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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

Relationships between simulated multicellular tumor spheroids (SMS) and EMT6 spheroids. An SMS is comprised of quasi-autonomous cell components interacting with adjacent cells and factors in their environment by adhering to a set of axiomatic operating principles. A clear mapping exists between SMS components and EMT6 counterparts. Following execution, the interacting components cause local and systemic behaviors. Measures of cell and system behaviors provide a set of attributes – the SMS phenotype. Validation was achieved when SMS attributes were measurably similar to a targeted set of EMT6 attributes. When that was accomplished, we could hypothesize that a semiquantitative mapping exists between in silico and in vitro events. We could also hypothesize that the set of axiomatic operating principles has a biological counterpart.
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Figure 1: Relationships between simulated multicellular tumor spheroids (SMS) and EMT6 spheroids. An SMS is comprised of quasi-autonomous cell components interacting with adjacent cells and factors in their environment by adhering to a set of axiomatic operating principles. A clear mapping exists between SMS components and EMT6 counterparts. Following execution, the interacting components cause local and systemic behaviors. Measures of cell and system behaviors provide a set of attributes – the SMS phenotype. Validation was achieved when SMS attributes were measurably similar to a targeted set of EMT6 attributes. When that was accomplished, we could hypothesize that a semiquantitative mapping exists between in silico and in vitro events. We could also hypothesize that the set of axiomatic operating principles has a biological counterpart.

Mentions: An approach to understanding how individual cell behaviors can contribute to a diverse set of system level attributes is to discover a set of simple yet sufficient principles that enable abstract, cell mimetic agents, using only locally available information, to exhibit behaviors closely analogous to cells in culture. For this context, we define a biological operating principle to be an abstract, inferential representation of an action within a reliably behaved cell system. To discover these principles, we created a quasi-autonomous computer analogue comprised of individual cell mimetic agents (CELLS) that adhered to a common, small set of axiomatic operating principles. We use axiom as commonly defined [1] and to emphasize that the analogue, unlike EMT6 cells in cultures, is a formal mathematical system and its execution is a form of deduction from the axioms within the analogue. Hereafter, we use AXIOM to emphasize that we refer only to the computational analogue. An AXIOM specified a behavior that depended on the local environment perceived by the CELL, given its internal state. Individual AXIOMS were implementations of in silico, axiomatic operating principles. Each axiomatic operating principle was derived from a postulated in vitro counterpart as described in Methods. The combined actions of an expanding population of CELLS, each adhering to the same set of operating principles, were sufficient to produce unique systemic behaviors. The system underwent several rounds of iterative refinement and parameter tuning. When measured, the resulting behaviors provided a set of systemic attributes that matched observed in vitro attributes closely for two different growth conditions. Once that was achieved, we could postulate that the axiomatic operating principles may have in vitro counterparts, as illustrated in Fig. 1. To date, such principles have been arrived at piecemeal by induction following experimentation. Experimental cell biology has been successful at discovering isolated cell level operating principles, but progress has been slow in providing a unified understanding of autonomous cellular behavior. We anticipated that iterative analogue refinement would lead to improved insight into cell level operating principles and plausible mappings to their biological counterparts. Even though the EMT6 cell line is tumor-derived, because it has proven stable and exhibits reliable behaviors, for the purposes of this research, we can treat EMT6 cells as being in a healthy, not diseased state.


Essential operating principles for tumor spheroid growth.

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

Relationships between simulated multicellular tumor spheroids (SMS) and EMT6 spheroids. An SMS is comprised of quasi-autonomous cell components interacting with adjacent cells and factors in their environment by adhering to a set of axiomatic operating principles. A clear mapping exists between SMS components and EMT6 counterparts. Following execution, the interacting components cause local and systemic behaviors. Measures of cell and system behaviors provide a set of attributes – the SMS phenotype. Validation was achieved when SMS attributes were measurably similar to a targeted set of EMT6 attributes. When that was accomplished, we could hypothesize that a semiquantitative mapping exists between in silico and in vitro events. We could also hypothesize that the set of axiomatic operating principles has a biological counterpart.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 1: Relationships between simulated multicellular tumor spheroids (SMS) and EMT6 spheroids. An SMS is comprised of quasi-autonomous cell components interacting with adjacent cells and factors in their environment by adhering to a set of axiomatic operating principles. A clear mapping exists between SMS components and EMT6 counterparts. Following execution, the interacting components cause local and systemic behaviors. Measures of cell and system behaviors provide a set of attributes – the SMS phenotype. Validation was achieved when SMS attributes were measurably similar to a targeted set of EMT6 attributes. When that was accomplished, we could hypothesize that a semiquantitative mapping exists between in silico and in vitro events. We could also hypothesize that the set of axiomatic operating principles has a biological counterpart.
Mentions: An approach to understanding how individual cell behaviors can contribute to a diverse set of system level attributes is to discover a set of simple yet sufficient principles that enable abstract, cell mimetic agents, using only locally available information, to exhibit behaviors closely analogous to cells in culture. For this context, we define a biological operating principle to be an abstract, inferential representation of an action within a reliably behaved cell system. To discover these principles, we created a quasi-autonomous computer analogue comprised of individual cell mimetic agents (CELLS) that adhered to a common, small set of axiomatic operating principles. We use axiom as commonly defined [1] and to emphasize that the analogue, unlike EMT6 cells in cultures, is a formal mathematical system and its execution is a form of deduction from the axioms within the analogue. Hereafter, we use AXIOM to emphasize that we refer only to the computational analogue. An AXIOM specified a behavior that depended on the local environment perceived by the CELL, given its internal state. Individual AXIOMS were implementations of in silico, axiomatic operating principles. Each axiomatic operating principle was derived from a postulated in vitro counterpart as described in Methods. The combined actions of an expanding population of CELLS, each adhering to the same set of operating principles, were sufficient to produce unique systemic behaviors. The system underwent several rounds of iterative refinement and parameter tuning. When measured, the resulting behaviors provided a set of systemic attributes that matched observed in vitro attributes closely for two different growth conditions. Once that was achieved, we could postulate that the axiomatic operating principles may have in vitro counterparts, as illustrated in Fig. 1. To date, such principles have been arrived at piecemeal by induction following experimentation. Experimental cell biology has been successful at discovering isolated cell level operating principles, but progress has been slow in providing a unified understanding of autonomous cellular behavior. We anticipated that iterative analogue refinement would lead to improved insight into cell level operating principles and plausible mappings to their biological counterparts. Even though the EMT6 cell line is tumor-derived, because it has proven stable and exhibits reliable behaviors, for the purposes of this research, we can treat EMT6 cells as being in a healthy, not diseased state.

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