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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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Basic concepts of portfolio selection. (A) Any asset can be mapped on the E(r)–σ(r), or yield–risk, space. Combining A and B creates a possible space of yield and risk depending on the mixture and covariance of the two assets against fluctuation. Maximum risk reduction is achieved when the prices of the two assets change in opposite directions because this offsets fluctuation. Increasing the number of assets involved generally reduces risk. The efficient frontier is achieved by optimally combining all available assets. Availability of a larger number of assets with different yield–risk characteristics improves the overall portfolio, analogous to an increase in the degree of design of freedom in highly optimized tolerance (Carlson and Doyle, 1999; Reynolds et al, 2002). In actual investment planning, investment with a fixed return asset is considered to form a capital market line, but this is not considered in biological applications because there is no zero-risk-fixed-yield genotype. (B) The probability distribution of expected return is shown for each asset and portfolio in (A) to visually illustrate their relationships.
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f1: Basic concepts of portfolio selection. (A) Any asset can be mapped on the E(r)–σ(r), or yield–risk, space. Combining A and B creates a possible space of yield and risk depending on the mixture and covariance of the two assets against fluctuation. Maximum risk reduction is achieved when the prices of the two assets change in opposite directions because this offsets fluctuation. Increasing the number of assets involved generally reduces risk. The efficient frontier is achieved by optimally combining all available assets. Availability of a larger number of assets with different yield–risk characteristics improves the overall portfolio, analogous to an increase in the degree of design of freedom in highly optimized tolerance (Carlson and Doyle, 1999; Reynolds et al, 2002). In actual investment planning, investment with a fixed return asset is considered to form a capital market line, but this is not considered in biological applications because there is no zero-risk-fixed-yield genotype. (B) The probability distribution of expected return is shown for each asset and portfolio in (A) to visually illustrate their relationships.

Mentions: As investors generally invest in multiple financial assets with different expected yields and risks, the question is how to find the optimal mix of assets with a desirable yield and acceptable risk. The concept of efficient frontier needs to be introduced here. The efficient frontier is a set of points that represent an optimal combination of assets (mostly securities in a financial context) that maximizes the return for any given level of s.d. Any point not on the efficient frontier represents a portfolio that is inferior to a portfolio on the efficient frontier, either because it generates less return at the same level of risk or is exposed to higher risk at the same expected level of return. In Figure 1A, Portfolio X is inferior to both Portfolios Y and Z. Portfolio Y has a higher expected return than X at the same level of risk, and Z has lower risk than X with the same expected return. Portfolio X can be reorganized to reach the efficient frontier. Thus, theoretically, any portfolio not on the efficient frontier can improve its yield without increasing risk, or reduce risk without undermining the expected yield. However, on the efficient frontier, any change in yield affects risk and vice versa. Trade-off between risk and yield takes place on an optimal portfolio that is on the efficient frontier. A similar trade-off concept is also investigated in the context of multiobjective optimization as the Pareto efficiency, originally proposed by Pareto (1935). For a Pareto-efficient solution, no individual parameter can be improved without undermining another parameter. A set of Pareto-efficient solutions constitute a Pareto surface, also called a Pareto frontier.


Violations of robustness trade-offs.

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

Basic concepts of portfolio selection. (A) Any asset can be mapped on the E(r)–σ(r), or yield–risk, space. Combining A and B creates a possible space of yield and risk depending on the mixture and covariance of the two assets against fluctuation. Maximum risk reduction is achieved when the prices of the two assets change in opposite directions because this offsets fluctuation. Increasing the number of assets involved generally reduces risk. The efficient frontier is achieved by optimally combining all available assets. Availability of a larger number of assets with different yield–risk characteristics improves the overall portfolio, analogous to an increase in the degree of design of freedom in highly optimized tolerance (Carlson and Doyle, 1999; Reynolds et al, 2002). In actual investment planning, investment with a fixed return asset is considered to form a capital market line, but this is not considered in biological applications because there is no zero-risk-fixed-yield genotype. (B) The probability distribution of expected return is shown for each asset and portfolio in (A) to visually illustrate their relationships.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f1: Basic concepts of portfolio selection. (A) Any asset can be mapped on the E(r)–σ(r), or yield–risk, space. Combining A and B creates a possible space of yield and risk depending on the mixture and covariance of the two assets against fluctuation. Maximum risk reduction is achieved when the prices of the two assets change in opposite directions because this offsets fluctuation. Increasing the number of assets involved generally reduces risk. The efficient frontier is achieved by optimally combining all available assets. Availability of a larger number of assets with different yield–risk characteristics improves the overall portfolio, analogous to an increase in the degree of design of freedom in highly optimized tolerance (Carlson and Doyle, 1999; Reynolds et al, 2002). In actual investment planning, investment with a fixed return asset is considered to form a capital market line, but this is not considered in biological applications because there is no zero-risk-fixed-yield genotype. (B) The probability distribution of expected return is shown for each asset and portfolio in (A) to visually illustrate their relationships.
Mentions: As investors generally invest in multiple financial assets with different expected yields and risks, the question is how to find the optimal mix of assets with a desirable yield and acceptable risk. The concept of efficient frontier needs to be introduced here. The efficient frontier is a set of points that represent an optimal combination of assets (mostly securities in a financial context) that maximizes the return for any given level of s.d. Any point not on the efficient frontier represents a portfolio that is inferior to a portfolio on the efficient frontier, either because it generates less return at the same level of risk or is exposed to higher risk at the same expected level of return. In Figure 1A, Portfolio X is inferior to both Portfolios Y and Z. Portfolio Y has a higher expected return than X at the same level of risk, and Z has lower risk than X with the same expected return. Portfolio X can be reorganized to reach the efficient frontier. Thus, theoretically, any portfolio not on the efficient frontier can improve its yield without increasing risk, or reduce risk without undermining the expected yield. However, on the efficient frontier, any change in yield affects risk and vice versa. Trade-off between risk and yield takes place on an optimal portfolio that is on the efficient frontier. A similar trade-off concept is also investigated in the context of multiobjective optimization as the Pareto efficiency, originally proposed by Pareto (1935). For a Pareto-efficient solution, no individual parameter can be improved without undermining another parameter. A set of Pareto-efficient solutions constitute a Pareto surface, also called a Pareto frontier.

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