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Violations of robustness trade-offs.

Kitano H - Mol. Syst. Biol. (2010)

Bottom Line: One intriguing aspect of the concept of biological robustness is the possible existence of intrinsic trade-offs among robustness, fragility, performance, and so on.At the same time, whether such trade-offs hold regardless of the situation or hold only under specific conditions warrants careful investigation.In this paper, we reassess this concept and argue that biological robustness may hold only when a system is sufficiently optimized and that it may not be conserved when there is room for optimization in its design.

View Article: PubMed Central - PubMed

Affiliation: The Systems Biology Institute, Minato, Tokyo, Japan. kitano@sbi.jp

ABSTRACT
Biological robustness is a principle that may shed light on system-level characteristics of biological systems. One intriguing aspect of the concept of biological robustness is the possible existence of intrinsic trade-offs among robustness, fragility, performance, and so on. At the same time, whether such trade-offs hold regardless of the situation or hold only under specific conditions warrants careful investigation. In this paper, we reassess this concept and argue that biological robustness may hold only when a system is sufficiently optimized and that it may not be conserved when there is room for optimization in its design. Several testable predictions and implications for cell culture experiments are presented.

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Related in: MedlinePlus

(A) In biological application of portfolio selection, each individual is mapped on the yield–risk space. A culture of cells may contain multiple different subtypes with mutations and epigenetic modifications. Assume a culture of cells (or organisms) composed of subtypes A, B, C, and D. At the initial stage, A and B may be dominant and C and D may be negligible (Culture 1). However, subtype C better fits the environment and grows faster than A and B (Culture 2). Subtype D starts to grow faster than the others and changes the subtype composition of the culture (Culture 3). At this stage, the composition of the culture may be sufficiently optimized for the given culture condition. Suppose the culture condition is changed now to have greater perturbations. Subtype D may not be able to tolerate it and will decrease the rate of proliferation and may even reduce in number, and subtype C may grow faster than the other subtypes (Culture 4). Alternatively, subtype D may continue to grow faster than other subtypes if the environment becomes even more stable. (B) A population of cells may evolve toward the efficient frontier. Under the risk-aversion indifference curve, the population arrives at the blue circle on the efficient frontier. The risk-aversion curve represents cases in which higher-level perturbations are imposed on the culture compared with a risk-neutral case. Under the stable condition in which selection pressures other than growth speed are not significant, the risk-neutral indifference curve is likely to be applied. The population follows Trajectory A and maximizes its growth rate at the cost of robustness. Imposing a higher level of perturbation may result in transition of the state through Trajectory B. (C) Cost-free resistance may be a result of taking Trajectory E or F to a new efficient frontier. There may be cases in which the population moves back to suboptimal regions (Trajectories G). Chemotherapy for cancer may shift the point inside the efficient frontier with different end points because of heterogeneous subpopulations. However, tumor cells may again evolve to gain proliferation potential despite the presence of anticancer drugs (Trajectories H). Tumor cells that undergo this transition may be too optimized for this specific therapeutic intervention, which implies possible efficacy when therapeutic regimens are switched. This may explain the collateral sensitivity of drug resistance tumor cells (Skipper et al, 1972).
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f4: (A) In biological application of portfolio selection, each individual is mapped on the yield–risk space. A culture of cells may contain multiple different subtypes with mutations and epigenetic modifications. Assume a culture of cells (or organisms) composed of subtypes A, B, C, and D. At the initial stage, A and B may be dominant and C and D may be negligible (Culture 1). However, subtype C better fits the environment and grows faster than A and B (Culture 2). Subtype D starts to grow faster than the others and changes the subtype composition of the culture (Culture 3). At this stage, the composition of the culture may be sufficiently optimized for the given culture condition. Suppose the culture condition is changed now to have greater perturbations. Subtype D may not be able to tolerate it and will decrease the rate of proliferation and may even reduce in number, and subtype C may grow faster than the other subtypes (Culture 4). Alternatively, subtype D may continue to grow faster than other subtypes if the environment becomes even more stable. (B) A population of cells may evolve toward the efficient frontier. Under the risk-aversion indifference curve, the population arrives at the blue circle on the efficient frontier. The risk-aversion curve represents cases in which higher-level perturbations are imposed on the culture compared with a risk-neutral case. Under the stable condition in which selection pressures other than growth speed are not significant, the risk-neutral indifference curve is likely to be applied. The population follows Trajectory A and maximizes its growth rate at the cost of robustness. Imposing a higher level of perturbation may result in transition of the state through Trajectory B. (C) Cost-free resistance may be a result of taking Trajectory E or F to a new efficient frontier. There may be cases in which the population moves back to suboptimal regions (Trajectories G). Chemotherapy for cancer may shift the point inside the efficient frontier with different end points because of heterogeneous subpopulations. However, tumor cells may again evolve to gain proliferation potential despite the presence of anticancer drugs (Trajectories H). Tumor cells that undergo this transition may be too optimized for this specific therapeutic intervention, which implies possible efficacy when therapeutic regimens are switched. This may explain the collateral sensitivity of drug resistance tumor cells (Skipper et al, 1972).

Mentions: Growth rate (yield or performance) is generally measured by the size of a colony, by numbers of cells, or by other means that reflect the number of cells in the population. Risk is an s.d. of growth rate under various possible perturbations. Experimentally, it can be measured by repeated perturbation experiments. In a heterogeneous cell culture, the projected position of the cell culture in the yield–risk space is determined by the population composition. This is illustrated in Figure 4. Initially, the cell culture is mainly composed of subtypes A and B, with a negligible amount of C (Culture 1 in Figure 4A). Subtype C has a better fit with the culture condition and has higher yield. Thus, the proportion of subtype C increases over that of subtypes A and B (Culture 2 in Figure 4A). Random mutation gives rise to subtype D. It has higher reproductive potential under this specific culture condition, and thus it quickly proliferates in the population (Culture 3 in Figure 4A). However, when extra perturbations are imposed on the culture, fast-growing but less-robust subtypes (subtype D) may substantially decrease in their proliferation speed or the number of cells. At the same time, low-yield but more-robust subtypes may continue to grow at a similar rate. These population changes result in a composition that better fits a condition with a higher degree of perturbations. In this case, the projected position of the culture on the yield–risk space map may move left to that of Culture 4 in Figure 4A. In contrast, the fast-growing subtype may establish its dominance when the environment reaches a more stable condition that is ideal for the fast but less-robust subtype (Culture 5 in Figure 4A). Both emergence and rebalancing scenarios are included, but for the sake of explanation, only the wild type and its mutational variants are used as subtypes. However, cells with different epigenetic modifications can be considered as subtypes if these modifications affect the yield–risk characteristics of the cell.


Violations of robustness trade-offs.

Kitano H - Mol. Syst. Biol. (2010)

(A) In biological application of portfolio selection, each individual is mapped on the yield–risk space. A culture of cells may contain multiple different subtypes with mutations and epigenetic modifications. Assume a culture of cells (or organisms) composed of subtypes A, B, C, and D. At the initial stage, A and B may be dominant and C and D may be negligible (Culture 1). However, subtype C better fits the environment and grows faster than A and B (Culture 2). Subtype D starts to grow faster than the others and changes the subtype composition of the culture (Culture 3). At this stage, the composition of the culture may be sufficiently optimized for the given culture condition. Suppose the culture condition is changed now to have greater perturbations. Subtype D may not be able to tolerate it and will decrease the rate of proliferation and may even reduce in number, and subtype C may grow faster than the other subtypes (Culture 4). Alternatively, subtype D may continue to grow faster than other subtypes if the environment becomes even more stable. (B) A population of cells may evolve toward the efficient frontier. Under the risk-aversion indifference curve, the population arrives at the blue circle on the efficient frontier. The risk-aversion curve represents cases in which higher-level perturbations are imposed on the culture compared with a risk-neutral case. Under the stable condition in which selection pressures other than growth speed are not significant, the risk-neutral indifference curve is likely to be applied. The population follows Trajectory A and maximizes its growth rate at the cost of robustness. Imposing a higher level of perturbation may result in transition of the state through Trajectory B. (C) Cost-free resistance may be a result of taking Trajectory E or F to a new efficient frontier. There may be cases in which the population moves back to suboptimal regions (Trajectories G). Chemotherapy for cancer may shift the point inside the efficient frontier with different end points because of heterogeneous subpopulations. However, tumor cells may again evolve to gain proliferation potential despite the presence of anticancer drugs (Trajectories H). Tumor cells that undergo this transition may be too optimized for this specific therapeutic intervention, which implies possible efficacy when therapeutic regimens are switched. This may explain the collateral sensitivity of drug resistance tumor cells (Skipper et al, 1972).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2913402&req=5

f4: (A) In biological application of portfolio selection, each individual is mapped on the yield–risk space. A culture of cells may contain multiple different subtypes with mutations and epigenetic modifications. Assume a culture of cells (or organisms) composed of subtypes A, B, C, and D. At the initial stage, A and B may be dominant and C and D may be negligible (Culture 1). However, subtype C better fits the environment and grows faster than A and B (Culture 2). Subtype D starts to grow faster than the others and changes the subtype composition of the culture (Culture 3). At this stage, the composition of the culture may be sufficiently optimized for the given culture condition. Suppose the culture condition is changed now to have greater perturbations. Subtype D may not be able to tolerate it and will decrease the rate of proliferation and may even reduce in number, and subtype C may grow faster than the other subtypes (Culture 4). Alternatively, subtype D may continue to grow faster than other subtypes if the environment becomes even more stable. (B) A population of cells may evolve toward the efficient frontier. Under the risk-aversion indifference curve, the population arrives at the blue circle on the efficient frontier. The risk-aversion curve represents cases in which higher-level perturbations are imposed on the culture compared with a risk-neutral case. Under the stable condition in which selection pressures other than growth speed are not significant, the risk-neutral indifference curve is likely to be applied. The population follows Trajectory A and maximizes its growth rate at the cost of robustness. Imposing a higher level of perturbation may result in transition of the state through Trajectory B. (C) Cost-free resistance may be a result of taking Trajectory E or F to a new efficient frontier. There may be cases in which the population moves back to suboptimal regions (Trajectories G). Chemotherapy for cancer may shift the point inside the efficient frontier with different end points because of heterogeneous subpopulations. However, tumor cells may again evolve to gain proliferation potential despite the presence of anticancer drugs (Trajectories H). Tumor cells that undergo this transition may be too optimized for this specific therapeutic intervention, which implies possible efficacy when therapeutic regimens are switched. This may explain the collateral sensitivity of drug resistance tumor cells (Skipper et al, 1972).
Mentions: Growth rate (yield or performance) is generally measured by the size of a colony, by numbers of cells, or by other means that reflect the number of cells in the population. Risk is an s.d. of growth rate under various possible perturbations. Experimentally, it can be measured by repeated perturbation experiments. In a heterogeneous cell culture, the projected position of the cell culture in the yield–risk space is determined by the population composition. This is illustrated in Figure 4. Initially, the cell culture is mainly composed of subtypes A and B, with a negligible amount of C (Culture 1 in Figure 4A). Subtype C has a better fit with the culture condition and has higher yield. Thus, the proportion of subtype C increases over that of subtypes A and B (Culture 2 in Figure 4A). Random mutation gives rise to subtype D. It has higher reproductive potential under this specific culture condition, and thus it quickly proliferates in the population (Culture 3 in Figure 4A). However, when extra perturbations are imposed on the culture, fast-growing but less-robust subtypes (subtype D) may substantially decrease in their proliferation speed or the number of cells. At the same time, low-yield but more-robust subtypes may continue to grow at a similar rate. These population changes result in a composition that better fits a condition with a higher degree of perturbations. In this case, the projected position of the culture on the yield–risk space map may move left to that of Culture 4 in Figure 4A. In contrast, the fast-growing subtype may establish its dominance when the environment reaches a more stable condition that is ideal for the fast but less-robust subtype (Culture 5 in Figure 4A). Both emergence and rebalancing scenarios are included, but for the sake of explanation, only the wild type and its mutational variants are used as subtypes. However, cells with different epigenetic modifications can be considered as subtypes if these modifications affect the yield–risk characteristics of the cell.

Bottom Line: One intriguing aspect of the concept of biological robustness is the possible existence of intrinsic trade-offs among robustness, fragility, performance, and so on.At the same time, whether such trade-offs hold regardless of the situation or hold only under specific conditions warrants careful investigation.In this paper, we reassess this concept and argue that biological robustness may hold only when a system is sufficiently optimized and that it may not be conserved when there is room for optimization in its design.

View Article: PubMed Central - PubMed

Affiliation: The Systems Biology Institute, Minato, Tokyo, Japan. kitano@sbi.jp

ABSTRACT
Biological robustness is a principle that may shed light on system-level characteristics of biological systems. One intriguing aspect of the concept of biological robustness is the possible existence of intrinsic trade-offs among robustness, fragility, performance, and so on. At the same time, whether such trade-offs hold regardless of the situation or hold only under specific conditions warrants careful investigation. In this paper, we reassess this concept and argue that biological robustness may hold only when a system is sufficiently optimized and that it may not be conserved when there is room for optimization in its design. Several testable predictions and implications for cell culture experiments are presented.

Show MeSH
Related in: MedlinePlus