Computational and Mathematical Methods in Medicine

Computational and Mathematical Methods in Medicine / 2016 / Article

Research Article | Open Access

Volume 2016 |Article ID 4910603 | 17 pages |

A Computational Model for Investigating Tumor Apoptosis Induced by Mesenchymal Stem Cell-Derived Secretome

Academic Editor: Said Audi
Received01 May 2016
Revised01 Aug 2016
Accepted08 Aug 2016
Published09 Nov 2016


Apoptosis is a programmed cell death that occurs naturally in physiological and pathological conditions. Defective apoptosis can trigger the development and progression of cancer. Experiments suggest the ability of secretome derived from mesenchymal stem cells (MSC) to induce apoptosis in cancer cells. We develop a hybrid discrete-continuous multiscale model to further investigate the effect of MSC-derived secretome in tumor growth. The model encompasses three biological scales. At the molecular scale, a system of ordinary differential equations regulate the expression of proteins involved in apoptosis signaling pathways. At the cellular scale, discrete equations control cellular migration, phenotypic switching, and proliferation. At the extracellular scale, a system of partial differential equations are employed to describe the dynamics of microenvironmental chemicals concentrations. The simulation is able to produce both avascular tumor growth rate and phenotypic patterns as observed in the experiments. In addition, we obtain good quantitative agreements with the experimental data on the apoptosis of HeLa cancer cells treated with MSC-derived secretome. We use this model to predict the growth of avascular tumor under various secretome concentrations over time.

1. Introduction

Apoptosis is a normal, genetically regulated process in which a cell undergoes a sequence of intracellular complex processes that trigger self-destruction. Cancers occur due to mutations of certain fundamental genes that disable the cells to perform apoptosis, giving rise to malignant tumor cells that grow uncontrollably. With its genetic instability, an individual tumor cell becomes a forerunner parent cell that has the potential to develop into a cluster, biologically complex tumor consisting of approximately cells.

Various cancer treatments have been explored with the ultimate goal of suppressing its growth and spreading and perhaps even eradicating cancerous cells. Recently, mesenchymal stem cells (MSCs) have become a topic of great focus in relation to cancer. MSCs are known to secrete a broad panel of proteins including growth factors, chemokines, and cytokines, which are called secretome [1]. Growing evidence suggests that MSCs have an important role in affecting the behavior of tumor cells [2]. While some studies reported that MSCs favor tumor growth, others showed that MSCs can suppress tumorigenesis [3, 4]. In particular, it has been reported that secretome contained in conditioned media (CM) of MSCs promotes apoptosis and autophagy of cancer cells [5]. Experiments done by Sandra et al. show that secretome significantly induces apoptosis in HeLa cancer cells in concentration and time dependent manner [6].

From intracellular perspective, there are two well-known major signaling pathways leading to apoptosis: the intrinsic pathway centered on mitochondria and the extrinsic pathway initiated by death receptors called Tumor Necrosis Factor (TNF). There is now evidence showing that these two pathways are connected and affect one another [7, 8]. Moreover, recent research has also revealed the third pathway, called the perforin pathway, which involves T-cell mediated cytotoxicity and is induced by granzyme B protein. Perforin pathway is also connected to the intrinsic pathway and all three pathways eventually converge into the activation of caspase 3 protein leading to cell death, chromatin condensation, chromosome fragmentation, nuclear degradation, and protein cytoskeleton [810].

Understanding the dynamics of secretome-induced apoptosis that can modulate cells’ life and death can immensely provide therapeutic potential. Despite numerous experimental studies, the underlying biological mechanism of tumor apoptosis induced by MSC secretome is not yet fully understood. Laboratory experiments may not be cost effective and are often quite challenging to perform as each experiment can only be done for specific cells and cannot be easily modified to investigate others. Computational model that simulates secretome-induced apoptosis provides general virtual solution that could complement experimental methods.

For a long time, various modeling techniques have been used to simulate avascular tumor growth [1120]. Continuous models consider the interactions between cell density and chemical concentrations that influence cell cycle events of tumor cell population. These models employ a system of partial differential equations to describe reaction-diffusion-convection of cells and their microenvironmental elements. Continuous models are computationally cost effective in general; however, they do not maintain cell-specific properties and individual cell interactions. On the other hand, discrete models such as cellular automata, extended Potts, and agent-based models focus on modeling single-cell phenomena and upscale it to obtain information about macroscopic phenomena of tumor growth. Drawbacks of the discrete approach lie in their parametrization and the computational costs, but it provides greater qualitative insight into the nature of the system. Hybrid discrete-continuous models provide the benefits of both implementations within the same simulation. Some of the models listed above are multiscale models that typically include cellular, subcellular, and extracellular levels. However, all of these models simulated cancer growth in an untreated environment, and hence none of them includes any apoptosis-related signaling network at their subcellular level. Previous modeling work on apoptosis itself, such as [2123], mostly focused on partial signaling pathways. Hong et al. [24] proposed a continuous ordinary differential equations (ODE) model for the apoptosis signaling network to study the effect of cisplatin. Even though their comprehensive model included three major pathways involved in cisplatin induced apoptosis, namely, the mitochondrial, death receptor-mediated, and endoplasmic reticulum-stress pathways, it is a single scale model at the molecular level and is not integrated to the other levels of the system.

In this study, we develop a multiscale hybrid discrete-continuous model that integrates continuous models of the apoptosis signaling pathways and chemical concentration dynamics at the molecular and extracellular levels into a discrete agent-based model at the cellular level. Our apoptosis signaling pathways model is a system of ordinary differential equations (ODEs) that comprehensively covers all three known pathways that are involved in secretome-induced apoptosis. Our simulation produces phenotypic patterns of avascular tumor growth as observed in the experiments. The model also verifies and obtains a good quantitative agreement with the experimental results by Sandra et al. [6] in studying the role of secretome in inducing apoptosis of HeLa cancer cells. This suggests that the model can potentially be used as a tool in predicting tumor apoptosis induced by various substances. With this model, we further quantify the contribution of each signaling pathway in inducing apoptosis. Lastly, we use the model to predict the effect of secretome of various concentrations on tumor spheroid growth.

2. Materials and Methods

Our model spans across three biological time scales: molecular scale, cellular scale, and extracellular scale, which are closely integrated. At the molecular scale, the apoptosis signaling network regulates cellular apoptosis induced by secretome. At the cellular level, a discrete agent-based model controls cell migration, proliferation, and death. At the extracellular level, a system of partial differential equations describes diffusion, consumption or production, and decay of extracellular substances, such as nutrient (oxygen), extracellular matrix, matrix-degradative enzyme, and growth inhibitors.

2.1. Molecular Scale: Apoptotic Signaling Pathways

Literature study has shown that the three major signaling pathways that are known to be involved in apoptosis are the extrinsic (death receptor) pathway, intrinsic (mitochondrial) pathway, and the perforin pathway [810]. The extrinsic and intrinsic pathways we use here are adopted from various sources [8, 10, 2426] with minor modifications. We integrate the perforin pathway in order to build a comprehensive model that covers all signaling pathways known to be involved in apoptosis induced by MSC secretome. When a cell detects nonzero concentration of the secretome in the medium, a cascade of molecular events occur along these pathways.

A schematic model of the pathways used in this paper is shown in Figure 1. The intrinsic pathway begins as secretome induces DNA damage, which further results in the activation of ATR and p53 proteins. As a response to the DNA damage, the proapoptosis proteins, such as Bax and Bak, will be activated, leading to the opening of mitochondrial permeability transition pore. This triggers the release of cytochrome c from mitochondria into the cytosol [2730]. On the other hand, the antiapoptosis protein, such as Bcl-2, will inhibit the release of cytochrome c. Cytochrome c will bind with Apaf-1 and activate caspase 9. Activated caspase 9 will then cleave and activate downstream caspases, such as caspase 3, which is also known as the apoptosis executor protein.

The extrinsic pathway is initiated by death receptors, called Tumor Necrosis Factor (TNF). The binding of TNF to its receptor causes the level of FasL to increase, which leads to the downstream activation of caspase 8. Activated caspase 8 can trigger the intrinsic pathway through the cleavage of Bid. The truncated Bid further stimulates Bax and Bak. Alternatively, the activated caspase 8 can bypass the intrinsic pathway by directly initiating the activation of caspase 3 [8, 31].

The perforin pathway involves T-cell mediated cytotoxicity and is perforin-granzyme dependent in activating caspase 10, which subsequently triggers the activation of caspase 3. The interconnection (cross-talk) between the perforin and intrinsic pathways occurs through the truncation of Bid by the activated granzyme B [8]. All three pathways eventually merge on the activation of caspase 3 that induces cellular apoptosis.

The change of concentration of each protein involved in the signaling pathways over time is given by an ordinary differential equation (ODE) of the formwhere is the concentration of the chemical, is the production rate, and is the consumption rate of . The biochemical kinetics involved in the model in Figure 1 are given in Table 1 and their corresponding system of ODEs are listed in Table 2. Blocks A, B, and C in Table 2 list the equations involved in extrinsic, intrinsic, and perforin pathways, respectively. Block D in this table lists the equations that are needed by all three pathways.

Extrinsic pathway

Intrinsic pathway

Perforin pathway

: the activated state of protein A; : the compound of proteins and ; : forward rate constant of reaction; : reverse rate constant of reaction; : cytochrome c in mitochondria; Cytc: the released cytochrome c.