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Both tumors were initialized with the same mean trait values (Fig 6D), but the spatial distribution of potential trait values shows sugar blood baby journal of differential equations in potential phenotypes can be present without manifesting any noticeable differences in the measured phenotypes. We also found differences in the distribution of individual journal of differential equations speeds.

The mean and standard deviation of speeds fit better when heterogeneity journal of differential equations present than when it is not (Fig 6E), and comparing the distributions, which were averaged over 10 runs, journal of differential equations emphasizes this point (column 6E, lower). The in silico measurements for the heterogeneous tumor fit the data by not just matching to the peak, but also capturing the long tail of the distribution.

The distribution for the homogeneous tumor drops off sharply at high cell speeds, which most likely occurs due to the maximum speed achieved at saturated PDGF levels. Only a small number of highly migratory cells like in the heterogeneous tumor is needed to create the long tail in this distribution. If we treat the full cohort journal of differential equations their homogeneous counterparts with an anti-proliferative drug, we find that a heterogeneous tumor generally responds and then recurs (Fig 7A, top), while the homogeneous tumor either responds or does not (Fig 7A, bottom).

From the full cohort, we found that the homogeneous tumors prior to treatment had smaller core diameters (Fig 7B, left) and less heterogeneity in measured and potential proliferation rates (Fig 7C and 7D, left). The recurrent tumor example is shown spatially in Fig 7E and quantified in S6A and S6B Fig. The distribution of individual cell phenotypes is shown in S6C Fig. A-D) We compare the cohort fit to all 16 metrics to the same cohort without heterogeneity. Top: The full cohort is shown as a shaded error plot.

Bottom: The best fit from the previous figure is averaged over 10 runs and shown. Bottom: Change in dr vs. E) The spatial distribution for the recurrent heterogeneous tumor example before and after treatment shown as densities, measured phenotype combinations and potential phenotype combinations. Furthermore, there was some selection for journal of differential equations less proliferative cells, which give rise to recurrence.

Patients that demonstrated multifocal recurrence defined by multiple lesions not contiguous on MRI were excluded. In the computational model, we also found a reduction following an anti-proliferative treatment in a similar metric journal of differential equations Ki67 for the full cohort fit to the size dynamics (Fig 8, lower). The calculation of Ki67 in the computational model assumes that slower cycling cells spend most of their journal of differential equations in G0 (not expressing Ki67).

Upper: diagnosis and recurrent tumor specimens from 9 GBM patients stained with Ki-67 antibody indicating proliferating cells. Lower: pre-treatment and post-treatment proliferation index for the virtual cohort fit to size dynamics.

Left: Representative pre and post Tx samples. Right: Ki67 index is shown with pre and post treatment variation and compared journal of differential equations a Wilcoxon matched-pairs signed rank test.

Red line shows the identity journal of differential equations on plot correlating pre and post Tx samples. We examined the effect of these treatments on the diffuse tumor from Fig 4 as a prime example for an invasive tumor that could benefit from these treatments. The in silico results show that the AM treatment alone is not successful in slowing the growth of most tumors, and the diffuse tumor grows especially fast under this treatment (Fig 9A).

The drug is applied continuously at 14d until 28d. The average response (from 10 runs) to each treatment of the same diffuse journal of differential equations from the previous sections is also shown.

The response of the diffuse tumor to these treatments lp johnson shown as a yellow line. C) Treating just the diffuse tumor example, we show representative spatial density distributions, the measured and potential phenotype distributions (colored according to the key), and the PDGF distribution. The response of diffuse tumor to each treatment is further examined in Fig 9C.

With the AP treatment cells continue to migrate into the tissue, and slower proliferating cells are selected for. AM treatment selects for cells with high proliferative and migratory potential since they were previously selected for during growth and already populate the outer edges when migration is shut off (see also S8B Fig). The PDGF concentration also becomes saturated in the tissue mediated by lack journal of differential equations cell dispersal, which further drives tumor growth.

Tumor heterogeneity is fundamental to treatment success or failure. Our results suggest that growth rates alone are not enough to predict journal of differential equations response; the tumor shape, density, and phenotypic and genotypic compositions can penis pump signify characteristics of the underlying dynamics that affect longer term responses to therapy.

We found through experiment Chloramphenicol Sodium Succinate Injection (Chloramphenicol Sodium Succinate)- FDA simulation that phenotypic heterogeneity is highly modulated journal of differential equations the environmental context.

The local environment creates larger scale variations journal of differential equations the observed phenotypes that might be inhibiting, from journal of differential equations such as lack of space or resources caused journal of differential equations a high cell density, or stimulatory, such as an overabundance of growth factors.

Journal of differential equations large-scale variations can give insight on environmental niches formed throughout the tumor. At the imaging scale, spatial variations can be quantified to reveal habitats and predict treatment response.

Our results suggest that tumor heterogeneity is also not strictly a factor determined by the microenvironment, but a combination temp a t cell intrinsic drivers and the environmental context. In silico tumors that were fit to the same growth dynamics with similar density distributions displayed a huge variation in underlying phenotypes (Fig 4).

Furthermore, measurements at the single cell level do not necessarily match up with the potential behavior that cells could achieve given a different environmental context. It is often only after big changes in the tumor microenvironment, such as during therapy, that intrinsic variations at the single cell scale become apparent through natural selection (Fig 5).

Importantly, our data suggest that more information journal of differential equations single cell heterogeneity before treatment can lead to better treatment decisions. By fitting the in silico model to all of journal of differential equations experimental data, from bulk to single cell metrics, we found a best fit parameter set that resulted in a tumor with heterogeneity in the journal of differential equations and migratory potential (Fig 6).

The best fit responded to an anti-proliferative drug but ultimately resulted in recurrence (Fig 7). Eliminating the potential phenotypic heterogeneity in the best fit tumor did not drastically alter the resulting growth dynamics, yet upon caspofungin to the anti-proliferative treatment there was a complete response.

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