Evolutionary dynamics of tumor-stroma interactions in multiple myeloma

Cancer cells and stromal cells cooperate by exchanging diffusible factors that sustain tumor growth, a form of frequency-dependent selection that can be studied in the framework of evolutionary game theory. In the case of multiple myeloma, three types of cells (malignant plasma cells, osteoblasts and osteoclasts) exchange growth factors with different effects, and tumor-stroma interactions have been analysed using a model of cooperation with pairwise interactions. Here we show that a model in which growth factors have autocrine and paracrine effects on multiple cells, a more realistic assumption for tumor-stroma interactions, leads to different results, with implications for disease progression and treatment. In particular, the model reveals that reducing the number of malignant plasma cells below a critical threshold can lead to their extinction and thus to restore a healthy balance between osteoclast and osteoblast, a result in line with current therapies against multiple myeloma

Multiplication factors for diffusible factors produced by osteoclasts (OC), osteoblasts (OB) and multiple myeloma cells (MM).

Multiplication factors for diffusible factors produced by osteoclasts (OC), osteoblasts (OB) and multiple myeloma cells (MM).</p

Bone remodeling in multiple myeloma.

Multiple myeloma cells (MM) produce growth factors that activate osteoclasts (OC), which increase bone resorption, or that inhibit osteoblast (OB) differentiation. OC and OB secrete growth factors that affect each other and MM cells.</p

Example of the dynamics for scenario 1.

In the presence of a small number of MM cells, the stable point on the OB-OC border becomes a saddle point and clonal selection leads to a stable coexistence of OC and MM cells. (N = 10, c3 = 1.4, c2 = 1.2, c1 = 1). The arrows show the direction of the dynamics, and the colors show its speed (the euclidean distance between the frequencies at time t and t+1).</p

Different types of dynamics for scenario 1.

(A) The game has one polymorphic stable point between OB and OC. In this case, clonal selection leads to the regular OC-OB balance and prevents invasion of MM cells. (B) The game has two polymorphic stable points. In this case, the final state of the game depends on the initial frequencies. The arrows show the direction of the dynamics, and the colors show its speed (the euclidean distance between the frequencies at time t and t+1).</p

Effect of group size in scenario 1.

<p>The effect of group size <i>N</i> on the position of the fixed points on the OC-OB and OC-MM edges. Same parameters as <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0168856#pone.0168856.g002" target="_blank">Fig 2</a>.</p

Comparison with models with pairwise interactions.

<p>A comparison of our model and the pairwise game of Dingli et al. [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0168856#pone.0168856.ref013" target="_blank">13</a>] with <i>b</i>>1 (row A), <i>b</i><1, <i>b+d</i><1 (row B) or <i>b</i><1, <i>b+d</i>>1 (row C). The arrows show the direction of the dynamics, and the colors show its speed (the euclidean distance between the frequencies at time <i>t</i> and <i>t</i>+1).</p

Dynamics with pairwise interactions in scenario 1.

<p>The dynamics described in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0168856#pone.0168856.g002" target="_blank">Fig 2</a> changes when <i>N</i> = 2, resulting in a new stable point between OC and OB, and a new polymorphic saddle point, in addition to the stable point between OC and MM. The arrows show the direction of the dynamics, and the colors show its speed (the euclidean distance between the frequencies at time <i>t</i> and <i>t</i>+1).</p