With a mathematical population model comprised of individually growing cells, we show that cyclin translation would suffice to explain the observed growth rate dependence of cell volume at START.

It emerges as a combination of the cell cycle, controlling the orderly orchestration of duplication and division, and the individual growth rate , reflecting extra and intracellular physiological conditions.

The cell cycle and the growth rate are coupled, such that proliferation and growth are balanced, avoiding abnormally large or small cells.

The growth or biosynthetic capacity of the cell determines the growth rate and the unstable regulator is presumed to be one of the G1 cyclins, most likely Cln3 [8].

Linking growth and division through cyclin translation leads to size homeostasis and a growth rate dependent sizer in G1

The volume trajectory for a single cell is biphasic With altered growth rates dependent on cell cycle stage as observed experimentally as well (Fig 1B) [15, 40—42].

Moreover, in both models there is a strong dependence of the cell volume at START on the individual growth rate in G1 phase (Figs 2B and 81—83), as observed experimentally [15].

Further analysis of the model shows that, in the short-term, mutant strains that enlarge their replication rate due to evolving an increased growth rate are more favoured than strains that suffer a lower immune-mediated death rate (‘immune tolerance’), as the latter does not completely evade ongoing immune proliferation due to inter-parasitic competition.

Analysis of this model suggests that, in order to enlarge its emergence probability, it is evolutionary beneficial for a mutated strain to increase its growth rate rather than tolerate immunity by haVing a lower immune-mediated deathrate.

We use Equation 8 in our model by setting R* = R2 — yim-t, which is the rescaled growth rate of the mutated strain, corrected for the fact that the baseline immunity rate will reduce its initial selective advantage.

Standard results from birth-death models states that the mean growth rate is equal to R2 — y, with variance equal to R2 + y [33].

(P1, (P2 Growth rate of initial, mutated infection x1, x2 Size of initial, mutated infection y Size of immune response

K Maximum size of immune response r Unscaled growth rate of immune response

R* ‘Effective’ initial reproductive ratio in the presence of immunity, R — yo p Scaled immune growth rate , r/o1

This is because the tau-leaping algorithm is accurate only if the eXpected number of events per time step is small [37]; since the growth rates of the pathogen strains and the lymphocytes are both large, a small time step is needed to make the simulation valid.

However, at low oxygen levels, glioblastoma will have drastically higher HIFloc levels which result in a much different phenotype and growth rate .

In fact, the top four rate constants that glioblastoma growth was most sensitive to when individually perturbed were the production of HIFloc (k8), production of IGFBP2 (k1), growth rate due to HIFloc (km) and promotion of HIFloc by IGFBP2 (kw).

The model was fitted for three outputs: glioblastoma growth rate ; HIFloc vs. 02 levels; and IGFI as a function of IGFBP2.

The glioblastoma growth rates were found for two distinct experiments (U87 and LN229) by fitting the same model and obtaining different initial conditions and growth rates for the two cell lines.

The growth rate of the glioblastoma tumor, Eq 5, was determined by regression analysis using the data from both our previous experiments on spheroid growth in vitro using the U87 glio-blastoma cell line and LN229 glioblastoma growth in mice [70].

Results are plotted in Fig 4, which shows that LN229 glioblastoma growth was most sensitive to the production of HIFloc (k8) production of IGFBP2 (k1), growth rate due to HIFloc (k1 1) and promotion of HIFloc by IGFBP2 (km).

Rate constants that glioblastoma growth rate were most sensitive to in LN229 cells.

Importantly, further studies show that although the growth rate of the population is zero at S = 81, the substrate consumption rate is not zero; see [36] for review.

This observation also agrees with previous studies [33—35]; in these studies, it is shown that as the substrate concentration 8 decreases, the growth rate 1 decreases, but 1 becomes zero at a nonzero substrate concentration.

Importantly, even when the growth rate of a population is zero (i.e., l = 0 at S = 81 in Fig.