Optimality In Biology

Optimality In Biology – a comprehensive collection of annotated examples

General Description

Optimality – the property of a system to maximize or minimize some function under given constraints – has been a central concept in many fields such as physics, computer science and engineering. In the realm of biology, natural selection leads to exquisite functional life forms all abiding to the laws of physics and chemistry yet show remarkable adaptation to the surrounding conditions. One manifestation of this process is that some characteristics of organisms can be shown to be close to optimally adapted to the constraints of their environment. This website and annotated collection aims to serve as a source of examples that will help discuss and disseminate this form of studying biological processes and inspire the analysis of other biological phenomena using these tools and perspectives.

In many respects the emphasis is on the constrains rather than on the issue of optimality per se, as eloquently framed by Parker and Maynard-Smith: “Optimization models help us to test our insight into the biological constraints that influence the outcome of evolution. They serve to improve our understanding about adaptations, rather than to demonstrate that natural selection produces optimal solutions.” (Parker & Maynard-Smith, Nature 1990). We encourage everyone interested in this fascinating subject to add examples, comments and join the discussion either by directly editing these pages or by communicating them through email (ron_milo@hms.harvard.edu) and we will add them.

Examples (we aim to have a short paragraph of description on each):

• Level of protein expression – Optimality and evolutionary tuning of the expression level of a protein. [1]: Different proteins have different expression levels. It is unclear to what extent these expression levels are optimized to their environment. Evolutionary theories suggest that protein expression levels maximize fitness, but the fitness as a function of protein level has seldom been directly measured. To address this, we studied the lac system of Escherichia coli, which allows the cell to use the sugar lactose for growth. We experimentally measured the growth burden due to production and maintenance of the Lac proteins (cost), as well as the growth advantage (benefit) conferred by the Lac proteins when lactose is present. The fitness function, given by the difference between the benefit and the cost, predicts that for each lactose environment there exists an optimal Lac expression level that maximizes growth rate. We then performed serial dilution evolution experiments at different lactose concentrations. In a few hundred generations, cells evolved to reach the predicted optimal expression levels. Thus, protein expression from the lac operon seems to be a solution of a cost-benefit optimization problem, and can be rapidly tuned by evolution to function optimally in new environments.

• Growth rate on different carbon sources - Escherichia coli K-12 undergoes adaptive evolution to achieve in silico predicted optimal growth [2]: Annotated genome sequences can be used to reconstruct whole-cell metabolic networks. These metabolic networks can be modelled and analysed (computed) to study complex biological functions. In particular, constraints-based in silico models have been used to calculate optimal growth rates on common carbon substrates, and the results were found to be consistent with experimental data under many but not all conditions. Optimal biological functions are acquired through an evolutionary process. Thus, incorrect predictions of in silico models based on optimal performance criteria may be due to incomplete adaptive evolution under the conditions examined. Escherichia coli K-12 MG1655 grows sub-optimally on glycerol as the sole carbon source. Here we show that when placed under growth selection pressure, the growth rate of E. coli on glycerol reproducibly evolved over 40 days, or about 700 generations, from a sub-optimal value to the optimal growth rate predicted from a whole-cell in silico model. These results open the possibility of using adaptive evolution of entire metabolic networks to realize metabolic states that have been determined a priori based on in silico analysis.

• The genetic code (Refs.)
• Age of reproductive maturity, number of eggs in a clutch, foraging strategy etc. (Stearns 1992)
• Codon usage and biases (Ref.)
• Shapes that minimize drag (Ref. fish, fungi spores, birds?)
• Prey interception strategy of bats (Ghose et al., PLOS Biology 2006)
• Optimal virulence level (Jensen et al., PLOS Biology 2006)
• Neural information transmission (Bialek 1997)
• tRNA levels
• morphogen gradients
• photosynthesis wavelength
• enzymes near the diffusion limit
• Optimal metabolic network operation (“Systematic evaluation of objective functions for predicting intracellular fluxes in Escherichia coli” Robert Schuetz, Lars Kuepfer1 & Uwe Sauer Also Jens Nielsen, 2007)

References:

1. Dekel E and Alon U. Optimality and evolutionary tuning of the expression level of a protein. Nature. 2005 Jul 28;436(7050):588-92. DOI:10.1038/nature03842 |
2. Ibarra RU, Edwards JS, and Palsson BO. Escherichia coli K-12 undergoes adaptive evolution to achieve in silico predicted optimal growth. Nature. 2002 Nov 14;420(6912):186-9. DOI:10.1038/nature01149 |

General references:

• Optimality theory in evolutionary biology, GA Parker, JM Smith - Nature, 1990,
• The evolution of life histories. Stearns, Stephen C., Oxford University. 1992
• An Introduction to Systems Biology: Design Principles of Biological Circuits, Uri Alon, Chapman & Hall/CRC; 1st ed. 2006.