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Essential operating principles for tumor spheroid growth.

Engelberg JA, Ropella GE, Hunt CA - BMC Syst Biol (2008)

Bottom Line: Each agent used an identical set of axiomatic operating principles.In sequence, we used the list of targeted attributes to falsify and revise these axioms, until the analogue exhibited behaviors and attributes that were within prespecified ranges of those targeted, thereby achieving a level of validation.The finalized analogue required nine axioms.

View Article: PubMed Central - HTML - PubMed

Affiliation: UCSF/UC Berkeley Joint Graduate Group in Bioengineering, University of California, San Francisco, CA, USA. jesse.engelberg@gmail.com

ABSTRACT

Background: Our objective was to discover in silico axioms that are plausible representations of the operating principles realized during characteristic growth of EMT6/Ro mouse mammary tumor spheroids in culture. To reach that objective we engineered and iteratively falsified an agent-based analogue of EMT6 spheroid growth. EMT6 spheroids display consistent and predictable growth characteristics, implying that individual cell behaviors are tightly controlled and regulated. An approach to understanding how individual cell behaviors contribute to system behaviors is to discover a set of principles that enable abstract agents to exhibit closely analogous behaviors using only information available in an agent's immediate environment. We listed key attributes of EMT6 spheroid growth, which became our behavioral targets. Included were the development of a necrotic core surrounded by quiescent and proliferating cells, and growth data at two distinct levels of nutrient.

Results: We then created an analogue made up of quasi-autonomous software agents and an abstract environment in which they could operate. The system was designed so that upon execution it could mimic EMT6 cells forming spheroids in culture. Each agent used an identical set of axiomatic operating principles. In sequence, we used the list of targeted attributes to falsify and revise these axioms, until the analogue exhibited behaviors and attributes that were within prespecified ranges of those targeted, thereby achieving a level of validation.

Conclusion: The finalized analogue required nine axioms. We posit that the validated analogue's operating principles are reasonable representations of those utilized by EMT6/Ro cells during tumor spheroid development.

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Related in: MedlinePlus

Influence of proNut on SMS growth. Gray diamonds: in vitro data as in Fig. 3. Other parameter values were those listed in Table 2. Colored lines are results of single experiments for the indicated values of proNut from 8.0 × 10-4 to 7.0 × 10-3 (same values as in Fig. 10). (A) high NUTRIENT; (B) low NUTRIENT. *: proNut value in Table 2.
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Figure 11: Influence of proNut on SMS growth. Gray diamonds: in vitro data as in Fig. 3. Other parameter values were those listed in Table 2. Colored lines are results of single experiments for the indicated values of proNut from 8.0 × 10-4 to 7.0 × 10-3 (same values as in Fig. 10). (A) high NUTRIENT; (B) low NUTRIENT. *: proNut value in Table 2.

Mentions: A CELL switched from PROLIFERATING to QUIESCENT state when the amount of NUTRIENT at its location dropped below the value of the parameter proNut. If NUTRIENT later increased above proNut, the CELL returned to the PROLIFERATING state. Changing the value of proNut changed the amount of NUTRIENT that CELLS required to remain in the PROLIFERATING state. When set to 8.0 × 10-4, CELLS transitioned directly from the PROLIFERATING to the NECROTIC state, as shown in Fig. 10. We do not distinguish between simulated necrotic and apoptotic cell death, instead conflating both into removal of NECROTIC CELLS. When referring to in vitro research we defer to the original documents for terminology. CELL growth at that setting under low NUTRIENT (Fig. 11) was low, as PROLIFERATING CELLS consume more NUTRIENT than QUIESCENT CELLS. Increasing proNut to 2.0 × 10-3 produced little change in morphology or growth rate, but both measures changed dramatically when proNut was raised to 3.0 × 10-3. At that value, a population of QUIESCENT cells became clearly evident, and the growth rate and stable maximum size was noticeably larger. That trend did not continue, however. As proNut increased further, first to 4.0 × 10-3 and then to 5.0 × 10-3, only small changes in morphology and growth curves were evident. The population of QUIESCENT CELLS was only slightly larger. Another sharp change was evident as proNut reached 6.0 × 10-3: the SMS destabilized (Fig. 10G) and the growth curve did not plateau (Fig. 11B). The results suggested that a window existed within which the number of PROLIFERATING CELLS, having higher consumption rates, balanced the number of QUIESCENT CELLS, which had lower consumption rates. When the level of NUTRIENT within a location dropped below the value quiNut, the CELL switched irreversibly to the NECROTIC state. As is evident from Additional file 1, Figs. S2 and S3, varying quiNut had less complex effects. As quiNut was increased, the growth rate, saturation size, and viable rim width all decreased.


Essential operating principles for tumor spheroid growth.

Engelberg JA, Ropella GE, Hunt CA - BMC Syst Biol (2008)

Influence of proNut on SMS growth. Gray diamonds: in vitro data as in Fig. 3. Other parameter values were those listed in Table 2. Colored lines are results of single experiments for the indicated values of proNut from 8.0 × 10-4 to 7.0 × 10-3 (same values as in Fig. 10). (A) high NUTRIENT; (B) low NUTRIENT. *: proNut value in Table 2.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2667182&req=5

Figure 11: Influence of proNut on SMS growth. Gray diamonds: in vitro data as in Fig. 3. Other parameter values were those listed in Table 2. Colored lines are results of single experiments for the indicated values of proNut from 8.0 × 10-4 to 7.0 × 10-3 (same values as in Fig. 10). (A) high NUTRIENT; (B) low NUTRIENT. *: proNut value in Table 2.
Mentions: A CELL switched from PROLIFERATING to QUIESCENT state when the amount of NUTRIENT at its location dropped below the value of the parameter proNut. If NUTRIENT later increased above proNut, the CELL returned to the PROLIFERATING state. Changing the value of proNut changed the amount of NUTRIENT that CELLS required to remain in the PROLIFERATING state. When set to 8.0 × 10-4, CELLS transitioned directly from the PROLIFERATING to the NECROTIC state, as shown in Fig. 10. We do not distinguish between simulated necrotic and apoptotic cell death, instead conflating both into removal of NECROTIC CELLS. When referring to in vitro research we defer to the original documents for terminology. CELL growth at that setting under low NUTRIENT (Fig. 11) was low, as PROLIFERATING CELLS consume more NUTRIENT than QUIESCENT CELLS. Increasing proNut to 2.0 × 10-3 produced little change in morphology or growth rate, but both measures changed dramatically when proNut was raised to 3.0 × 10-3. At that value, a population of QUIESCENT cells became clearly evident, and the growth rate and stable maximum size was noticeably larger. That trend did not continue, however. As proNut increased further, first to 4.0 × 10-3 and then to 5.0 × 10-3, only small changes in morphology and growth curves were evident. The population of QUIESCENT CELLS was only slightly larger. Another sharp change was evident as proNut reached 6.0 × 10-3: the SMS destabilized (Fig. 10G) and the growth curve did not plateau (Fig. 11B). The results suggested that a window existed within which the number of PROLIFERATING CELLS, having higher consumption rates, balanced the number of QUIESCENT CELLS, which had lower consumption rates. When the level of NUTRIENT within a location dropped below the value quiNut, the CELL switched irreversibly to the NECROTIC state. As is evident from Additional file 1, Figs. S2 and S3, varying quiNut had less complex effects. As quiNut was increased, the growth rate, saturation size, and viable rim width all decreased.

Bottom Line: Each agent used an identical set of axiomatic operating principles.In sequence, we used the list of targeted attributes to falsify and revise these axioms, until the analogue exhibited behaviors and attributes that were within prespecified ranges of those targeted, thereby achieving a level of validation.The finalized analogue required nine axioms.

View Article: PubMed Central - HTML - PubMed

Affiliation: UCSF/UC Berkeley Joint Graduate Group in Bioengineering, University of California, San Francisco, CA, USA. jesse.engelberg@gmail.com

ABSTRACT

Background: Our objective was to discover in silico axioms that are plausible representations of the operating principles realized during characteristic growth of EMT6/Ro mouse mammary tumor spheroids in culture. To reach that objective we engineered and iteratively falsified an agent-based analogue of EMT6 spheroid growth. EMT6 spheroids display consistent and predictable growth characteristics, implying that individual cell behaviors are tightly controlled and regulated. An approach to understanding how individual cell behaviors contribute to system behaviors is to discover a set of principles that enable abstract agents to exhibit closely analogous behaviors using only information available in an agent's immediate environment. We listed key attributes of EMT6 spheroid growth, which became our behavioral targets. Included were the development of a necrotic core surrounded by quiescent and proliferating cells, and growth data at two distinct levels of nutrient.

Results: We then created an analogue made up of quasi-autonomous software agents and an abstract environment in which they could operate. The system was designed so that upon execution it could mimic EMT6 cells forming spheroids in culture. Each agent used an identical set of axiomatic operating principles. In sequence, we used the list of targeted attributes to falsify and revise these axioms, until the analogue exhibited behaviors and attributes that were within prespecified ranges of those targeted, thereby achieving a level of validation.

Conclusion: The finalized analogue required nine axioms. We posit that the validated analogue's operating principles are reasonable representations of those utilized by EMT6/Ro cells during tumor spheroid development.

Show MeSH
Related in: MedlinePlus