A Hybrid Computation Model to Describe the Progression of Multiple Myeloma and Its Intra-Clonal Heterogeneity

Anass Bouchnita,Anass Bouchnita,Anass Bouchnita,Anass Bouchnita,Anass Bouchnita,Mark Koury,Vitaly Volpert,Vitaly Volpert,Vitaly Volpert,Vitaly Volpert,Vitaly Volpert,Vitaly Volpert,Rajae Aboulaich,Fatima-Ezzahra Belmaati

doi:10.3390/computation5010016

Abstract

Multiple myeloma (MM) is a genetically complex hematological cancer that is characterized by proliferation of malignant plasma cells in the bone marrow. MM evolves from the clonal premalignant disorder monoclonal gammopathy of unknown signiﬁcance (MGUS) by sequential genetic changes involving many different genes, resulting in dysregulated growth of multiple clones of plasma cells. The migration, survival, and proliferation of these clones require the direct and indirect interactions with the non-hematopoietic cells of the bone marrow. We develop a hybrid discrete-continuous model of MM development from the MGUS stage. The discrete aspect of the modelisobservedatthecellularlevel: cellsarerepresentedasindividualobjectswhichmove,interact, divide, and die by apoptosis. Each of these actions is regulated by intracellular and extracellular processes as described by continuous models. The hybrid model consists of the following submodels that have been simpliﬁed from the much more complex state of evolving MM: cell motion due to chemotaxis, intracellular regulation of plasma cells, extracellular regulation in the bone marrow, and acquisition of mutations upon cell division. By extending a previous, simpler model in which the extracellular matrix was considered to be uniformly distributed, the new hybrid model provides a more accurate description in which cytokines are produced by the marrow microenvironment and consumed by the myeloma cells. The complex multiple genetic changes in MM cells and the numerous cell-cell and cytokine-mediated interactions between myeloma cells and their marrow microenviroment are simpliﬁed in the model such that four related but evolving MM clones can be studied as they compete for dominance in the setting of intraclonal heterogeneity.

Highlights

Multiple myeloma (MM) is initiated through the acquisition of genetic changes that transform the plasma cells from normal to malignant
While the previous model considers the cytokines in the extracellular matrix to be uniformly distributed, the present study provides a more accurate description by considering that these cytokines are produced by the bone marrow including the stromal cells (BMSCs) and consumed by the myeloma cells
The motion of the malignant cells depends on their distance from the BMSC

Summary

Introduction

Multiple myeloma (MM) is initiated through the acquisition of genetic changes that transform the plasma cells from normal to malignant. A wide variety of genetic changes involving many different genes have been documented in MM cases In addition to these sequential genetic changes, MM cells require specific interactions with the non-hematopoietic cells of the bone marrow including the stromal cells (BMSCs), osteoblasts, osteoclasts, and cells associated with vascular supply of the marrow [1,2]. The second type of mathematical models describing tumor growth is the discrete model which usually represents cells as individual objects that interact with each other. We develop a hybrid model describing the development and intra-clonal heterogeneity in MM as described in Walker et al [29] In this model, malignant cells are represented by elastic spheres that can move, grow, interact, divide and die by apoptosis. We study the dynamics of clonal competition and its role in the progression of MM

Hybrid Model of MM Development

Cell Motion

Extracellular Regulation

Intracellular Regulation

Results

Discussion