Animals and experiments
Sixteen eight week old pfp/rag2 mice and twenty eight week old rag2 mice were used for this experiment. The mice were C57BL6 (pfp/rag-2) mice obtained from Taconic, Hudson, NY (# 001177-MM; B6.129S6-Pfp(tm1)Cirk-RAG2(tm1)Fwa, N12). Both strains of mice were kept under pathogen-free conditions in individually ventilated cages (IVC-Rack, Techniplast Germany) and were fed with sterile standard food (ssniff, Soest, Germany) and water ad libitum. The animals were killed when the tumors started to ulcerate or when the tumor weight exceeded 20% of the original mouse body weight at the beginning of the experiment[
43].
The experiment was supervised by the institutional animal welfare officer and approved by the local licensing authority (Behörde für Soziales, Gesundheit, Familie, Verbraucherschutz; Amt für Gesundheit und Verbraucherschutz, Hamburg, Germany, project No. G 09/58).
Cell culture
The human colon adenocarcinoma cell line HT29 was purchased from the European Cell Culture Collection (Porton Down, Wiltshire, UK). Cells were grown in RPMI 1690 – L-Glutamine (GIBCO, Invitrogen Corp., Grand Island, NY) medium supplemented with 10% fetal calf serum, 1% penicillin and streptomycin and cultured in a humidified atmosphere of 37°C and 5% carbon dioxide.
Each mouse was injected subcutaneously with one million viable tumor cells suspended in 200 μl culture medium RPMI 1690 + L-Glutamine (GIBCO, Invitrogen Corp., Grand Island, NY) between the scapulae.
Histology
After sacrificing the animals primary tumors were excised and fixed in 4% buffered formaldehyde for 24 h and rinsed with phosphate buffered saline. The tissues were then dehydrated in a series of graded ethanol and embedded in paraffin wax. Five μm thick sections were cut and stained with haematoxylin and eosin (H.E.).
In order to achieve a random distribution of the lung, the lungs were fixed en bloc and were sectioned after fixation into one mm thick lung slices. The slices were placed in warm agar and pressed down with a glass piston. After hardening of the agar the lung slices were processed to paraffin wax.
The agar blocks containing the lung slices were sectioned into five μm thick sections. The total number of sections of each lung was noted. In addition to every 10
th section, two series of serial sections (n = 30) out of the middle of the paraffin wax block were preserved for further immunohistological evaluation. Ten of the 10
th sections containing the most lung pieces of each wax block were H.E. stained. Metastases were counted in each of the ten stained sections under a microscope (Zeiss, Axioplan2). The number of metastases of each mouse was calculated by using the following term (Mean number of metastasis * total number of sections – 20%), according to an earlier established formula[
44].
DNA extraction and real-time PCR for detection of circulating tumor cells
DNA extraction of murine blood was performed using the QIAamp DNA Blood Mini Kit and for DNA isolation of cell culture cells the QIAamp DNA Mini Kit (Qiagen, Hilden, Germany) was used, according to manufacturers′ instructions. Real-time polymerase chain reaction (PCR) and melting curve analyses were performed in glass capillaries with the Light Cycler 2.0 System. For the real-time PCR, the LightCycler Fast Start DNA MasterPLUS SYBR-Green I Kit (Roche Diagnostics GmbH, Mannheim, Germany) was used. Two μl of DNA solution was used as a template for the PCR reaction and incubated in a total reaction volume of 10 μl, containing 1x SYBR-Green I Master mix including Taq DNA polymerase, Taq PCR buffer, a dNTP mixture and 1 mmol/l MgCl2-, 10 pmol specific Alu primers. Forward Alu primer (TGG CTC ACG CCT GTA ATC CCA) and reverse Alu primer (GCC ACT ACG CCC GGC TAA TTT) were synthesized by MWG Biotech AG (Ebersberg, Germany). The PCR conditions were initially 10 min. 95°C, followed by 50 cycles of 5 s 95°C, 5 s 67°C and 20 s 72°C (measurement of fluorescence). Melting curve analysis (0 s 95°C, 12 s 65°C and 0 s 95°C) was performed directly after each PCR run[
45]. To quantify circulating tumor cells a standard curve with 10 fold dilution of extracted DNA from 1×10
6 cell culture cells HT29 was established. Control probes were isolated from mouse blood without inoculated tumor cells. Human tumor cells were quantified by real-time polymerase chain reaction (PCR) using established primers specific for the human alu sequences as previous described. For each sample, analyses were performed in triplicates and performed as independent experiments at least twice.
Quantitative methods and statistics
The percentage of cells showing mitotic figures in ten different areas of the tumor, delineated by an eyepiece graticule (310 μm2), was determined by counting a minimum of 500 cells from each animal. The areas of measurement were standardized: one corner of the eyepiece graticule was positioned at the tumor-host interface with an objective lens of magnification 10 and counting of the mitotic figures was carried out at the same site using an objective lens of magnification 400. Only cells that were in easily recognizable meta- and anaphases were counted as mitotic.
All values are presented as mean values. Statistically significant differences between both samples were calculated by a Mann–Whitney U test. Graph Pad Prism 6.0 (Intuitive Software for Science, San Diego, CA, USA) was used for statistical calculations. Differences were considered significant at p <0.05.
Simulating the cancer spread
Computer simulations of cancer spread were performed in order to identify parts of the metastatic progress most influenced by NK cells. A previously developed computer model uses a discrete event simulation approach to analyze the metastatic progression[
30,
31].
The main components of the computer model are so called compartments. They describe all parts that contain malignant cells such as the primary tumor, blood and distant metastases. The primary tumor and metastases are modelled as “continuous” compartments utilizing mathematical functions to describe the growth and spreading behavior of the tumor.
The growth of the primary tumor and metastases is modelled by a Gompertzian growth function that describes a sigmoid course:
(1)
The function x(t) provides the number of cells in the tumor at the time t. The parameter a represents the growth rate constant while b represents the size of the tumor at its saturated level. The parameter t
0
allows to comprise a start size of the tumor, e.g. if the primary tumor starts as a single cell t
0
will be 0. If the tumor starts as a cluster of cells, due to the injection of tumor cells into the mouse, t
0
can be parameterized to display the size of the cluster. If a start size is given, t
0
is automatically computed via an inverse function by the simulation software.
In this work it was assumed that 104 cells of the injected one million tumor cells survived in the mice to form the primary tumor. Simulations with 103 and 105 cells were equally performed, but since the results do not differ significantly only results for 104 cells are shown.
For the maximum tumor size b a value of 4.5 g was assumed. This value was estimated based on the experimental data. The value of the primary tumor growth rate constant a was computed using the determined mean values for the primary tumor weight and the duration of the experiment. The values are presented in the Results section.
The spread of metastases is described by the colonization rate
β(
x):
where
x is the number of cells in the tumor,
m is the colonization constant and
α is the fractal dimension of blood vessels infiltrating the tumor which describes how well the tumor is supplied with blood. This value was assumed to be 0.663 which describes a superficial vascularity of the primary tumor[
47]. This seems plausible since the primary tumor grows very fast. The colonization constant
m was derived from the experimental data and is presented in the Results section.
To save computation time the colonization rate β(x) models only those malignant cells that eventually are able to establish a new metastasis. The so described cells can be killed by NK cells in the model. All disseminated tumor cells that die due to other factors than NK cells, either in the blood stream or in distant tissue are not displayed by β(x).
The blood is modelled as a “discrete” compartment where the behavior of cells is described employing events only. An event describes what happens in a compartment at a specific time, e.g. intravasation, apoptosis or extravasation. The probability with which different types of events occur can be parameterized for each discrete compartment.
Starting with the primary tumor that grows according to the function x(t), the first intravasation event is created conforming to the colonization rate β(x). After processing the intravasation event a new event is created which describes what happens next to the cell in the blood compartment, e.g. get killed by NK cells or extravasate and create a new metastasis. The probability of NK cell induced cell death in the blood compartment was determined based on the experimental data, as described in the Results section. Furthermore, the next intravasation event for the primary tumor is created conforming to the colonization rate β(x).
New metastases also grow according to the function x(t). Three different growth rate constants were considered for the lung metastases: 1/3, 1/2 and the same growth rate constant as the primary tumor. Metastases from metastases were neglected in the simulations, since the metastases are too small to be able to spawn metastases by themselves in the short duration of the experiment.
To determine why the metastases in pfp/rag2 and rag2 display the observed difference in size a potential dormancy of 21 and 30 days with a standard deviation of 7 days of the lung metastases was simulated. For modelling details on dormancy see next section.
A snapshot of the simulated system, containing the actual time, the size of the primary tumor, the number of metastases, the number of cells in all metastases and a size histogram of all metastases, is saved at a parameterizable interval. After the simulation covered a determined time span it will stop. Each configuration is simulated 100 times. Afterwards the mean and the standard deviation are computed.
A detailed description of the simulation process can be found in[
30] and[
31].
Simulating dormancy and late dormancy
To simulate dormancy an extended version of the growth function stated in equation (
1) was introduced to the computer model:
(3)
The parameter
t
d
and
t
ld
allow comprising dormancy and late dormancy[
48‐
50] into the simulation. They display the duration of the dormancy phases. The duration can be parameterized with mean and standard deviation.
When a new metastasis is created which undergoes a dormancy phase, its status is set to “dormant” and the exact duration of the dormancy
t
d
is computed based on the stated mean and standard deviation. As long as the metastasis is in dormant state the simulation software will return a value of 1, whenever the size of the metastasis is enquired. As soon as the computed duration of the dormancy elapsed, the status of the metastasis is reset. The metastasis will now start growing conforming to the growth function stated in equation (
3). The parameter
t
d
represents the offset between the creation of the metastasis and the time point when it starts to grow.
When a new metastasis is created which undergoes a late dormancy, the first step is to compute the size at which the metastasis passes into the late dormancy phase. The size is computed based on a parameterizable mean and standard deviation. The time point when the metastasis reaches the computed size is computed via an inverse of the growth function. Until this time point the metastasis will grow unrestricted conforming to the growth function stated in equation (
3) with a value of 0 for the parameter
t
ld
. Similar to normal dormancy its status is then changed into dormant state and the duration of the late dormancy phase
t
ld
is computed based on the stated mean and standard deviation. The simulation software will return the computed size whenever the size of the metastasis is enquired until the late dormancy phase elapsed. After the status of the metastasis is reset it will continue growing conforming to the growth function equation (
3), but with an updated value for
t
ld
to include the accrued offset.