4.D) ESTATUTOS SOCIALES Y OTROS CONVENIOS General

In TUGME, tumor cell cycle is modeled by a series of phases, correspondingly mimick- ing the phases of an entire cell cycle in reality. Single cell behaviors, such as cell volume

growth, metabolism, division and the cell cycle control, are modeled by discrete events associated with the corresponding phases.

The cell cycle model is a key module in TUGME, since it directly determines the growth dynamics of the multicellular tumor systems, while the other modules aect the cell cycle dynamics. Basically modeling tumor growth is to investigate the cell behavioral mechanisms in terms of joint regulations of biological, biochemical and biophysical processes of high relevance. Hence, the cell cycle model may vary signicantly for a variety of hypotheses. For example, if CSCs and common tumor cells are separately considered, the cell cycle model should at least distinguish the proliferation potential between these two types of cells. The cell cycle module of TUGME is expected to facilitate testing dierent hypotheses by enabling easy implementations of dierent cell cycle models.

In TUGME, the cell cycle model is hierarchically organized consisting of interfaces and implementations as it is shown in gure 4.19. In general, there are two types of cell cycle models in terms of how real cell cycle phases are modeled. The rst type simply splits cell cycle into the G1 phase and the rest phases SG2M. The second type of models consists of exactly the real cell cycle phases, namely the G1, S, G2 and M phases.

The G1 phase is always explicitly modeled because it is particularly important to tumor cell proliferation, which has been introduced early in section 3.3.4 in chapter 2. This is also why we merge the rest S, G2 and M phases as one in the rst general type of cell cycle models. We provide the second general cell cycle model type in case some users are interested in modeling some detailed dynamics of full cell cycle phases. Beside these phases, a state when G1-phase tumor cells suspend the proliferation temporarily is treated as a special phase named the G0 phase. It is important to model the mechanisms controlling transitions between the G1 and the G0 phases, since the period of time that tumor cells stay in the G0 phase directly aects the overall cell proliferation rate or the growth rate of a tumor. Besides, tumor cell necrosis is modeled as a separate state that diers to the apoptosis of normal somatic cells. In a word, a tumor cell can be in only one of the three states, namely the proliferating, the quiescent, and the necrotic states. If the CSC theory is considered, CSCs dierentiate into common tumor cells which can undergo apoptosis too.

Dening the phases and/or the states for cells are just part of the work of establishing a cell cycle mode. The next step is to explicitly dene the cell cycle rules. First of all, one needs to specify a distribution type that the duration of each cell cycle phase obeys, as the cell cycle phase duration isn't xed but random. The phase duration distribution of all the phases are Gaussian distributions but with dierent means and

Figure 4.19: Diagram illustrating the interface and several implementations of cell cycle models. The symbol # indicates a protected eld of a C++ class.

standard divinations in our cell cycle models. A Gaussian distribution allows negative values, which is obviously unrealistic for modeling the phase duration. This problem is handled by replacing all the negative random numbers with zero. Secondly, cell volume growth has to be modeled properly. It is dened by increasing the cell volume instead of its radius or diameter with a constant rate in our model. The growth rate is actually calculated by dividing the volume dierence between the mature and the newly born tumor cells by the duration of the G1 phase. Since the radii of the mature and newly born tumor cells are parameters that do not change once specied for a model and τG1 is a random number, the actual volume growth rate varies from cell to cell. The

volume growth of tumor cells is restricted in the G1 phase, since an actual tumor cell undergoes signicant volume growth in this phase and has slight volume growth in the rest phases except the M phase [2]. Theoretically, this growth model can be described by the equation 4

3πR 3

M = 2 · 43πR 3

Y based on the assumption of spherical cell shape,

where RM and RY stand for the radii of the mature and newly born cells separately.

Thirdly, one needs to dene the mechanisms that control the behavior of tumor cells according to the biological, biochemical and biophysical conditions.

In TUGME, two cell cycle controlling rules are dened distinguished by how the con- versions between the proliferating and quiescent state of tumor cells is modeled. The rst rule is relatively simple, where a newly born cell enters the G1 phase directly and it can denitely complete this phase without disruptions by nally entering the G0 phase without checking any conditions. In the G0 phase, a checkpoint is implemented, where it can advance into three states: 1) switching to necrosis when the corresponding thresholds are met; 2) staying in the G0 state when the quiescent thresholds are satis- ed; 3) otherwise, advancing into the S phase (resuming the cell cycle) when the cell manages to pass all requirements for proceeding its division. The general procedures of this version of the cell cycle model are shown in gure 4.20.

Figure 4.20: Flowchart illustrating the phase transitions of an entire cell cycle.

The second rule is characterized by allowing the inter-switch between the G1 phase and the G0 phase, which is impossible in the rst case. According to this rule, a newly born cell is initially set in the G1 phase too. However, cells are designated to switch from the G1 phase to the G0 state once the quiescent conditions are met, and G0-state cells can switch back (resuming the cell cycle) if the corresponding conditions are satised. The main steps of the G1 phase and the G0 state of this cell cycle controlling rule are illustrated in gure4.21 and4.22.

Finally, a dividing cell is replaced by two daughter cells at the end of its division (the SG2M or M phase). The radius of each daughter cell is set such that each of them has exactly half of the spherical volume of the mother cell. They are initially placed within the volume of the mother cell, which mimicking the daul-bell shape of a real cell at the end of its division. The daughter cells are assumed to have no preference in orientation and start to adjust their positions according to the biomechanical condition right after separating from each other. Hence, they are placed within the mother cell

Figure 4.21: Flowchart illustrating the state transitions in the G1 phase.

Figure 4.22: Flowchart illustrating the state transitions in the G0 state.

with a random orientation chosen from the uniform distribution in three dimensions. Figure 4.23illustrates how the daughter cells are placed within the mother cell with a given orientation.