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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

SMS cross-sections at 17 DAYS. Scale bar: 100 μm. Parameter values were those listed in Table 2. White circles: proliferating CELLS; light gray circles: quiescent CELLS; dark gray circles: NECROTIC CELLS. The background gradient (from red to black) represents NUTRIENT levels relative to the maximum value in red. (A) Growth occurred at high NUTRIENT, which maps to 0.28 mM oxygen and 16.5 mM glucose. (B) Growth occurred at low NUTRIENT, which maps to 0.08 mM oxygen and 0.8 mM glucose.
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Figure 2: SMS cross-sections at 17 DAYS. Scale bar: 100 μm. Parameter values were those listed in Table 2. White circles: proliferating CELLS; light gray circles: quiescent CELLS; dark gray circles: NECROTIC CELLS. The background gradient (from red to black) represents NUTRIENT levels relative to the maximum value in red. (A) Growth occurred at high NUTRIENT, which maps to 0.28 mM oxygen and 16.5 mM glucose. (B) Growth occurred at low NUTRIENT, which maps to 0.08 mM oxygen and 0.8 mM glucose.

Mentions: To distinguish clearly in silico components and processes from corresponding components and processes within EMT6, we use SMALL CAPS when referring to the former. Variable names are in italics, and each is defined in the order it is introduced. CELL growth leads to formation of Simulated MULTICELLULAR Spheroids (SMS). Measurements of SMS attributes during execution mimic characteristics of EMT6 spheroid growth. Figure 2 shows an example qualitative measurement of the SMS as a two dimensional cross-section. It shows that SMS displayed the characteristic layered structure of EMT6 spheroids. The PROLIFERATING layer appears thicker than is often seen in EMT6 spheroids, but note that while the majority of CELLS in the VIABLE rim are in the PROLIFERATING state, only the CELLS on the outer layer of the SMS are actively creating new CELLS. Figure 3 shows that SMS growth curves were similar to reported EMT6 spheroid growth curves when CELLS used the parameters listed in Table 2 and the nine axiomatic operating principles listed in Table 3. AXIOM application was rigid in the sense that when a precondition was met, the appropriate AXIOM was always applied. AXIOMS 7 and 9 were stochastic. During a simulation cycle, a CELL could subsequently apply more than one AXIOM, such as 1, 4, 7, and 9 for a PROLIFERATING CELL or 3 and 5 for a NECROTIC CELL.


Essential operating principles for tumor spheroid growth.

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

SMS cross-sections at 17 DAYS. Scale bar: 100 μm. Parameter values were those listed in Table 2. White circles: proliferating CELLS; light gray circles: quiescent CELLS; dark gray circles: NECROTIC CELLS. The background gradient (from red to black) represents NUTRIENT levels relative to the maximum value in red. (A) Growth occurred at high NUTRIENT, which maps to 0.28 mM oxygen and 16.5 mM glucose. (B) Growth occurred at low NUTRIENT, which maps to 0.08 mM oxygen and 0.8 mM glucose.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 2: SMS cross-sections at 17 DAYS. Scale bar: 100 μm. Parameter values were those listed in Table 2. White circles: proliferating CELLS; light gray circles: quiescent CELLS; dark gray circles: NECROTIC CELLS. The background gradient (from red to black) represents NUTRIENT levels relative to the maximum value in red. (A) Growth occurred at high NUTRIENT, which maps to 0.28 mM oxygen and 16.5 mM glucose. (B) Growth occurred at low NUTRIENT, which maps to 0.08 mM oxygen and 0.8 mM glucose.
Mentions: To distinguish clearly in silico components and processes from corresponding components and processes within EMT6, we use SMALL CAPS when referring to the former. Variable names are in italics, and each is defined in the order it is introduced. CELL growth leads to formation of Simulated MULTICELLULAR Spheroids (SMS). Measurements of SMS attributes during execution mimic characteristics of EMT6 spheroid growth. Figure 2 shows an example qualitative measurement of the SMS as a two dimensional cross-section. It shows that SMS displayed the characteristic layered structure of EMT6 spheroids. The PROLIFERATING layer appears thicker than is often seen in EMT6 spheroids, but note that while the majority of CELLS in the VIABLE rim are in the PROLIFERATING state, only the CELLS on the outer layer of the SMS are actively creating new CELLS. Figure 3 shows that SMS growth curves were similar to reported EMT6 spheroid growth curves when CELLS used the parameters listed in Table 2 and the nine axiomatic operating principles listed in Table 3. AXIOM application was rigid in the sense that when a precondition was met, the appropriate AXIOM was always applied. AXIOMS 7 and 9 were stochastic. During a simulation cycle, a CELL could subsequently apply more than one AXIOM, such as 1, 4, 7, and 9 for a PROLIFERATING CELL or 3 and 5 for a NECROTIC CELL.

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