Materials
Male Fisher 344 rats were purchased from Japan SLC (Shizuoka, Japan). The rat aorta smooth muscle cell line, A7r5, was obtained from DS Pharma Biomedical Co. Ltd (Osaka, Japan). The human cervical cancer cell line, HeLa, and the human osteosarcoma cell line, HOS, were obtained from the Health Science Research Resources Bank (Osaka, Japan). Cell culture medium was purchased from Sigma-Aldrich (St. Louis, MO). Fetal bovine serum (FBS) was purchased from JRH Biosciences (Lenexa, KS). Antibiotics were purchased from Life Technologies Japan Ltd. (Tokyo, Japan). Other reagents were purchased from Wako Pure Chemical Industries Ltd. (Osaka, Japan), Sigma-Aldrich, and Life Technologies Japan Ltd.
Preparation and culture of rat mesenchymal stem cells
Rat mesenchymal stem cells (MSCs) were isolated and primarily cultured as previously described [24]. Briefly, bone marrow cells were obtained from the femoral shafts of 7-week-old male Fisher 344 rats, which were anesthetized and euthanized by exposing of carbon dioxide. The cells were obtained from at least two rats and pooled in order to reduce the influence of individual differences. The culture medium was Eagle’s minimal essential medium (with Earle’s Salt and l-glutamine) containing 15% FBS and antibiotics (100 units/mL penicillin G, 100 µg/mL streptomycin sulfate, and 0.25 µg/mL amphotericin B). The medium was replaced twice a week, and cells at passages 2–3 were used in this study. This study was carried out in strict accordance with the recommendations in the Guide for the Care and Use of Laboratory Animals of the University of Kitakyushu. The protocol was approved by the Committee on the Ethics of Animal Experiments of the University of Kitakyushu.
Cell culture
A7r5 cells, HeLa cells, and HOS cells were cultured in DMEM supplemented with 10% FBS and antibiotics (100 units/mL penicillin G, 100 µg/mL streptomycin sulfate). The medium was replaced twice a week.
Cell staining
Cells were seeded in a 35-mm culture dish at around 1 × 104 cells/cm2. The cells were fixed with 4% paraformaldehyde and stained with 0.4% trypan blue solution. The cells were imaged at 8.4× magnification using a stereomicroscope (SZX12; Olympus, Tokyo, Japan) equipped with a DP70 color charge-coupled device camera (Olympus).
Image extraction of cell distribution
The obtained cell images were analyzed using Image J software (NIH, Bethesda, MD). Each cell image was split into each RGB color channel. Then, the red channel image, which was the image with the highest contrast against the background, was subtracted from the background light shadow. The image was binarized with the adequate threshold intensity value, which was determined by referring to the highly magnified image. The size of the square image was dependent on each cell type (rat MSC, 3.5 × 3.5 mm; Hela and HOS cells, 3 × 3 mm; A7r5 cells, 4 × 4 mm). After clipping the square image from the binarized image, the resolution of the image decreased to 100 × 100 px. The clipping cell size was determined by the area of approximately 1 × 104 cells. We prepared more than five images for each condition.
Cell dynamics simulator
Simulator specification
The 2D cell simulator was developed using Java (Oracle, Redwood Shores, CA). The cell distribution of the simulator was modeled by the cellular automata. The calculated space was set to 120 × 120 cell units and the displayed space on the screen was 100 × 100 cell units of the center of the calculated space (Fig. 1). Each unit indicates whether it is occupied by cells (black point) or it is vacant (white point). The model includes cell movement and division regulated by cell–cell interactions (cell–cell adhesion inhibits cell movement and cell–cell contact inhibition inhibits cell division). One cycle of the calculation of cellular events (movement and division) indicates 10 min in a virtual environment. Because cells in the early stages of cell culture exhibit a proliferation lag, we simulated cell proliferation behavior after 24 h of culture. Therefore, the cell seeding number, s
0
, was used to represent the cell number after 1-day culture in each cell type.
Cell dynamics
Each cell unit contacts the neighboring 8 units (Fig. 2). According to a previous study using cellular automata dynamical simulation of cell culture [21], the influence probabilities for the center unit from the neighboring 8 units are 1/12 and 2/12 at a diagonal position (P
inf×) and a side position (P
inf+) of a center unit, respectively (Fig. 2). Each influence probability was derived from the ratio of the central angle to 2π rad on a circle with a radius equal to the length of one side of the unit square.
Figure 3 shows a flowchart of the cellular automata simulation. The method of cellular automata was applied in all cell occupied units.
The cell movement event is produced according to the probability, P
mot
, which depends on the cell motility parameter mot; P
mot
= 1/(6 mot). The mot means the time (h) for a single unit transfer of the cell on average. During the cell movement event, the cell can escape from the event according to the influence of the surrounding cells. The total influence of surrounding cells, P
su
, is determined based on the influence probabilities, a diagonal position of cell number n
×, and a side position of cell number n
+, P
su
= n
×
P
inf× + n
+
P
inf+ = (n
× + 2n
+)/12.
Using the cell–cell adhesion parameter a, the cell escapes from the movement event with the probability, P
motesc
,
$$P_{motesc} = 1 - \left( {1 - \frac{a}{100}} \right)^{{12P_{su} }} .$$
If the cell does not escape from the event, the cell moves around a vacant unit depending on the influence probabilities.
The cell division event is produced according to the probability, P
div
, which depends on the cell doubling time (h) t
d
,
$$P_{div} = \, {\alpha \mathord{\left/ {\vphantom {\alpha {\left( { 6t_{d} } \right)}}} \right. \kern-0pt} {\left( { 6t_{d} } \right)}}_{,}$$
where α (=0.7147) is the offset of the cell division due to overlap with the immediately preceding cell division. During the cell division event, the cell can escape from the event according to the influence of the surrounding cells. The total influence is determined by the influence probabilities (P
inf×, P
inf+) and the cell number of the diagonal position and the side position of the cell, ci = 12 n
×
P
inf× + 12 n
+
P
inf+ = n
× + 2 n
+. According to the cell–cell contact inhibition parameters, the cell escapes from the division event with the probabilities P
ci
. The P
ci
can be fixed arbitrarily; but, in this study, we used four different parameters as null (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1), weak inhibition (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.9, 1), positive inhibition (0, 0, 0, 0, 0, 0, 0, 0, 0.4, 0.8, 0.95, 1), and strong inhibition (0, 0, 0, 0, 0, 0.3, 0.6, 0.8, 0.9, 0.96, 0.99, 1). If the cell does not escape from the event, one of the daughter cells occupies a surrounded vacant unit depending on the influence probabilities, and the other daughter cell occupies the unit of the original mother cell.
Estimation of cell proliferation parameters
The simulated cell proliferation parameters could be estimated from the growth curve and cell proliferation images. Cell proliferation was serially simulated with various cell proliferation parameters. Then, the simulated cell number was evaluated and rated by comparing with the experimentally obtained data using least square analysis. Within the several higher conditions, the most matching parameters were finally determined by visually comparing the simulated cell images with the experimentally obtained cell images.