
published: 21 October 2015
doi: 10.3389/fbioe.2015.00166
Edited by:
Tim Wilhelm Nattkemper,
Bielefeld University, Germany
Reviewed by:
John Pinney,
Imperial College London, UK
Mikhail P. Ponomarenko,
Russian Academy of Sciences, Russia
*Correspondence:
Mónica Suárez Korsnes
monica.suarez.korsnes@nmbu.no
Specialty section:
This article was submitted to
Bioinformatics and Computational
Biology, a section of the
journal Frontiers in Bioengineering and
Biotechnology
Received: 13 August 2015
Accepted: 02 October 2015
Published: 21 October 2015
Citation:
Korsnes MS and Korsnes R (2015)
Lifetime distributions from
tracking individual BC3H1 cells
subjected to yessotoxin.
Front. Bioeng. Biotechnol. 3:166.
doi: 10.3389/fbioe.2015.00166
Lifetime distributions from
tracking individual BC3H1 cells
subjected to yessotoxin
Mónica Suárez Korsnes1*and Reinert Korsnes 2,3
1Department of Chemistry, Biotechnology and Food Science, Norwegian University of Life Sciences, Ås, Norway,
2Norwegian Institute of Bioeconomy Research, Ås, Norway, 3Norwegian Defense Research Establishment, Kjeller, Norway
This work shows examples of lifetime distributions for individual BC3H1 cells after
start of exposure to the marine toxin yessotoxin (YTX) in an experimental dish. The
present tracking of many single cells from time-lapse microscopy data demonstrates
the complexity in individual cell fate and which can be masked in aggregate properties.
This contribution also demonstrates the general practicality of cell tracking. It can serve
as a conceptually simple and non-intrusive method for high throughput early analysis
of cytotoxic effects to assess early and late time points relevant for further analyzes
or to assess for variability and sub-populations of interest. The present examples of
lifetime distributions seem partly to reflect different cell death modalities. Differences
between cell lifetime distributions derived from populations in different experimental
dishes can potentially provide measures of inter-cellular influence. Such outcomes may
help to understand tumor-cell resistance to drug therapy and to predict the probability of
metastasis.
Keywords: cell tracking, lifetime statistics, yessotoxin, cell death, inter-cellular influence
1. INTRODUCTION
This work calls for attention to describe variability of individual cell responses in clonal cell
populations subject to toxic exposure. The present work evaluates individual BC3H1 cell responses
after toxic exposure to the marine toxin yessotoxin (YTX). YTX is a small molecule compound,
which can trigger a broad spectrum of cellular responses for possible medical applications (Korsnes
et al., 2006a,b, 2014;López et al., 2008, 2011a,b;Korsnes, 2012;Alonso et al., 2013). Time-lapse
observations of BC3H1 cells exposed to YTX provide a description of the diversity of individual
cell responses to toxic exposure. A small fraction of cells withstand the exposure much more than
others, whereas some cells die long before the majority. The presence of such minorities may have
interest for assessments of long term effects of a toxin. Parameters in simulation models of cellular
responses to toxic insults may be tuned to reproduce the complexity and features of observed lifetime
distributions. Tracking of individual cells can in this way contribute to reverse engineering of cellular
signaling.
Typical cell viability analyzes are based on measurements of cell metabolism at a limited set of
time points. Some of these measurements are intrusive (i.e., affecting the target of measurement).
Subsets of dead cells may tend to dissolve in the growth media and in this way being excluded from
temporally sparse measurements. Flow cytometry is used due to its massive throughput combined
with fluorescent labeling (Nolan and Sklar, 1998). However, it also samples only at specific time
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Korsnes and Korsnes Lifetime distributions from cell tracking
points and do not follow single cells over time. Wei et al. (2008)
demonstrated non-invasive detection of cell viability based on
wavelet decomposition of dark field microscopy images of cells.
However, no current cell viability analysis directly provides mea-
surements of single cell lifetime distributions. The inherent uncer-
tainties of common measurements of cell viability may partly
explain the lack of attention to the stochastic aspects of single cell
behavior.
Lifetime distributions of cells after toxic exposure may affect
the understanding of results from bulk cell analyzes. Such tech-
niques do not provide the correct distribution of a response,
which is important to develop mathematical descriptions of cel-
lular behavior (Teruel and Meyer, 2002). Cell viability assays, for
example, typically provide estimates of aggregate properties of
many cells subject to a common treatment. An example of such
an aggregate property is the widely used half maximal inhibitory
concentration (IC50). This measure normally results from expos-
ing cell populations to a compound at different concentrations
for estimating which concentration is needed to inhibit given
biological processes by half. It is tempting to attribute variations
of results form such assays to procedural errors or unavoidable
noise (Xia et al., 2014). The next step in following this intu-
ition is to reduce uncertainty by repeating experiments and to
calculate the average of the results. This value is assumed to
converge to a biologically meaningful quantity with increased
number of experiments. However, the parameter IC50 may not
reflect biological properties of any individual cell. The present
lifetime distributions also indicate that IC50 can be sensitive to
time points for the cell viability measurements which it often relies
on. Hence, one may expect it to be reproducible only if it is defined
in terms of experimental conditions in addition to its original
definition.
An experiment can, from a practical point of view, be consid-
ered deterministic only if the variation of outcomes decreases with
decreased perturbations in experimental conditions (at least when
they are small enough). The opposite of deterministic is normally
phrased as stochastic or chaotic. Throwing dice can, therefore in
practice, only be described probabilistic. Note that the outcome
from dice throwing has no direct physical meaningful expectation
value (3.5). There is similarly no guarantee that the mean value
of results from cell assays has a direct biological interpretation
since the result may be considered stochastic and multi-modal
with unlikely outcomes “between” different modes. The average
of values from measurements of single cells in a cell assay may
also not reflect the average over several experiments.
Several authors address variability among individual cells in
clonal populations. Sources of the variability are the proximity
to an inductive signal from a neighboring cell, their lineage,
oncogenic lesions, natural differences in protein levels, cell-cycle
state and epigenetic differences (Rubin, 1990;Elowitz et al., 2002;
Rieder and Maiato, 2004;Weaver and Cleveland, 2005;Losick and
Desplan, 2008;Huang, 2009;Spencer and Sorger, 2011;Fromion
et al., 2013). Although, interline and intraline variation is expected
in cancer cell populations, cell fate decisions do not appear to
be genetically predetermined, because sister cells can undergo
different cell fates (Gascoigne and Taylor, 2008). Variability may
also result from noise in gene expression (Elowitz et al., 2002;
Losick and Desplan, 2008;Raychaudhuri et al., 2008;Spencer
et al., 2009).
Stochasticity requires both a means to generate noise but at the
same time mechanisms to stabilize decisions reached in response
to it. Noise alone is insufficient to create binary switches between
alternative cell fates and therefore mechanisms to amplify fluctu-
ations are necessary to stabilize one choice or another (Losick and
Desplan, 2008). Stochastic choices can make cells autonomous and
cell fate decisions may be independent of other nearby cells.
If cells affect each other during an experiment, the assay may
not be “ergodic” due to collective effects. Ergodicity is a central
term in mathematical statistics and it is often implicitly assumed
in many experimental settings. The assumption can mean that
the average over individuals in a cell population due to a bulk
treatment reflects the average over many cell assays. Interactions
between cells may make this assumption unrealistic and can in
principle make averages of measures from different assays not
directly meaningful. It is well known that simple ways of interac-
tions between individuals can lead to complex collective behavior
in higher organisms (for example flocking). There should be no
reason to assume “simpler” statistics for cells.
A major challenge is to identify what aspects of cellular vari-
ability bear significant biological meaning (Li and You, 2013).
A variety of sources can induce diversity, which may presum-
ably not be critical for its biological role. Variability may stem
from redundant perturbations and a source of randomization can
create variation in different mechanisms. It is unclear, however,
to what extent and under what situations cellular mechanisms
are used to exploit gene expression variability that can affect cell
phenotype (Blake et al., 2006). Research on the yeast S. cerevisiae
reveals that increased variability in gene expression can provide
an evolutionary advantage. Blake et al. (2003) and Becskei et al.
(2005) suggested that variation in the rates of transition between
different states of promoter activity in the TATA box may play a
role in determining the level of stochasticity in gene expression.
The sequence of the TATA box can, therefore, enable cell–cell vari-
ability in gene expression being beneficial after an acute change in
environmental conditions (Blake et al., 2006).
This work demonstrates that cell tracking can provide infor-
mation on cellular variability. Tracking many objects in changing
environments has in general many applications and work on it
has a long history over 50years and now entering also biomed-
ical research (Mallick et al., 2013). Cell tracking is an emerging
technology based on treatment of cells (labeling and contrast
enhancements), various imaging techniques (microscopy) and
also algorithms for automatic feature extraction. The initiative
Open Bio Image Alliance1reflects this development organizing
competitions on cell tracking (so-called “challenges”) to promote
development of open-source software for cell tracking. Sacan
et al. (2008) represents an early contribution in this develop-
ment. Note that cell feature extraction from images can help to
resolve ambiguities during multi-target tracking. The capacity
to distinguish between individual cells is, therefore, relevant to
relax requirements on data collection or to increase reliability.
Holmquist et al. (1978) represents an early attempt to formalize
1http://www.openbioimage.org/
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Korsnes and Korsnes Lifetime distributions from cell tracking
automatic feature extraction. There are numerous similar later
attempts, which may be relevant for joint tracking and classifying
of many cells (Mattie et al., 2000;Wei et al., 2008;Basu et al., 2014;
Jusman et al., 2014), and which can serve to apply theory of joint
multi-target classification and tracking (Mahler, 1994;Goodman
et al., 2013).
The present work illustrates possible information gain from
computer-assisted tracking of individual BC3H1 cells after expo-
sure to YTX. The actual tracking was based on visual control
via computer terminal to produce reliable lifetime data. A real-
istic way to develop systems for quick and low cost estimation
of individual cell lifetimes is first to develop a usable “hybrid”
approach where automatic algorithms gradually replace visually
based control. This strategy allows early to produce lifetime statis-
tics without bias due to automatic algorithms tending to lose
tracks of, for example, specially long living or motile cells.
Following many cells over time can promote awareness of
sub-populations and other types of diversity not otherwise easily
detected. It can potentially complement measurements of the
proteomic dynamics and gene sequencing in individual cells and
contribute to clinical assessments. Results from such tracking
may also help to reverse engineer cellular processes to develop
simulation models for better prediction of how toxins may affect
organisms.
2. YESSOTOXIN
Yessotoxin (YTX) is a small molecule marine polyether com-
pound produced by dinoflagellates and which can accumulate
in filter-feeding bivalves (Murata et al., 1987;Ogino et al., 1997;
Satake et al., 1997;Draisci et al., 1999;Paz et al., 2004). It has
numerous analogs (Miles et al., 2005). The understanding of its
mechanisms of action in cells is developing (Malaguti et al., 2002;
Alfonso et al., 2003;Malagoli et al., 2006;Korsnes et al., 2007,
2013;Martín-López et al., 2012;Fernández-Araujo et al., 2014,
2015;Rubiolo et al., 2014). It can at low concentrations induce
various cytotoxic effects and programed cell death mechanisms
in different types of cells (Leira et al., 2002;Ronzitti and Rossini,
2008;Young et al., 2009;Korsnes and Espenes, 2011;Korsnes
et al., 2011). The diversity of toxic responses raises attention for
potential medical and therapeutic applications of YTX (López
et al., 2008, 2011b;Korsnes, 2012;Alonso et al., 2013;Alonso and
Rubiolo, 2015;Fernández-Araujo et al., 2015).
The specific molecular target of YTX is generally unclear. How-
ever, phosphodiesterases, heterogeneous nuclear ribonucleopro-
teins (hnRPps), heat shock, and Ras proteins have been reported
as YTX targets in human lymphocytes, HepG2 cells, and blood cell
membranes (Alfonso et al., 2003;Young et al., 2009;Ujihara et al.,
2010). The specific organelle targets appear to be the mitochon-
dria and the ribosome (Bianchi et al., 2004;Korsnes et al., 2006a,
2014).
3. MATERIALS AND METHODS
3.1. Toxin
YTX was provided by Christopher. O. Miles at the National
Veterinary Institute of Norway. YTX was dissolved in methanol
as a 50-µM stock solution. The stock solution was diluted in
Dulbecco’s modified Eagle’s medium (DMEM, Sigma) achiev-
ing a final concentration of 100nM YTX and 200 nM in 0.2%
methanol. Control cells were incubated with 0.2% methanol as
vehicle. Control cells and treated cells were exposed up to 48 h.
3.2. Cell Culture
BC3H1 cell lines were isolated from primary cultures derived
from mouse (ATCC Number CRL-1443). BC3H1 cells closely
resemble cells in an arrested state of skeletal muscle differentiation
than smooth muscle cells (Schubert et al., 1974;Taubman et al.,
1989). Both cell lines were purchased from the American Type
Culture Collection (Manassas, VA, USA) at a seeding density of
2×106cells per cm2. Cells were maintained undifferentiated at
37°C in a humidified 5% CO2atmosphere.
3.3. Time-Lapse Video Microscopy
BC3H1 cells were plated in 35 mm ×10 mm glass bottom dishes
(Willco, USA) for time-lapse imaging. Cells were cultured in
medium (DMEM with phenol red, containing 50 nM Hepes,
7.2pH, and 20% fetal bovine serum). The temperature in the
box was maintained at 37°C using a heat controller. Cells were
observed in a Zeiss LSM 700 microscope and analyzed using
the phase contrast optics. All images were taken using a Plan
Apochromat 20×/0.8 ph2M27 objective. The time-lapse images
were generated using a ZEN 2010 imaging software. Cells were
continuously imaged each 2.5 min for up to 48 h by time-lapse
microscopy using phase contrast optics. Tracking of randomly
selected cells through these sub-sequential images provided direct
samples of lifetimes of cells.
3.4. Cell Tracking
The time-lapse video microscope provided images in jpeg format
for each 2.5 min. The co-author (Reinert Korsnes) developed a
computer program to support cell tracking through these images.
It was written in Ada 2012 using for graphics the GLOBE_3D
system developed by Gautier de Montmollin.2The Ada compiler
was GNAT Ada from AdaCore.3A common type laptop computer
running Linux was used for processing.
The present cell tracking is computer-aided and not fully auto-
matic. The computer program, which we developed, kept track of
a user controlled cursor pointing on a cell in a video on a desktop
screen (this design makes it ready to include automation support).
This video did consist of displaying images originally in jpeg
format from the microscope. No special image treatments were
applied. The user could affect the display of the image sequence
(enlargement, speed, and direction in time). Figures 1 and 2
illustrate the imagery data. The computer program did for each
track generate a random position more than 100 µm from the
image border. The nearest cell inside this inner zone of the image
at start of recording, then, was chosen for tracking. The reason
to choose (by random) cells away from the image border was
to avoid that they moved outside the image scene before dying.
150 cells were tracked in each experimental well. Few of these
2http://globe3d.sourceforge.net
3http://www.adacore.com/
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Korsnes and Korsnes Lifetime distributions from cell tracking
FIGURE 1 |Phase contrast image of BC3H1 cells short after YTX
exposure.
cells (less than ten) did divide during tracking. A track followed
by random one of the daughter cells, when it encountered a cell
division. No tracks were lost.
The lifetime of a cell was defined as the duration from start of
toxin exposure to when it died. Cells in the image scene normally
moved and changed shape at least each 10–20 min. A significant
part of the cells did undergo a necrosis-like death rounding up to a
steady shape. When finding a cell reached this steady state, the cell
track was followed back in time to detect the time of start of this
steady state. This time was defined as time of death. The present
estimate of this time was within a precision of less than 30 min.
Tracked cells undergoing apoptosis-like death in the way that they
fractionated during few minutes, were given time of death at the
moment of this event. The above procedure is relatively simple to
implement as a computer algorithm.
3.5. Kernel Density Estimation
Let the stochastic variable Trepresent lifetime of a randomly
selected cell after being exposed to a toxin. The kernel density
estimation (KDE) provides a non-parametric way to reconstruct
the probability density of Tfrom random samples (Rosenblatt,
1956;Parzen, 1962). Let t1,t2,...,tnrepresent such samples
(measurements) of lifetimes for nrandomly selected cells. Assume
a distribution m(probability measure) equally concentrated on
the points t1,t2,...,tnof the real line such that
m({t}) = 1
nif t∈ {t1,t2, . . . , tn}
0 otherwise (1)
Given the Gaussian kernel:
K(t) = 1
√2πe−t2
2(2)
which for h>0 gives a family of kernels Kh(t) = 1
hK(t
h)conserv-
ing its integral Kh(x)dx =1. The parameter there repre-
sents time and his termed bandwidth. The convolution between
the discrete (singular) measure mand a kernel Khgives a “smooth
version” phof the distribution m:
ph(t)=(Kh∗m)(t) = R
Kh(t−s)dm(s)(3)
This smooth (“diffused”) version of the singular measure m
is considered as an estimate of the distribution of the original
stochastic variable Tabove. The present work applies kernel
density estimation on the above simple level justified by the
principle of Occam’s razor. Note, however the similarities of the
above convolution [Eq. (3)] and diffusion (for example physical
heat conduction) provide inspiration for more precise estimation
(Botev et al., 2010;Berry and Harlim, in press).
3.6. Weibull Analysis
The Weibull distribution is known as “Type 3” of three possible
types of approximate distributions of the extreme (maximum or
minimum) of a set of random variables (Fisher and Tippett, 1928;
Leadbetter et al., 1983). It covers the case where the extreme
value has a light tail with finite upper bound. It is a versatile
and widely used model for lifetimes of successful functioning of
systems in general. Its applicability is so wide that lifetime (or
failure) analysis has been termed “Weibull analysis.” A convex
combination of two Weibull distributions can express the distri-
bution of life length of systems of two possible (but unknown)
types.
A single population two parameter Weibull probability density
distribution has the following form:
f(t;λ, k) = k
λt
λk−1e−(t
λ)k
if t≥0
0 otherwise (4)
where kis a shape parameter and λhere defines time scale. The
corresponding cumulative distribution is
F(t;λ, k) = 1−e−(x
λ)k
(5)
Assume the convex combination of two Weibull distributions:
f(t) = ω1f(t;λ1,k1) + ω2f(t;λ2,k2)(6)
where ω1+ω2=1 and ωi≥0. f(t) is also a probability density
function (non-negative and with integral equal to 1). The corre-
sponding cumulative distribution is
F(t) = ω1F(t;λ1,k1) + ω2F(t;λ2,k2)(7)
4. RESULTS
Subsequent phase contrast microscopy images in this work pro-
vide lifetime distributions for BC3H1 cells after YTX exposure.
Figure 1 shows an example of such an image at start of exposure,
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Korsnes and Korsnes Lifetime distributions from cell tracking
FIGURE 2 |Example of subsequent images of BC3H1 cells exposed to 100 nM YTX. Images taken at 2.5min interval. The time of image 1 is 30h treatment
after exposure to YTX. The white arrow illustrates tracking of a cell, which dies during the time of image 6–9.
whereas Figure 2 shows subsequent similar images after 30 h of
exposure. The cells obviously do not behave uniformly. Some
of them exhibit apoptotic-like cell death morphologies, whereas
others appear to die necrotic-like (Figure 3). Figure 4 shows
kernel density estimates [cf Eq. (3)] of distributions for observed
lifetimes of BC3H1 cells after the start of exposure to YTX at
concentrations of 100 and 200 nM. The bandwidth his, here,
according to Silverman’s rule of thumb (Silverman, 1986;Bowman
and Azzalini, 1997). The distribution for 100nM has a significant
upper tail indicating a mixture of mechanisms in action when the
cells die. A single peak seems to dominate the distribution for
200 nM.
Successful parametric ways to reconstruct probability distri-
butions from measurements typically require fewer samples as
compared to non-parametric ways, or it can provide more pre-
cise results given the same data. This is intuitively reasonable
since the approach exploits restrictions on the set of possible
outcomes from experiments and in this simple way represents
sparse sampling or compressive sensing. Optimal use of data
is here of interest in possible applications of cell tracking since
tracking may cost and early information on lifetime distributions
(over many days) may have direct interest in clinical situations
(for example to monitor and control development of cancer).
Parametric reconstruction can also support understanding of
underlying processes. Figure 5 shows an attempt to fit a mixed
(bimodal) Weibull model [Eq. (7)] to the same lifetime data,
as in Figure 4. It shows the result from fitting this model to
the empirical distribution function (varying the parameters: k1,
λ1,k2,λ2,ωicondition on ω1+ω2=1, ωi≥0). Figure 5 also
illustrates the probability density function for these parameters
[cf Eqs (4) and (6)].
Cells may affect each other in experimental wells via, for
example, cytoskeletal contacts and in ways affecting survival after
toxic exposure. Hence, the lifetimes of cells in the same exper-
imental well may not be independent giving somehow different
lifetime distributions for cells in distinct wells. Figure 6 illustrates
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Korsnes and Korsnes Lifetime distributions from cell tracking
FIGURE 3 |Two sequences of four images respectively showing typical apoptotic- and necrotic-like death events among BC3H1 cells exposed to
yessotoxin. The necrotic-like cell death process is much slower than the apoptotic-like cell death.
FIGURE 4 |Kernel density estimates of distributions of lifetimes of
BC3H1 cells after YTX exposure at concentrations 100 and 200 nM.
Vertical bars indicate individual observations (samples).
this possible effect showing lifetime distributions of BC3H1 cells
exposed to 100 nM YTX in four different populations (experi-
ments). The distributions significantly vary despite carefulness to
repeat the experiments the same way.
5. DISCUSSION
The present experiments show examples on how cells in the same
cell line can display individual variation in their response to a toxic
exposure. Korsnes (2012) showed still photos illustrating diversity
in cell death response after YTX exposure. Sub-sequential images
provide more reliable interpretations since it gives information
from before and after given time points. Tracking from time lapse
of living cells may therefore, when the appropriate instrumenta-
tion and software tools become more available, be a valuable tool
to estimate how cells react to stress. Clarification of the biological
significance of the present observed variations, however, needs
further investigations. For example, Figure 5 indicates two dom-
inating mechanisms of cell death, but lifetime data from similar
experiments do not exhibit the same structure.
Differences in cell fate decisions in isogenic populations have
been explained by oncogenic lesions, which are genetically pre-
determined, cell-cycle state or as a result of their lineage or their
proximity to an inductive signal from other cells (Rieder and
Maiato, 2004;Weaver and Cleveland, 2005). However, stochastic
distributions of cell fates can also take place independent of cell
cycle or history (Losick and Desplan, 2008;Spencer et al., 2009).
Different mechanisms for cellular variability may be biologi-
cally significant and therefore evolutionary conserved. Examples
of such mechanisms in multi-cellular organisms driving specific
cell fates where stochastic activation is coupled in some cases
with a positive feedback loop or in other cases with a negative
feedback regulation, have been described (Heitzler and Simpson,
1991;Serizawa et al., 2003;Lomvardas et al., 2006).
Mechanisms that have evolved to exploit stochastic variation
at the level of single cells or whole tissues during development
may also operate at much higher levels of biological organiza-
tion, such as insect colonial organisms (Hölldobler and Wilson,
2008). Stochastic establishment of gamer-gates may be favored
by natural selection to ensure the emergence of reproductive
individuals upon the demise of the queen. When the queen or
other gamer-gates die, the colony must maximize its potential for
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Korsnes and Korsnes Lifetime distributions from cell tracking
FIGURE 5 |Results from mixed Weibull analysis giving estimates of distributions of lifetimes of BC3H1 cells after YTX exposure at concentrations 100
and 200 nM. The parameters for the mixed Weibull distribution (kand λ) result from model fit to the empirical cumulative distribution (right). Red vertical bars indicate
individual observations (samples). The smoothed histograms K1.0 ×mand K0.5 ×m[cf Eq. (3)] are here for visual control and illustration.
FIGURE 6 |Kernel density estimates of distributions of lifetimes in four
separate populations of BC3H1 cells after exposed to 100 nM YTX
(i.e., each of the four populations were in separate experimental
wells). Influence between cells in the same well may explain the difference
between the distributions. These variations between distributions can,
therefore, potentially provide measures of such inter-cellular influence.
replacing these reproductively dominant individuals, which may
otherwise be limited by deterministic rules (Kilfoil et al., 2009).
It may be reasonable to speculate that randomization in cell
populations can have a function in contexts of optimization. It
is a common experience in computer science, soft programing
and practice in artificial learning systems that randomization
can offer the simplest distributed search for optimal solutions or
states. Concepts from theory on communication networks may
also support understanding of cellular variability. Randomization
often plays a role in decentralized control and signaling in net-
works with local autonomy. Distribution of roles between enti-
ties generally requires communication (signaling). Analogies to
collaborative behavior among higher organisms may also help to
understand potential significance of variability among cells. Indi-
viduals of higher organisms typically have to prioritize between
mutually exclusive activities. Randomization can be part of a
system for decentralized distribution of roles to achieve synergies.
Variability may also play a role in the innate immune system to
obstacle intrusion.
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Korsnes and Korsnes Lifetime distributions from cell tracking
Exchange of information can facilitate specialization where
minorities in cell populations can function as sensitive sensors
reporting to the others. Sensitivity, control and signaling have
typically a cost in terms of energy and risk. It is, for example,
a generic fact that sensitive sensors are vulnerable. The decision
to take the role as special (sensitive and “expendable”) sensor on
behalf of the majority should, therefore, presumably be taken by
random with appropriate low probability.
The present recordings of BC3H1 cells after YTX exposure
allow following single cellular events as seen in Figures 2 and 3.
Individual cell variation in a clonal cell population is greater than
previously recognized. Cells exhibit complex fates over time and
they behave differently. Their cytoskeletons undergo extensive
remodeling until they reach loss of motility before they die. Cells
interact between each other and it is conceivable to believe that
they might receive inductive signaling from neighboring cells.
This can make correlations of lifetimes of cells in the same exper-
imental dish and hence give different distributions derived from
distinct dishes.
Precise estimates of lifetime distributions may provide infor-
mation of interest in a variety of cellular studies and toxicology.
The effect of a toxin may, for example, partly depend on cell
cycle. Lifetime distributions may, therefore, be sensitive to phases
in a synchronized cell population. However, caution must be
exercised applying artificial cell synchronization. Eventual loss of
cell synchrony can occur because not all the cells progress through
the cell cycle at the same rate (Engelberg, 1964;Murphy et al.,
1978). In fact, variability of cell-cycle kinetics is inherent from
cell to cell and occurs to some extent using any synchronization
method (Davis et al., 2001).
Different sets of samples of a stochastic variable (such as life-
time of a cell) will exhibit the same distribution if they were
independent. However, samples of lifetimes of individual cells in
separate experimental dishes tend to have different distributions.
Hence, cells in the same dish do not seem to live independently.
Figure 6 shows four distributions of lifetimes of BC3H1 cells
after exposure to 100 nM yessotoxin. The distributions are here
respectively from separate experiments where the cells are in the
same Willco dish facilitating potential inter-cellular influence. The
variability of the distributions may not be due to experimental
errors but rather result from stochastic choices and cell–cell inter-
actions. A statistical challenge is to test if a given observed dis-
tribution belongs to a family of distributions resulting from such
an experiment. Traditional statistical assessments for equality of
distributions like the Kolmogorov–Smirnov test will not apply in
this situation. The treatment of these types of data may provide
information on inter-cellular influence in cancer cells and help to
predict their probability of metastasis. It may also help to detect
change in cell populations during treatments and provide early
warning for more detailed clinical investigations.
AUTHOR CONTRIBUTIONS
MK conceived the study and conducted the laboratory experi-
ments, RK made the computer programming; both authors ana-
lyzed the results and wrote the manuscript.
ACKNOWLEDGMENTS
This study was supported by Olav Raagholt og Gerd Meidel
Raagholts legacy, Astri og Birger Torsteds legacy, and Giske og
Peter Jacob Sørensen research foundation. The work was also
supported by internal funding at the Norwegian University of Life
Sciences (NMBU).
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