^{1}

^{1}

^{1}

^{1}

^{1}

^{2}

^{3}

^{1}

^{1}

^{2}

^{*}

Conceived and designed the experiments: AP DS RB TN CL. Performed the experiments: PR DS RB JP TN. Analyzed the data: AP PR DS JP CL GL. Wrote the paper: AP DS CL GL.

The authors have declared that no competing interests exist.

The spontaneous emergence of phenotypic heterogeneity in clonal populations of mammalian cells

We have investigated the “extrinsic” and the “intrinsic” mechanisms using computer simulations and experimentation. First, we simulated

The observations emphasize the importance of the “ecological” context and suggest that, consistently with the “extrinsic” model, local stochastic interactions between phenotypically identical cells play a key role in the initiation of phenotypic switch. Nevertheless, the “intrinsic” model also shows some other aspects of reality: The phenotypic switch is not triggered exclusively by the local environmental variations, but also depends to some extent on the phenotypic intrinsic robustness of the cells.

Phenotypic heterogeneity in genetically homogenous cell populations is frequently observed in

Since cell lines and primary cells are commonly used to investigate regulatory processes and gene expression during cell differentiation, understanding phenotypic differentiation in clonal populations is a fundamental problem in biology. There are two mutually non exclusive basic models for this phenomenon. In the first model the phenotypic switch is thought to occur as the consequence of extrinsic factors. Two initially identical cells may become different because they encounter different local environments that induce alternative adaptive responses. By changing its phenotype the cell itself contributes changes of the local microenvironment and thus elicits responses from the surrounding cells that are likely to lead to continuous dynamic changes in the population. According to the second model, the phenotype switch is intrinsic to the cells. The phenotypic changes therefore may occur even in an homogenous environment and may result from asymmetric segregation of intrinsic fate determinants during cell division that lead to the change in gene expression patterns.

These two hypotheses can be investigated in cell cultures. One example studied in our laboratory showed that two subpopulations appear spontaneously in proliferating C2C12 mouse myogenic cells

In the present study we investigated the “intrinsic” and “extrinsic” hypotheses of phenotypic differentiation using simple multi-agent computer modelling. In this approach each cell is considered as an autonomous “agent”. Only the rules determining the action of individual agents are defined, while the behaviour of the whole system emerges from the collective behaviour of all agents. The computer simulations showed that both the “intrinsic” and “extrinsic” models could in principle produce heterogeneous populations, but the spatial distribution of the different cell types was different across the two models. The predictions made by the models concerning the distribution of the different cell types were compared with the spatial distribution of the SP and MP cells in the C2C12 cell line. The results indicate that both models capture certain aspects of the

We have designed a simple agent-based model to analyse the possible outcomes of the “extrinsic” and the “intrinsic” mechanisms of phenotypic differentiation. Agent-based models follow a bottom-up simulation strategy, defining simple rules that govern the behavior of individual agents (the cells, in our case) without a global view of the whole system. In the next sections we the describe the general model, followed by the intrinsic and extrinsic variants of the growth model.

Our models are based on a limited number of simplified assumptions about how individual cells migrate, interact with each other, divide and die. These universal features were deduced from direct observations on real life cultures of myogenic C2C12 cells and their control values (i.e. model parameters) were chosen to represent observed realistic ranges.

Since cell migration plays a crucial role in the model, the migration characteristics were defined on the basis of videomicroscopic observations of growing C2C12 cell cultures (more than 3000 cell velocity values over an 18h period). In accordance with earlier reports

_{d}” is the probability of division; p_{1} and p_{2} are the probabilities of the A and B type cells to change their phenotype in the “intrinsic” model; N_{ex} is the threshold, given by the number of neighbours.

In the model, all cells divided at each iteration step, but the survival of the daughter cells depended on the local cell density. The highest local density, N_{max death}, above which the daughter cell cannot survive (i.e. it dies) was defined as the number of neighbours within a circular region around the cell with radius R. The number of neighbours for each cell is therefore determined at each iteration step. In all simulations the arbitrary value of R = 1 was used-it is important to note that the actual value of R gains a meaning only in relation to the value of N_{max death} because the cells _{max death} = D give similar results to R = 2 and N_{max death} = 4xD. In an early version of the model the cells always died when the value of N_{max death} was reached. This led to the formation of large empty patches (never observed in real cell cultures), so in order to make the model more realistic, we implemented cell death as a probabilistic event. The probability that a cell will die, p_{death} increases from 0 to 1 following a sigmoidal curve as a function of N_{max death}. As a result, the excessive cell density variations in the virtual cell population disappeared. Although not confirmed by direct observation, the assumption that cell death will depend on the local cell density is intuitively easy to understand: cell density correlates with the gradient of nutrients, oxygen and toxic metabolites making less likely in dense regions than in sparse ones.

We explored the parameter space defined by the migration velocity and N_{max death}. Values from 40 to100 cells/R for N_{max death} provided a cell density that approximated the observed maximal number of neighbours in a circle with a radius of 8 to 20 µm in real cultures of C2C12 cells (close to confluence). The average cell migration velocity emerged as a crucial parameter for the model. Low average velocity values (<0.2) led to the formation of small clusters of cells separated by empty strips. Because such patterns were never observed in real cultures and the real cell average velocity was higher than 0.2, we programmed velocity values between 0.3 and 1.0. The observed cell distribution pattern was random at all N_{max death} values, as estimated by the nearest neighbour distance method (see

The “extrinsic” and the “intrinsic” hypotheses for the generation of cellular heterogeneity were implemented varying the parameters defined above. We assumed the existence of two cell types: A and B. In both cases, the same rules for migration, division and death (as described above) were applied to type A (representing the SP cells) and B (representing the MP cells).Type A cells can differentiate into B cells and

In the “intrinsic” model we addressed the question of cell autonomy of the phenotypic switch. At each simulation step, type A cells have a fixed probability p_{AtoB} to transform into B cells, and B cells have a probability p_{BtoA} to become A cells (the environment plays no role in the switching). The simulations start with a single A cell which replicates to fill the available space, reaching a maximum size at an equilibrium between growth and death. B cells appear with a frequency determined by p_{AtoB}. We explored the effects of varying the values of p_{AtoB} and p_{BtoA} between 0 and 0.5. If p_{BtoA} = 0, B cells overgrow A cells and the whole population becomes B type. If B cells can switch to A (p_{BtoA}≠0), the size of the two subpopulations, [A] and [B], reaches a steady state equilibrium with a ratio [A]/[B] that depends on p_{BtoA}/p_{AtoB}. (

_{BtoA}. Note corresponding increase in proportion of type A cells (in red) and their random distribution. _{AtoB} = 0.7 and p_{BtoA} = 0.02, but similar results were obtained for other values of p.

We were most interested in the case where the ratio [A]/[B] is small, because it corresponds to the (real) cultured examined (see later). The _{AtoB} = 0.70 and p_{BtoA} = 0.02. As a result of the high probability of A to B conversion and the relatively low probability of the B to A reversion, A cells become the rare phenotype, representing a small fraction of the population. Obviously, this is symmetrical to the case where p_{AtoB} = 0.02 and p_{BtoA} = 0.70. As indicated above, the A and B cells are distributed randomly at equilibrium (

_{max death} = 40 was used.

In the “extrinsic” variant of the model, the phenotypic switch was programmed as a consequence of the change in the cellular microenvironment. Type A cells switch to type B if the number of neighbours in a circular region with a radius R around them is higher than a fixed number N_{ex}. Type B cells switch to type A if the local density drops below the limit N_{ex}. The local cell density, therefore, plays a role in the induction of the phenotypic switch correspond which is similar to cell survival: cell density here is also expected to correlate with the gradient of nutrients, secreted factors, oxygen, toxic metabolites, etc. Therefore, in our context, A and B cells represent two forms of phenotypic adaptation to high- and low density environments. However, we do not make explicit hypotheses concerning the precise mechanism underlying this phenotypic switch.

A typical simulation starts with a single A cell, with type B cells appearing first at the centre of the growing population (where the cell density is the highest). Local fluctuations in cell density due to random cell movement and cell death sometimes allow B cells to switch back to type A. During the growth phase, A cells are observed on the periphery of the population (_{ex}/R ratio (see _{ex} is close to N_{max death}, the number of A and B cells is nearly equal. When compared to the “intrinsic” model, the spatial distribution of the cells in this “extrinsic” model is markedly different. The rare phenotype A cells typically form groups or clusters in areas with low local cell density for all tested values of N_{ex}. The B cells are distributed randomly when N_{ex}<N_{max death}, but some clustering appears when N_{ex} approaches N_{max death} and the sizes of the two subpopulations become comparable (not shown). We also examined the effect of migration velocity on the spatial distribution of cells and found that clustering of A cells was not affected by this parameter (

_{ex}. Note the increasing proportion and clustering of type A (red) cells with increasing N_{ex}. In all simulations N_{max death} = 40 was used. _{ex} using the standardized nearest neighbour distance. Type A cells were clustered (_{ex} values analysed.

The results of a typical run are shown in _{ex}. While the non-random distribution of type A cells in the periphery of the exponential growth phase is evident, the clustering of A cells at the equilibrium phase was demonstrated by the standardized nearest neighbour distance method (

The computer simulations show that both the “intrinsic” and “extrinsic” mechanisms are able to generate heterogeneous populations of cells with a stable proportion of the two cell types. The comparison of the “intrinsic” and “extrinsic” models provided testable predictions. Type A cells in the “extrinsic” model had on average fewer neighbours than B cells (

The dissimilarity in the distribution of the rare phenotype SP cells in culture and the type A cells in both the “extrinsic” and “intrinsic” models indicates that the phenotypic switch (at least in our system) may follow an intermediate scheme, where each model emulates reality only partially. One possibility is that low density _{ex} neighbours (again, within a circular region of radius R). Type B cells can switch back only if the local cell density becomes lower than the limit N_{ex}. However, the cells encountering a favourable microenvironment undergo phenotypic change with an intrinsic probability p_{AtoB} and p_{BtoA} , so a fraction of cells keep their original phenotype even in a permissive microenvironment (_{AtoB} and p_{BtoA} = 1, the model is equivalent to the “extrisic” version. The results shown in _{ex} = 30 values (the same as in _{AtoB} = 0.7 and p_{BtoA} = 0.4. Although the distribution of the number of neighbours is no longer bimodal, the simulations show a type A cell neighbour distribution (

_{AtoB} and p_{BtoA}. B: Results of a typical simulation of the “hybrid” model during the growth phase and at equilibrium. Note the simultaneous presence of small clusters and dispersed single type A cells. p_{AtoB} = 0.7 and p_{BtoA} = 0.4. C: The distribution of the number of neighbours around the A and B cells (left and right respectively) in the hybrid model. The average number of neighbours and the standard deviation are indicated for each panel. Note the more dispersed distribution of type A cell neighbours. D: Analysis of the spatial distribution randomness of SP and MP cells using Ripley's L statistics. The upper panel shows the type A cell L-function (red line) with values larger than 0 and outside the range defined by the upper-and lower-envelope functions (black line) (this indicates significant clustering of type A cells at small R distances). The type B cells (green line) are randomly distributed, because the L(h) values are close to 0 at all scales (R).

In order to clarify whether the non-random distribution of the rare phenotype cells is observed only in the C2C12 line or whether it is a general feature, we analysed clonal populations of primary human myoblasts. These were obtained by cloning of individual cells from a primary myoblast (muscle biopsy) culture. The cultures were allowed to grow to several hundred cells, fixed and immunostained with an anti-desmin antibody (a muscle-specific intermediate filament protein and one of the earliest markers of activated muscle precursor cells). Desmin is present in all myoblasts, but its expression level depends on the degree of commitment of the cell to the myogenic differentiation path

The basic model presented in this paper simulates the growth of a clonal cell population and provides a simple framework for testing the “intrinsic” and “extrinsic” hypotheses on the origin of phenotypic heterogeneity. The values of the parameters controlling cell motility, cell cycle length and cell death were deduced from observations on living cell cultures and were the same in both the “intrinsic” and the “extrinsic” versions. One could call into question the assumption that both A and B cell types follow the same rules of proliferation and migration. However, the opposite case, i.e. different proliferation and/or migration behaviour, would be more restrictive in the context of our model because it would be based on the assumption that proliferation and migration differences are part of the phenotypic differences between the two cell types. The results presented here show that even in the more general and parsimonious case of identity of proliferation and migration, phenotypic heterogeneity in a clonal cell population is possible. Differences in these characteristics between the two cell types would act to reinforce the heterogeneity.

We have examined two different hypotheses for the origin of phenotypic heterogeneity by computer simulation and experimental analysis. Computer simulations show that in the “extrinsic” model, the rare A phenotype cells were clustered in regions of low local cell densities, whereas the “intrinsic” model predicted random distribution of all cells in the cell culture.

According to the “extrinsic” model, cell differentiation depends on external cues. In the “intrinsic” model the spontaneous phenotypic switch occurs in a cell autonomous way with a given probability where intracellular interactions do not play a role. In the “intrinsic” model, since the phenotype switch is a relatively rare event, each cell type produces two daughter cells of the same type. Whether these cells remain close to each other depends on cell migratation. Random cell migration acts as a homogenizing factor that can disrupt clusters formed by cells of the same lineage. However, it also acts as the source of local heterogeneity of cell density. This constitutes a source of variability in the immediate environment of each cell such as the number of cell to cell contacts, the establishment of local concentration gradients of nutrients, oxygen or molecules secreted by the cells. Hence, in the “extrinsic” model random cell migration locally promotes the phenotypic switch.

The higher incidence of the A type cells in the low density regions in the “extrinsic” model was expected, because the phenotypic switch was conditioned by the low number of neighbours. However, clustering of the A cells in the “extrinsic” model and even distributions of these cells in the “intrinsic” model could not be predicted, based on the model's initial conditions, because the key parameter, cell migration, is stochastic. Clustering of the A cells is, therefore, a distinctive key prediction that could be analysed experimentally. It is worth noting, that in our models stable subpopulations of A and B type cells are maintained only if the phenotypic switch is reversible.

A computer simulation model of a complex phenomenon such as cell differentiation is inevitably general and based on a number of simplifications. On the other hand, an experimental system is always unique, so the experimental testing of the predictions of an abstract model must reconcile these two facets. The C2C12 cell line appeared as a good compromise for the experimental analysis of the clustering prediction. Reversible differentiation of the rare stem-like SP cells into myoblast-like MP cells and

The observation that the SP cells had the tendency to be grouped in regions of low local cell density is consistent with the “extrinsic” model and stresses the importance of the local microenvironment in the initiation of the phenotypic switch. This conclusion was corroborated by the observation of position-dependent emergence of phenotypic heterogeneity in a population of primary myoblasts. Nevertheless, the “intrinsic” model also captures a part of reality, because rare phenotype cells were also found dispersed in regions of high cell density. Therefore, the “intrinsic” and “extrinsic” mechanisms are likely to correspond to two idealized solutions that act together. This is confirmed by the “hybrid” model, which provides a phenotype distribution in the population similar to that observed in the real cell culture.

What is the biological meaning underlying the “intrinsic” and “extrinsic” characteristics? We think that the “extrinsic” model refers to the cell's capacity to react to fluctuations in the environment by changing its gene expression pattern conditioned by the local concentration gradients of factors and metabolites secreted by the cells, nutrients, oxygen etc. However, the phenotypic change is not a continous transition initiated automatically by the variation of the local environment, rather it is like switch of a multistable system from one stable state to another. The cellular phenotype is robust and can resist small stochastic variation of the environment which can only induce fluctuations around the stable phenotypic state. Large fluctuations, however, destabilize the cell and generate changes. In this sense, the “intrinsic” probability in the hybrid model refers to the phenotypic robustness based on epigenetic mechanisms and transcription regulation networks rather than to a spontaneous propensity for differentiation. As a consequence, adaptation of a cell to the local microenvironment may constitute the first step in the emergence of a new cellular phenotype. Cell-to-cell interactions could then act to preferentially stabilize the new state. As a result, the cell type composition of the originally homogenous population becomes heterogeneous and tends to a steady-state equilibrium, in spite of the fact that the phenotype of each individual cell may vary. Stochastic processes are usually considered as a deleterious noise, but as it was suggested earlier

Current conceptual models tend to abandon the classical assumption of a strict hierarchy during differentiation and understand cell differentiation as a dynamic process

Although our experiments were carried out on

Records of cell migration were done using a Zeiss Axiovert 100M confocal microscope. C2C12 cells were maintained under controlled CO_{2} atmosphere and temperature. Bright field images were recorded every 10 minutes for 18 hours. Image acquisition was done at high resolution (1024×1024 pixels) with aid of Zeiss LSM 510 software for PC. Migration velocities were calculated with a “Manual Tracking” plug-in (Fabrice Cordelières, Institut Curie, Orsay, France) of ImageJ software (

The computer simulation was performed using the Netlogo language, specifically designed to make simple agent-based models (Wilensky, U. 1999. NetLogo. _{death} is calculated for each cell after the division. A value N_{max death }and a standard deviation, SD of N_{max death} is defined before each run for the maximal number of neighbours in a circle with a radius R. The value of p_{death} increases from 0 to 1 as a function of this parameter following a sigmoidal curve. As a result, the distribution of the life lengths of the cells follows a Gaussian distribution.

The total size of the population was determined by the sum of the divisions and deaths. Although no rule was defined for growth of the whole population, it followed a typical logistic kinetics and the maximal density of the cell population in any circular area with a radius R of the virtual culture dish oscillates around the value of N_{max death}.

C2C12 cells were obtained from the American Type Culture Collection (CRL 1772) and routinely propagated in proliferation Dulbecco's Modified Eagle's Medium (DMEM, Gibco BRL) with 4,5 g/ml of glucose, supplemented with 20% (v/v) foetal calf serum (FCS, Hyclone), 100 U/ml penicillin and 100 µg/ml streptomycin. The cultures were grown at 37°C under a humidified atmosphere of air with 7% CO2. Initial plating density was between 2 .10^{3} and 3.10^{3} cell/cm^{2} and the cells were cultured for 6 days. 35 mm glass bottom culture dishes (Mat Tek Corporation) were used for cell culture and two photon analyses.

The primary human mononuclear cells from muscle biopsies were obtained from the Genethon's cell bank and cultured in Skeletal muscle cell growth medium (Promocell–C-23060) supplemented with 10% calf serum (PAA–A15-043), glutamax (Gibco–35050.038) and 50 µg/ml gentamicine (Gibco–15751.037). Individual cells were cloned by cell sorter (MoFlo–Dako) and allow to expand in a colony of several hundred cells.

The C2C12 cells were stained by the DNA dye Hoechst 33342 (Sigma-Aldrich B-2261) at a final concentration of 11 µg/ml for 90 min at 37°C under mild shaking. The controls were incubated in the presence of 100 µM of verapamil (Sigma V-106 batch 28 H4699). The images were collected by a two-photon microscope under conditions of Hoechst excitation and processed by a software

The colonies of primary cells were fixed with pure methanol (for 60 min at−20°C) and immunostained by an anti-desmin monoclonal antibody (1/40-Sigma–clone DE-U-10 Product n°D1033).

The number of neighbours around each cell in the simulations and the cell cultures was calculated automatically on the basis of the digitalized images and the distributions of the frequencies were compared by two sided t-test. The results were confirmed by the non-parametric Wilcoxon-Rank-Sum test.

The standardized nearest neighbour distance method was used to describe the degree of spatial clustering of the A and B cell distributions obtained in the “extrinsic” and “intrinsic” models. This method uses the average distance from every cell to its nearest neighbour to determine if the cells are clustered, distributed homogenously or dispersed. The standardized nearest neighbour distance,

In order to test the significance spatial clustering of the cells in the simulations and in the cell cultures the Ripley's L-function was used

The authors are grateful to Susan Elsevier Saint-Juste and Otto Merten for critical reading of the manuscript.