Essential operating principles for tumor spheroid growth

BMC Systems Biology

Table 3 SMS AXIOMS.

AXIOM	Environment	Action	Parameters used	*In vitro* source
1	NUTRIENT > proNut	Switch to PROLIFERATING state	proNut	Cell quiescence is regulated by the glucose and oxygen supply [19].
2	NUTRIENT <quiNut	Switch to NECROTIC state	quiNut	Cell death is regulated by the glucose and oxygen supply [19].
3	quiNut <NUTRIENT <proNut	Switch to QUIESCENT state	proNut, quiNut	Cell quiescence is regulated by the glucose and oxygen supply [19].
4	State = PROLIFERATING or QUIESCENT	Consume NUTRIENT equal to proConsumeRate or quiConsumeRate	proConsumeRate, quiConsumeRate	Cells consume oxygen and glucose at varied levels [17].
5	State = NECROTIC; removeCounter < 0	Remove CELL	removeDelay	Necrotic cells eventually break up and are consumed [35].
6	Inside CELL adjacent to empty space	Move into empty space		Cells move and mix with other cells within the spheroid [18].
7	Outside CELL adjacent to empty space	Move into empty space with prob. p_m	moveEmptyBias	Cells move and mix with other cells within the spheroid [18].
8	Outside CELL with 0 neighbors	Randomly move in space		Cells can be shed from the exterior of the spheroid [21].
9	State = PROLIFERATING; prolifCounter < 0; CELL has empty neighbors	Create new CELL with prob. p_b	prolifDelay, proBias	Cells create new cells within the SMS, causing it to increase in size [19].

In each time step a CELL will execute one or more of these AXIOMS based on the environment the CELL is exposed to and its internal variables. The AXIOMS are executed in the order specified within Additional file 1, Fig. S4. Random numbers for probability functions are generated from a uniform distribution in [0,1), except as noted in the text.

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