The regulation of many cell functions is inherently linked to cell-cell contact interactions. However, effects of contact interactions among adherent cells can be difficult to detect with global summary statistics due to the localized nature and noise inherent to cell-cell interactions. The lack of informatics approaches specific for detecting cell-cell interactions is a limitation in the analysis of large sets of cell image data, including traditional and combinatorial or high-throughput studies. Here we introduce a novel histogram-based data analysis strategy, termed local cell metrics (LCMs), which addresses this shortcoming.

The new LCM method is demonstrated via a study of contact inhibition of proliferation of MC3T3-E1 osteoblasts. We describe how LCMs can be used to quantify the local environment of cells and how LCMs are decomposed mathematically into metrics specific to each cell type in a culture, e.g., differently-labelled cells in fluorescence imaging. Using this approach, a quantitative, probabilistic description of the contact inhibition effects in MC3T3-E1 cultures has been achieved. We also show how LCMs are related to the naïve Bayes model. Namely, LCMs are Bayes class-conditional probability functions, suggesting their use for data mining and classification.

LCMs are successful in robust detection of cell contact inhibition in situations where conventional global statistics fail to do so. The noise due to the random features of cell behavior was suppressed significantly as a result of the focus on local distances, providing sensitive detection of cell-cell contact effects. The methodology can be extended to any quantifiable feature that can be obtained from imaging of cell cultures or tissue samples, including optical, fluorescent, and confocal microscopy. This approach may prove useful in interpreting culture and histological data in fields where cell-cell interactions play a critical role in determining cell fate, e.g., cancer, developmental biology, and tissue regeneration.

Cell-cell recognition is critical to a wide range of problems in biology and medicine [

Here, CI of proliferation, a known cell-cell recognition phenomenon, is used as a model system for developing algorithms for the analysis of cell-cell recognition from microscopy data. Usually, the effects of cell density on proliferation are studied as relationships between

In this paper, we introduce a complementary approach that allows focused analysis on nearest-neighbor cells, but permits sampling from cultures with high cell densities and use of any type of surface. We had previously applied this technique to screen large image databases from cell cultures on combinatorial libraries of biomaterials[

Poly (DL-lactic-glycolic acid) (PLGA, block copolymer, 50:50 ratio of PGA and PLA, 40,000~75,000 Da) and poly (ε-caprolactone) (PCL, 114,000 Da, M_{w}/M_{n }= 1.43) were obtained from Sigma Aldrich, St Louis, MO. PLGA and PCL, respectively, were dissolved in chloroform to 8% and 5% mass and spin coated on silicon chips (22 × 22 mm). To provide adhesion of these polymers to the silicon during cell culture, the silicon was pretreated with a Piranha etch (70% H_{2}SO_{4}/21% H_{2}O/9% H_{2}O_{2 }at 80°C for 1 h) followed by 1 min in a HF acid bath and a final rinse in DI water (filtered at 0.2 μm).

Established from newborn mouse calvaria, [

Cell proliferation was assayed by BrdU immunohistochemistry. Briefly, PLGA- and PCL-coated wafers were mounted into Costar^{® }6-Well TC-Treated Microplates (Corning, NY). The tissue culture treated polystyrene (TCPS) surfaces of the microplate wells were used as controls. After sterilization (70% ethanol solution, 30 min), MC3T3-E1 cells (passage 6) were seeded onto the coated wafers at 4 × 10^{4 }cells/cm^{2}. This relatively high seeding density was selected to highlight the effects of contact inhibition of cell growth and other space-sensitive cell-to-cell interactions. After seeding, microplates were shaken for 10 min on a shaker (Instrument model, operation frequency) to obtain uniform seeding. Cells were cultured in DMEM (Cellgro^{® }Dulbecco's Modification of Eagle's Medium, Mediatech, Inc., VA) with 10% fetal bovine serum (ATCC^{® }SCRC-1002™, ATCC, VA), L-glutamine and streptomycin at 37°C in a humidified 5% CO_{2 }atmosphere. At 5 h post seeding, surfaces were washed with Dulbecco's Phosphate-Buffered Saline (DPBS, with Ca^{++ }and Mg^{++}) to remove non-attached cells, and fresh culture medium was then added. At 18 h post seeding, 2 mM BrdU (5-bromo-2-φ-deoxyuridine, Sigma, MO) in PBS was added to the culture medium to reach a final concentration of 20 μM. After 6 h of BrdU incorporation, cells were fixed with 3.6% paraformaldehyde and BrdU incorporation was assayed by immunohistochemistry (primary antibody: mouse anti-BrdU, BD Biosciences, CA; secondary antibody: goat anti-mouse, Rhodamine conjugated, Rockland Immunochemicals, Inc., PA; counter staining: Hoechst 33342, Molecular Probes, Invitrogen Corporation, CA).

Low calcium concentration suppresses contact inhibition of cell growth by deactivating calcium-dependent cadherins[^{++ }on cell spreading and proliferation, BrdU incorporation experiments in low Ca^{++ }medium were performed on TCPS surfaces. Fifteen minutes before the introduction of BrdU, cells were rinsed twice with DPBS (without Ca^{++ }and Mg^{++}) and afterword cultured in the low Ca^{++ }medium (0.5% FBS in Ca^{++ }and Mg^{++ }free DPBS)[

Cell locations and proliferation were quantified using fluorescent microscopy (Olympus BX51 Clinical Microscope). A robotic translation stage was used to image predetermined locations on each culture surface using a MicroFire™ monochromic digital camera (SKU S99826, Optronics, CA). The image locations were fixed on a 16 × 20 grid with horizontal and vertical spacing of 1280 μm and vertical spacing of 960 μm. For each location a 1189 × 892 μm^{2 }BrdU staining image and Hoechst counter staining image were acquired at a resolution of 1600 × 1200 pixels^{2}. All images and contextual information were organized and stored in an Oracle^{® }10 g (Oracle, CA) database for further image processing and data analysis.

The Image Processing Toolbox of Matlab™ R14 (MathWorks, MA) was employed for image processing. Due to the volume of image data dynamic, self-adapting algorithms were developed for automated image processing. Binary images of both surface lateral patterns of cell nuclei counter staining were obtained from raw grayscale microscopic images by a

Binary images of cell nuclei were segmented by the _{i }= 0.5, the histogram was divided into resting (background) and proliferating (foreground) parts. Means and standard deviations of the foreground and background, respectively denoted as _{bi}, _{fi}, _{bi}, and _{fi}, were determined by fitting each peak to a Gaussian curve. A new threshold was calculated as _{i+1 }= (_{fi}_{fi }+ _{bi}_{bi})/(_{fi }+ _{bi}) and was repeated until convergence on a stable threshold. Compared with more common iterative selection methods, which use a simple mean intensity, the modified VAIS procedure is more robust when background and foreground intensities have different variances. Indeed, the variance of the BrdU signal intensity from non-proliferating cells was significantly greater than that of the proliferating cells [see Additional File

Cell density and proliferation were described with summary statistics such as number of resting and proliferated cells computed for each image. This provides a set of global metrics for features in each image. As indicated in Figure

Source codes that implement the algorithms presented in this section have been made available by the authors. [see Additional File ^{th }image the number of P-class and R-class cells is _{Pk }and _{Rk}, the distance _{ijk }between the centroids of the nuclei of the ^{th }P-cell and the ^{th }R-cell can be calculated readily from the results of image analysis. In the ^{th }image, the set of all such distances, _{k }is defined as

And for all images an overall set

A set of

where _{0}, _{1}, ..., _{N }is a user-defined distance scale over which analysis is to be performed. The centroid of each interval in _{dist }is defined as

and the resultant centroid set for _{dist }is

The _{dist }is used to sort set

where _{i-1}, _{i}), which is centered at

The total number of elements in set

After normalizing by _{PR}, the frequency function LCM is

and

Normalization is necessary to interpret LCMs in a meaningful manner and to compare the probability of cell responses under different cell environments. One method of normalization is to relate observed occurrences to random occurrences. Given the finite image size and generally non-overlapping nature of cultured cells, the distribution of random cell occurrences is not Gaussian. The random distribution for cell-cell distance, _{std}, was calculated as the any cell-any cell distribution (_{AA}) of 1× 10^{10 }randomly-chosen nuclei positions on a simulated image 1600 pixels by 1200 pixels. The normalized LCM

Other LCMs (_{AA}, _{PA}, _{RR}) are normalized similarly, which allows direct comparisons of different types of cell distances on different surfaces.

In addition to normalizing by the standard distribution, _{std}, direct ratios between LCMs are used also in our analysis, in which case _{std }cancels, as indicated in the next equation.

The ratio _{PR|PA }highlights the specific effects of non-proliferated cells on the central proliferating cell relative to the effects of any given cell. Thus, the probability of cell responses under different cell environments can be compared meaningfully. Furthermore, each set of cell-to-cell distances can be decomposed into subsets, which allows investigation of the contribution of each subset to the overall effect. Therefore, ratios of cell backgrounds may be constructed and used as classifiers for screening and identifying significant cell environment patterns. These ratios also define

where

Applying equations (12) and (13) to equation (11),

Thus, _{k }= {_{k}, _{k}}={_{1k}, _{2k}, ..., _{NPk}, _{1k}, _{2k}, ..., _{NRk}}, and removed self-to-self cell pairs (_{ijk }where _{ijk }where

Furthermore, each set of cell-to-cell distances can be decomposed into subsets, which allows isolation of each subset's contribution. For example, consider _{PR|PA }defined above. As described graphically in Figure _{PR|PA }is transformed into _{PR|PP}. By removing the shared, or overlapping, component _{PR|PP }has higher "contrast" for observing effects of R-cells on P-cells than _{PR|PA}.

Local cell metrics are naturally connected to Bayesian analysis, which is a powerful statistical method used for classification[_{PR }in equation (8), a naïve Bayes model can be established as follows. Consider a "test" cell chosen at random. It is desired to predict the possibility this cell will be in proliferating status, based upon the local environment of non-proliferating cells, which is given by the following conditional probability function

where

In the above function, the components

Assuming the occurrence probabilities around the non-proliferating cell distances

A key development is to notice that

The naïve Bayes model allows prediction of the probability of proliferation as a function of the LCMs,

To provide a benchmark for establishing the effectiveness of local metrics, contact inhibition of cell proliferation was studied using global analysis first. For each image in the database, the overall cell proliferation is plotted versus cell density, shown in Figure ^{2 }of 0.128 (on PLGA) or 0.109 (on PCL), indicating that the contact inhibition effect masked by "noise" in the data. Furthermore, it is obvious that in Figure

Linear Regression from Global Analysis Results from Figure 3

Surface | SSE | R^{2} | RMSE | Adj R^{2} | |
---|---|---|---|---|---|

PCL | -6.106 × 10^{-4} | 0.5314 | 0.1312 | 0.04396 | 0.1280 |

PLGA | -5.237 × 10^{-4} | 1.846 | 0.1111 | 0.07251 | 0.1086 |

*SSE = Sum of squared error, RMSE = root mean squared error, R^{2 }= linear correlation coefficients

The noise level inherent to proliferation measurements, which are normally carried out over a small seeding density range, make contact inhibition a robust test-case for comparing local _{std}. The reference _{std }is shown in Figure _{AA }for MC3T3-E1 osteoblasts on PLGA. The profile of _{std }is similar to a beta- or chi-distribution with asymmetry due to the non-overlapping nature of the nuclei centers at close distances. The computed _{std }distribution is nearly identical to the experimental _{AA }distribution at large distances (> 100 μm). This is expected since _{AA }indicates the likelihood of finding any two cells (whether proliferating or not) separated by a given distance, which should in principle be random. Figure _{PA}, which is the likelihood of finding a proliferated cell a certain distance from any cell. If cell-cell distance has any relation to proliferative status then _{PA }and _{AA }should differ from one another and from _{std}, but only at close distances where cell-cell contact is likely to occur.

_{AA }and _{PA }for MC3T3-E1 on a PLGA surface and the computed standard curve, _{std}. These data represent the frequency at which any cell is located a certain distance from any other cell (_{AA}) or from a proliferated cell (_{PA}) in the experiments. The standard curve was computed from a Monte Carlo simulation and represents a uniformly random probability of locating any cell a given distance from any other cell on the same sized area as our microscope images. Number of images used was 353.

Figures _{PA}/_{std}, _{AA}/_{std }and _{PP}/_{std }at close distances, indicate the non-random effects of contact inhibition when the values become less than one. Specifically, CI occurs when the distance between cell nuclei becomes less than about 50 μm. The typical mean cell area was around 2500 μm^{2}, resulting in a mean diameter of 56 μm, which corresponds closely to the onset of CI. Representative images of cultured MC3T3-E1 cells on these surfaces have been presented in previous work[_{PP }>_{AA }>_{PA }on each of the three surfaces examined, TCPS, PLGA and PCL. We hypothesize that the local enhancement peak is due to two daughter cells (from the same parent cell) that are very close, which have not had enough time to migrate away during the BrdU staining time period. If so, then this cell division peak should appear on the _{PP }curve but not the _{PR }curve, which was observed comparing Figures _{PP}) to Figures _{PR}). In addition, in the Monte Carlo simulation of random cell positions (_{std}), with no proliferation, this local peak is absent.)

_{std}, the random cell-cell distribution determined from Monte Carlo simulation. Number of images used was 353.

_{PR|RR }on a PCL surface. Number of images used was 288.

_{PR|RR }on a TCPS surface. Number of images used was 291.

Direct ratios between experimentally-determined distributions can be chosen specifically to illuminate the CI phenomena of interest. Specifically, common components in the numerator and denominator not related to CI phenomena may be removed, thus isolating the phenomena of interest. This process is examined in Figures _{PA|AA }profile, which is classified into two regions: the _{PA|AA }falls to ~1/6) and the _{PA|AA }does not fully decouple the division and daughter-cell migration phenomena (indicated by PP) from the proliferation phenomena (indicated by

with

where ∅ is the empty set. The two shared components of _{PA|AA }leads to _{PR|RR}, shown in Figures _{PR|RR }should be more sensitive to CI of proliferation, because non contact inhibited cell pairs have been removed. In Figure _{PR|RR }ratio is classified into two regions: the _{min }= 8 μm, where contact inhibition effects are maximized. To our knowledge, this is the

The physical meaning of the LCM ratio _{PR|RR }can be can be illustrated by recognizing that it is the posterior odds (PO) of proliferation as a function of cell-cell distance. Consider two cells that are well-separated at 40 μm, and another two cells that are at a close distance of 8 μm, where the extreme in contact inhibition behavior is found (minimum _{PR|RR }in Figure _{PR/RR }= _{PR|RR }(8)/_{PR|RR }(40) = 1/32. This means there is a 32 fold lower chance of proliferation at 8 μm than at a distance of 40 μm.

The profiles of _{PR/RR }from the other polymer surfaces are shown in Figure _{PR|RR, min }and _{min }on the different surfaces. The different location and strength of contact inhibition might be due to surface features such as roughness, crystallinity, hydrophobicity, surface charge, or protein adsorption, factors which are known to influence osteoblast proliferation[_{PP/PR }is decreasing, and the _{min }is increasing. We illustrate this point, however, not to make a definite mechanistic argument about surface effects on proliferation, which is certainly more complicated than roughness alone. Rather, the point made is that the LCM method is capable of sensitive detection of differences in proliferation for cells cultured on different surfaces.

Minima in _{PR|RR }Curve Indicating Maximum Contact Inhibition

Surface | _{PR|RR, min} | _{min}(μm) |
---|---|---|

PLGA | 31.6 | 8 |

PCL | 15.8 | 9 |

TCPS | 35.5 | 6 |

The effect of calcium depletion on LCMs is presented in Figure _{PR/RR}, in Figure

_{PR|RR }examining effects of calcium depletion on proliferation of MC3T3-E1 cultured on TCPS surfaces. Number of images used was 204.

We have shown that global summary statistics are not adequate metrics for detecting local cell interactions, due to noise and non-local effects inherent to cell-cell contact phenomena. A novel data analysis strategy,

We have demonstrated the new local metrics by considering the contact inhibition of proliferation of the osteoblast cell line MC3T3-E1. A quantitative and probabilistic description of the contact inhibition effect as a function of cell-cell distance has been achieved. In fact, the probability of proliferation is shown to be strongly dependent on the distance to, and proliferative state of, neighboring cells. The LCMs were also sensitive to effects of the culture surface, and of calcium composition in the culture media, on proliferation.

JCM directed the experimental design, data analysis method development, and writing of the manuscript. JS performed most cell culture experiments and implemented the LCM method, including programming, and wrote the manuscript. PJZ helped in data interpretation and statistical analysis. CCC performed the calcium-depletion experiments and analysis. All authors have read and approved this manuscript.

Click here for file

Click here for file

We gratefully acknowledge support from NIH Grant Numbers RR17425 and HK072039.