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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

Illustration of a CELL determining its level of STRESS. (A) InitialStress is calculated based on the number of empty spaces. (B) The change in STRESS is calculated based on number of outside neighbors and their initialStress values, with some CELLS increasing in STRESS (black values), some decreasing (red values) and others staying the same (gray values). (C) STRESS is calculated by summing the value of initialStress and the change in the value of STRESS.
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Figure 13: Illustration of a CELL determining its level of STRESS. (A) InitialStress is calculated based on the number of empty spaces. (B) The change in STRESS is calculated based on number of outside neighbors and their initialStress values, with some CELLS increasing in STRESS (black values), some decreasing (red values) and others staying the same (gray values). (C) STRESS is calculated by summing the value of initialStress and the change in the value of STRESS.

Mentions: In order to avoid extreme, abiotic SMS surface irregularities, each CELL creates new CELLS and moves based on its STRESS value. STRESS maps somewhat to the adhesion mechanisms used in [2,6]. It also maps to a combination of surface tension and adhesion. However, it was only necessary to have it operate at the SMS surface. CELLS having smaller STRESS values will be more likely to create new CELLS and less likely to move inward into empty spaces. To calculate STRESS, a CELL uses a two-pass algorithm in each cycle. First, it determines its initialStress: it subtracts two from the number of empty spaces in the neighborhood. During the second pass, a CELL counts the number of CELLS in its neighborhood that are on the SMS edge (outsideNeighbors). As illustrated in Fig. 13, CELLS then calculate their final stress depending on outsideNeighbors. If outsideNeighbors ≠ 2, finalStress = initialStress + 1. If outsideNeighbors = 2, the CELL queries these two neighbors and sums their initialStress, and if that sum < 0, finalStress = initialStress - 1. If the sum is > 1, finalStress = initialStress + 1, and if the sum is 0 or 1, finalStress = initialStress. This algorithm has the effect of transmitting the STRESS felt by one CELL to its neighbors, enabling CELLS to have different final STRESS values even if their neighborhoods are identical. Figure 14 shows sequential screen shots of the stress felt by CELLS in a growing SMS and demonstrates the preferential nature of proliferation. Figure 14a shows the initial arrangement. In Fig. 14b, the starred CELL has moved to fill an empty space, changing the local CELL arrangement and each CELL'S resulting STRESS value. Consequently, the starred CELL has a very low STRESS value and a corresponding higher chance of proliferating. When its prolifCounter reaches zero, the starred CELL creates a new CELL, as illustrated in Fig. 14c, returning that portion of the SMS to its original arrangement.


Essential operating principles for tumor spheroid growth.

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

Illustration of a CELL determining its level of STRESS. (A) InitialStress is calculated based on the number of empty spaces. (B) The change in STRESS is calculated based on number of outside neighbors and their initialStress values, with some CELLS increasing in STRESS (black values), some decreasing (red values) and others staying the same (gray values). (C) STRESS is calculated by summing the value of initialStress and the change in the value of STRESS.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 13: Illustration of a CELL determining its level of STRESS. (A) InitialStress is calculated based on the number of empty spaces. (B) The change in STRESS is calculated based on number of outside neighbors and their initialStress values, with some CELLS increasing in STRESS (black values), some decreasing (red values) and others staying the same (gray values). (C) STRESS is calculated by summing the value of initialStress and the change in the value of STRESS.
Mentions: In order to avoid extreme, abiotic SMS surface irregularities, each CELL creates new CELLS and moves based on its STRESS value. STRESS maps somewhat to the adhesion mechanisms used in [2,6]. It also maps to a combination of surface tension and adhesion. However, it was only necessary to have it operate at the SMS surface. CELLS having smaller STRESS values will be more likely to create new CELLS and less likely to move inward into empty spaces. To calculate STRESS, a CELL uses a two-pass algorithm in each cycle. First, it determines its initialStress: it subtracts two from the number of empty spaces in the neighborhood. During the second pass, a CELL counts the number of CELLS in its neighborhood that are on the SMS edge (outsideNeighbors). As illustrated in Fig. 13, CELLS then calculate their final stress depending on outsideNeighbors. If outsideNeighbors ≠ 2, finalStress = initialStress + 1. If outsideNeighbors = 2, the CELL queries these two neighbors and sums their initialStress, and if that sum < 0, finalStress = initialStress - 1. If the sum is > 1, finalStress = initialStress + 1, and if the sum is 0 or 1, finalStress = initialStress. This algorithm has the effect of transmitting the STRESS felt by one CELL to its neighbors, enabling CELLS to have different final STRESS values even if their neighborhoods are identical. Figure 14 shows sequential screen shots of the stress felt by CELLS in a growing SMS and demonstrates the preferential nature of proliferation. Figure 14a shows the initial arrangement. In Fig. 14b, the starred CELL has moved to fill an empty space, changing the local CELL arrangement and each CELL'S resulting STRESS value. Consequently, the starred CELL has a very low STRESS value and a corresponding higher chance of proliferating. When its prolifCounter reaches zero, the starred CELL creates a new CELL, as illustrated in Fig. 14c, returning that portion of the SMS to its original arrangement.

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